NATIONAL CENTER FOR EDUCATION STATISTICS 

Statistical An~lysis Report February 1996 

National Education Longitudinal Study of 1988 

High School Seniors' 

Instructional Experiences 

in Science and Mathematics 

U.S. Department of Education 

Office of Educational Research and Improvement NCES 95-278 

0 
NATIONAL CENTER FOR EDUCATION STATISTICS 

Statistical Analysis Report February 1996 

National Education Longitudinal Study of 1988 

High School Seniors' 

Instructional Experiences 

in Science and Mathematics 

Thomas B. Hoffer 

Whitney Moore 

National Opinion Research Center (NORC) 

Peggy Quinn, Project Officer 

National Center for Education Statistics 

Larry E. Suter, Deputy Director 

Research, Evaluation and Communication Division 

National Science Foundation 

The work reported here was funded by the National Science Foundation 

through an Interagency Agreement with the National Center for 

Education Statistics. 

U.S. Department of Education 

Office of Educational Research and Improvement NCES 95-278 
U.S. Department of Education 

Richard W. Riley 

Secretary 

Office of Educational Research and Improvement 

Sharon P. Rooinson 

Assistant Secretary 

National Center for Education Statistics 

Jeanne E. Griffith 

Acting Commissioner 

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High School Seniors' Instructional 

Experiences in Science and Mathematics 

Summary of Major Findings 

This study examines the instructional experiences of a national sample of 1992 high school seniors 

in the subjects of science and mathematics. The study analyzes data from the National Education 

Longitudinal Study of 1988 (NELS:88). The information on instruction comes from the NELS:88 1992 

smvey of teachers, which collected questionnaires from the science and mathematics teachers of 9,853 

sampled seniors enrolled in public and private high schools across the United States. Two general 

questions are addressed: To what extent are high school seniors' instructional experiences affected by 

their social backgrounds and by the schools they attend? To answer these questions, multiple regression 

analysis is used to sort out the influences of social background and schooling variables on instructional 

variables and achievement score differences. 

Factors Affecting Instruction 

We focused on three sets of explanatory variables, organized under the rubrics of student 

background, intra-school organizational factors, and between-school factors to answer the question of why 

students' instructional experiences differ. Before examining the instructional variables, it is important to 

take stock of who takes senior-year science and math. Many seniors do not take science or mathematics, 

and thus we examined the relationship of these factors with enrollment. 

• Overall, 66 percent of the seniors were enrolled in mathematics courses, and 48 percent 

were enrolled in science courses. Most of the students enrolled in science and 

mathematics classes were in relatively higher-level courses, but about one-third were 

taking low-level or basic courses. About 27 percent of math enrollees were in first-year 

algebra or lower courses, while 33 percent of the science students were in biology 1 or 

lower. 

• Overall, students taking senior science courses and students taking senior mathematics 

courses tend to come from more affluent families. Males are slightly more likely to take 

senior-year mathematics. Among those taking senior-year mathematics, females are more 

likely than males to be enrolled in the higher-level mathematics classes. Enrollment rates 

of whites, blacks, and Hispanics do not differ significantly; however, Asians are 

significantly more likely to take both subjects. Asians are also much more likely to be 

enrolled in advanced placement (AP) and other higher-level classes within science and 

math. 

• Students in Catholic high schools and National Association of Independent Schools 

institutions are more likely to take senior-year science and mathematics. The school 

policy variables that are most strongly related to senior enrollments are the numbers of 

math and science courses students are required to complete for graduation. 

The instruction variables we examined included the teacher's emphases on various learning 

objectives, the allocation of instructional time, and the methods of instruction. The learning objectives 

measured were higher-order thinking skills, mechanical operations, and everyday applications. The time 

allocation measures included the extent to which whole-group instruction was used, the amount of time 

devoted to maintaining order in the class, the amount ofhomework ordinarily assigned, and-in sciencethe amount of time devoted to laboratory sessions, the frequency of computer use, and student oral 

presentations. Instructional methods were measured by responses to questions about the relative roles of 

lectures, discussions, small group work, and individualization. 

iii 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

• Student background variables are associated with instructional differences, but these 

associations mostly reflect the correlation of student background variables with the 

achievement level of the class. The most powerful predictor of instructional differences 

is the achievement level of the class, which overshadows the influences of social 

background and school characteristics. 

• Some effects of background persist even after the impact of class achievement level is 

factored out. Students from higher socioeconomic status (SES) families tend to have 

mathematics teachers who assign more homework and place greater emphasis on higherorder skills. In science, higher SES is associated with more laboratory opportunities. 

• Teachers of higher-level students are more likely to have undergraduate and graduate 

specializations in their respective field (mathematics or science). However, differences 

in educational credentials of teachers of students at the same class achievement levels are 

generally not associated with instructional differences. 

• School policy variables are related to several aspects of instruction. School demographic 

factors such as location and SES composition generally have weak and inconsistent 

relationships with classroom instruction. Policy variables which do make a difference 

relate to work conditions of teachers. Higher-order thinking skills are emphasized more 

by teachers who report more discussions with colleagues. 

Effects of Instructional Variables on Achievement 

Efforts to link the measures of students' instructional experiences to their achievement outcomes 

are unavoidably tentative because of the NELS:88 study design. Achievement was measured at the end 

of 10th grade and the end of 12th grade, but instructional experiences were only measured for 12th grade. 

As a result, we may not have very good measures of the instruction which students received in the period 

spanned by the achievement test scores. Measurement error of this sort has the effect of making 

relationships seem weaker that they actually are. Since the lack of grade 11 instructional measures is 

likely to bias the estimated effects of 12th grade instruction in the direction of insignificance, our strategy 

has been to look for strong relationships and to discount the weak ones. Nonetheless, all the regression 

analyses of 12th grade achievement included controls for 10th grade achievement, social background, and 

school characteristics. 

The strongest effects that emerge from this analysis are those associated with the students' class 

compositions, which we have referred to as their class achievement levels. Here we find that students in 

higher-level classes learn much more over the two year period than otherwise comparable students in 

lower-level classes. The results are strongest in mathematics but are present in science as well. The 

effects ofclass achievement-level are only partially explained by the instructional variables measured here, 

and we can only speculate on the additional mechanisms that produce the remaining learning differentials. 

iv 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Some of the instructional measures we examined for mathematics show significant associations 

with learning. 

• Controlling for sophomore achievement level, social background, school characteristics, 

achievement level of the class, and teacher credentials, we still find that students whose 

teachers place greater emphasis on higher-order skills and lower emphasis on the 

relevance of mathematics score higher. 

• Students lose when their teachers have to spend more time maintaining order in the class. 

The losses from spending more time maintaining order are not confined to lowerachieving students in the lower-level classes. When high-achievers are in classes where 

order is problematic, their achievement is also lower. 

The results from our analysis of science are not nearly as strong as for math. While class 

achievement-level effects are again evident, the instructional variables measured in the NELS:88 survey 

do not show much connection with the variability in sophomore-to-senior achievement growth. The 

weakness of the results in science may be due to either the content of the test not matching the students' 

actual learning, or the content of the instructional measures not matching the actual instruction that 

occurred. 

V 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Acknowledgments 

The topic of this report was originally conceived by Larry Suter of the National Science 

Foundation. The NSF supported the 1992 survey of mathematics and science teachers in the National 

Education Longitudinal Study of 1988 (NELS:88), from which the data are drawn. After the teacher data 

were collected, NSF contracted with NCES and the National Opinion Research Center (NORC) to produce 

a report illustrating the use of these data, and particularly how they might be combined with other aspects 

of the NELS:88 data base to inform current policy debates. Larry helped work out the details of the study 

design, and provided helpful comments at several stages of the analysis and report writing. While the 

original conception and primary support for this study are attributable to NSF, the review process was 

organized by NCES. The authors are grateful for the help and encouragement of Peggy Quinn and Jeffrey 

Owings at NCES, who also contributed constructive criticisms at several points. 

Several colleagues at NORC helped with various aspects of the report production. Leslie Scott, 

the Project Manager for the NELS:88 second follow-up, provided helpful guidance at several points. 

Virginia Bartot and John Taylor were extremely helpful as we navigated our way into the NELS:88 

database. Jiahe Qian helped with initial phases of the data analysis. Karen Rosenthal provided editorial 

assistance. Expert document production support at NORC was provided by Jeffrey Cothran, who designed 

the graphics and pulled together the text, tables, and figures into their final form. 

The authors are grateful for the helpful comments received from several reviewers. At NORC, 

Steven Ingels, Norman Bradburn, and Ken Rasinski read and commented on early drafts. At NCES, Bob 

Burton served as the primary adjudication officer, and provided careful readings and several useful 

comments, as well. Mary Frase ofNCES gave the report an extraordinarily thorough review, and provided 

numerous suggestions for improvements for which we are most grateful. We were also extremely 

fortunate to receive reviews from a number of outstanding researchers with interests in the substantive 

issues of the report: Mark Berends of RAND, Aaron Pallas of Michigan State University, Barbara 

Schneider of NORC and the University of Chicago, and Joan Talbert of Stanford University. 

vii 
Table of Contents 

High School Seniors' Instructional 

Experiences in Science and Mathematics 

Page 

Summary of Major Findings . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 

Factors Affecting Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . iii 

Effects of Instructional Variables on Achievement ............................. iv 

Acknowledgments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . vii 

List of Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xi 

List of Figures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xiii 

Appendices . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv 

Chapter I: Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1 

Background Perspectives: Policy Issues and School Effects Research . . . . . . . . . . .... . 1 

Which Aspects of Instruction are Important, and Why? . . . . . . . . . . . . . . . . . . . . . . ... . 5 

Research Questions . . . . . . . . . . . . . . . . . . . . . . . . . . ........................ . 9 

Limitations of the Present Study . . . . . . . . . . . . . . . . . ....................... . 10 

1992 Seniors: The NELS:88 Second Follow-Up Sample ...................... . 11 

12th Grade Science and Mathematics Course Enrollment Patterns ................ . 12 

Measures of Instruction: Course Content . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14 

Measures of Instruction: Quantity of Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25 

Measures of Instruction: Quality of Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 29 

Data Quality Issues . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . ........ . 32 

Summary ........................................................ . 33 

Chapter Il: Types of Courses and Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35 

Class Achievement Levels and Instructional Emphases . . . . . . . . . . . . . . . . . . . . . . . . . 37 

Class Achievement Levels and Instructional Time . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39 

Class Achievement Level and Instructional Methods . . . . . . . . . . . . . . . . . . . . . . . . . . . 46 

Teacher Credentials and Instructional Practice . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48 

Summary ......................................................... 53 

Chapter ill: Instruction and Student Background . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 

Student Background and Course Enrollment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 55 

Background and Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63 

Summary......................................................... 69 

Chapter IV: Instruction and School Characteristics . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 

School Characteristics and Course Enrollments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71 

School Characteristics and. Classroom Instruction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75 

Summary......................................................... 83 

ix 
High School Seniors' Instruction~/ 

Experiences in Science and Mathematics 

Table of Contents (Cont'd) 

Page 

Chapter V: Instruction and Student Outcomes . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 

The NELS:88 Achievement Tests . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85 

Research Questions and Analytic Strategy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86 

Instruction and Overall Achievement Growth . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87 

Effects- of Instructional Variables for High- and Low-Achieving Students . . . . . . . . . . . . 91 

Analysis of Proficiency Gains by Sophomore Achievement Levels . . . . . . . . . . . . . . . . . 94 

Summary.-................-... : .....·.............................. 100 

Chapter VI: Conclusions . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 

Summary and Implications · . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103 

Suggestions for Further Research . . . . . . . . . . . . . . . . . . . . . . . . . . ; . . . . . . . . . . . . 106 

Conclusion ........ ·. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 107 

References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 109 

X 
List of Tables 

High School Seniors' Instructional 

Experiences in Science and Mathematics 

Page 

Table 1.1: Percentage of Seniors Enrolled in Different Types of Mathematics 

and Science Courses, 1991-1992 School Year. . . . . . . . . . . . . . . . . . . . . . . . . . 13 

Table 1.2: Percentage of Twelfth-Grade Mathematics Students Whose Teachers 

Report Different Topics Covered: 1991-1992 School Year. . . . . . . . . . . . . . . . . 15 

Table 1.3: Percentage of Twelfth-Grade Biology Students Whose Teachers 

Report Different Topics Covered: 1991-1992 School Year. . . . . . . . . . . . . . . . . 16 

Table 1.4: Percentage of Twelfth-Grade Chemistry Students Whose Teachers 

Report Different Topics Covered: 1991-1992 School Year. . . . . . . . . . . . . . . . . 17 

Table 1.5: Percentage of Twelfth-Grade Physics Students Whose Teachers 

Report Different Topics Covered: 1991-1992 School Year. . . . . . . . . . . . . . . . . 18 

Table 1.6: Percentage of Twelfth-Grade Mathematics Takers Whose Teachers 

Report Various Emphases: 1991-1992 School Year . . . . . . . . . . . . . . . . . . . . . 19 

Table 1.7: Percentage of Twelfth-Grade Science Takers Whose Teachers 

Report Various Emphases: 1991-1992 School Year. . . . . . . . . . . . . . . . . . . . . . 23 

Table 1.8: Percentage of 12th Grade Math and Science Students with 

Different Average Amounts of Daily Homework Assigned: 

1991-92 School Year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 26 

Table 1.9: Percentage of 12th Grade Math Students Whose Teachers 

Report Spending Different Amounts of Time on Various 

Activities: 1991-1992 School Year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 27 

Table 1.10: Percentage of 12th Grade Science Students Whose Teachers 

Report Spending Different Amounts of Time on Various 

Activities: 1991-1992 School Year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28 

Table 1.11: Percentage of seniors with mathematics or science teachers 

reporting different frequencies of using various instructional 

methods: 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30 

Table 2.1: Correlations between the teacher's report of the achievement 

level of the student's class and the teacher-reported frequency 

of using various instructional methods (standard errors in 

parentheses): 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47 

Table 2.2: Multiple regression estimates of the relationships of teacher 

education level and the achievement level of the class with 

selected instructional variables (t-values in parentheses): 1992. . . . . . . . . . . . . . 52 

xi 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

List of Tables (Cont'd) 

Table 3.1: 

Table 3.2: 

Table 3.3: 

Table 3.4: 

Table 4.1: 

Table 4.2: 

Table 4.3: 

Table 5.1: 

Table 5.2: 

Table 5.3: 

Table 5.4: 

Table 5.5: 

Table 5.6: 

Page 

Means of math instructional variables reported by the teachers 

of 12th-grade math students, by student background characteristics: 

1991-92 School year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64 

Means of science instructional variables reported by the teachers 

of 12th-grade science students, by student background characteristics: 

1991-92 School year. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65 

Regression coefficients for selected student background variables 

from regressions of mathematics instructional variables: 1992. . . . . . . . . . . . . . 67 

Regression coefficients for selected student background variables 

from regressions of science instructional variables: 1992. . . . . . . . . . . . . . . . . . 68 

Adjusted odds ratios of students taking mathematics and science 

in 1991-1992 school year, by school characteristics . . . . . . . . . . . . . . . . . . . . . . 73 

Estimated effects of school variables on mathematics instruction 

variables, from OLS regressions: 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77 

Estimated effects of school variables on science instruction, 

from OLS regressions: 1992. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80 

Effects of Oass Achievement Level, Teacher Education, and 

Instructional Variables on Sophomore-to-Senior Achievement 

Growth in Mathematics, from OLS Regressions: 1992. . . . . . . . . . . . . . . . . . . . 88 

Estimated Effects of Class Achievement Level, Teacher Education, 

and Instructional Variables on Sophomore-to-Senior Achievement 

Growth in Science, from OLS Regressions: 1992. . . . . . . . . . . . . . . . . . . . . . . 90 

Estimated effects of class-achievement level, teacher, and instruction 

variables on grade 12 composite mathematics achievement, by grade 10 

composite science achievement quartile, from OLS regressions: 1992. . . . . . . . . 92 

Estimated effects of achievement level, teacher, and instruction variables on 

composite grade 12 science achievement, by grade 10 composite science 

achievement quartile, from OLS regressions: 1992. . . . . . . . . . . . . . . . . . . . . . 93 

Estimated effects of achievement level, teacher, and instruction variables on 

the probability of proficiency at different levels of grade 12 

mathematics: 1992. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96 

Estimated effects of achievement level, teacher, and instruction variables on 

the probability of proficiency at different levels of grade 12 

science: 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 98 

xii 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

List of Figures 

Page 

Figure 1.1: Schematic Diagram of Factors Hypothesized to Affect High 

School Students' Achievement Score Gains . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 6 

Figure 1.2: Percentage of 12th-Grade Mathematics Students Whose Teachers 

Report Various Emphasis: 1992 .................................... 21 

Figure 1.3: Percentage of 12th-Grade Science Students Whose Teachers 

Report Various Emphasis: 1992 .................................... 24 

Figure 1.4: Percentage of Seniors with Mathematics Teachers Reporting 

Different Frequencies of Using Various Instructional Methods: 1992 .......... 31 

Figure 1.5: Percentage of Seniors with Science Teachers Reporting 

Different Frequencies of Using Various Instructional Methods: 1992 .......... 31 

Figure 2.1: Percentage of Grade 12 Mathematics and Science Students Enrolled 

in Classes at Each Class Achievement Level: 1992 . . . . . . . . . . . . . . . . . . . . . . 36 

Figure 2.2: Average Emphasis Math Teachers of 12th-Grade Students Place on 

Different Objectives, by Achievement Level of the Class: 1992 .............. 38 

Figure 2.3: Average Emphasis Science Teachers of 12th-Grade Students Place on 

Different Objectives, by Achievement Level of the Oass: 1992 .............. 38 

Figure 2.4: Average Minutes Per Week Allocated for Science Labs, by 

Achievement Level of Student's Class: 1992 ........................... 40 

Figure 2.5: Average Minutes Per Day of Homework Assigned by Teachers 

of 12th-Grade Math and Science Students by Achievement 

Level of the Class: 1992 ......................................... 42 

Figure 2.6: Average Percentage of Class Time Spent on Various Activities, 

As Reported by Teachers of 12th-Grade Math Students, by 

Achievement Level of the Class: 1992 ............................... 44 

Figure 2.7: Average Percentage of Class Time Spent on Various Activities, 

As Reported by Teachers of 12th-Grade Science Students, by 

Achievement Level of the Class: 1992 ............................... 45 

Figure 2.8: Percent of 12th-Grade Math Students Whose Teachers Had Different 

Levels of Educational Credentials, by Achievement Level of the 

Class: 1992 .................................................. 49 

xiii 
High School Seniors' Instructional 

Experiences ·in Science and Mathematics 

Figure 2.9: 

List of Figures (Cont'd) 

Page 

Percent of 12th-Grade Science Students Whose Teachers Had 

Different Levels of Educational Credentials, by Achievement 

Level of the Class: 1992 ......................................... 50 

Figure 3.1: Percentage of 12th-Graders Taldng Mathematics and Science 

Courses, by Students Background Characteristics: 1992 ................... 56 

Figure 3.2: Percentage of 12th-Grade Mathematics Students Enrolled in 

Classes With Different Achievement Levels, by Students Background 

Characteristics: 1992 ........................................... 59 

Figure 3.3: Percentage of 12th-Grade Science Students Enrolled in Classes 

With Different Achievement Levels, by Students Background 

Characteristics: 1992 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 61 

xiv 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Appendix A: 

Appendix B: 

B.1. 

B.2. 

B.3. 

Appendix C: 

Appendix D: 

Appendices 

Page 

Supplemental Descriptive Data and Standard Error Tables 115 

Methodological and Technical Notes ............................... 137 

Description of the Sample . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 139 

Sampling Errors . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 140 

Description of Measures ......................................... 141 

Identifying Courses in, the NELS:88 2nd Follow-up Teacher Data ............ 151 

Regression Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 157 

xv 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Chapter I 

Introduction 

As American education moves into the 21st century, public interest in improving student learning 

is increasing. Some of the more prominent reform proposals have focused on the roles of accountability 

systems, school choice, teacher professionalism, and family responsibilities. Compelling arguments for 

the seminal importance of each of these mechanisms have been made, but are often made without 

acknowledging a very simple fact. This is that the focus of efforts to improve outcomes must ultimately 

fall upon the classroom and, even more specifically, upon the organization and delivery of instruction. 

Teachers teach and students learn in classrooms. While state, district, and school policies can have large 

effects on outcomes, their ultimate effects on student learning are largely mediated by classroom processes. 

Despite the centrality of the classroom, systematic research on it using large-scale surveys is still 

in its infancy. The U.S. Department of Education national longitudinal surveys collected virtually no 

information on classroom instruction in the National Longitudinal Study of 1972 or the 1980 High School 

and Beyond study. The analytic thrust of those studies was much more in the direction of explaining 

differences among individuals in terms of social background, social-psychological, curriculum program, 

and school organizational variables. New ground was broken by the Second International Science and 

Mathematics Studies (SISS and SIMS), conducted from· 1980 to 1986. These studies collected extensive 

information about content coverage in the early and late secondary school grades. While their findings 

continue to stimulate research and policy debates (McKnight, et al., 1987; Westbury, 1992 and 1993; 

Baker, 1993; Stedman, 1994), the surveys had several shortcomings with respect to sampling adequacy 

and measurement of processes, outcomes, and organizational contexts. Many of these problems have been 

overcome by the National Education Longitudinal Study of 1988, or NELS:88. NELS:88 collected data 

from teachers about how they conduct their classrooms so that the data could be linked back to the 

individual students in those classes as well as to a wealth of information about the schools in which they 

worked. These data were collected during the spring terms of 1988, 1990, and 1992, when the sampled 

students were mostly in grades 8, 10, and 12. 

This report draws on the NELS:88 second follow-up (1992) survey of science and mathematics 

teachers to shed light on the instructional experiences of high school seniors in those subjects. The main 

objectives here are to describe the types and variability of science and mathematics instruction, and to 

assess the extent to which differences are associated with ability grouping, student social background, and 

school characteristics. Beyond that, we provide some preliminary analyses of the relationships between 

students' instructional experiences and their academic growth over the last two years of high school. 

In the sections which follow, we set forth the conceptual framework of the study and describe the 

sample and measures we use. With these in place, we present univariate statistics describing the NELS:88 

variables used throughout the remaining chapters. 

Background Perspectives: Policy Issues and School Effects Research 

The specific instructional variables and relationships among variables examined in this report were 

selected because of policy and theoretical interests. This section provides some background on the nature 

of these interests, and thus gives the context for the report as a whole. · 

1 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Policy Issues. Current interest in research on classroom processes reflects a convergence of policy 

and theoretical concerns. On the side of policy, questions about the nature and quality of secondary-grade 

instruction in science and mathematics have attracted considerable attention over the past decade, due in 

large part to the mediocre showings of U.S. students in international comparisons of science and especially 

mathematics. The main response of the federal government has been to establish general goals for the 

nation's schools, and to support efforts by state and local governments and teacher professional 

associations to develop standards of what should be taught and how learning should be assessed. 

Thus far, the states have relied mainly on the leadership of various national organizations to work 

out the details of the content standards in mathematics and science. To a much greater extent than their 

counterparts in the humanities, history, and social science, the national professional associations of 

secondary science and mathematics teachers are pursuing refonn programs that include recommendations 

for classroom practice. In both fields, the associations are calling for a shift away from disseminating 

infonnation to having students fonnulate questions, propose methods for answering them, and then try to 

arrive at some sort of answer. These proposals often fly under the banners of "inquiry learning" in 

science, and "constructivism" in mathematics (National Council of Teachers of Mathematics, 1989; 

National Science Teachers Association, 1992). 

The refonn proposals arise from widespread perceptions that (a) student achievement levels in 

science and mathematics are unacceptably low, (b) most teachers rely mainly on lecture and recitation 

methods and emphasize memorization and mechanical operations (Mullis, Dossey, Owen, and Phillips, 

1991, pp. 64-66); and (c) students are typically not engaged by the subject matter. The goal is to have 

more students achieving at higher levels; the means are to increase student engagement through enlivened 

yet demanding instruction. 

In both science and mathematics, the refonn initiatives are more advanced in the areas of general 

principles, curriculum design, and assessment of student progress than in the area of instructional practice. 

One does not find mention in the documents of the professional associations specifics on, say, the optimal 

balance between problem-solving exercises and routine drill, or between lectures and small-group work. 

What one does find are recommendations about orienting principles of instruction and, to a lesser extent, 

the relative emphasis teachers should give to different types of skills and the relative time allocations to 

different methods. With these caveats, the following recommendations follow from the refonn proposals 

of the science and mathematics teacher associations: 

• Teachers should emphasize problem-solving and scientific reasoning in all mathematics 

and science classes, not just classes emolling the most advanced students. Corrolaries 

include: 

• Mathematics teachers should minimize the practices teaching specific operations 

and then assigning students mechanical drill exercises to learn those skills. 

• Science teachers should minimize the practice of having students 

memorize vocabulary and definitions. 

• Science teachers should minimize the use of lecture-recitation fonnat in 

favor of greater use of naturalistic obseivation and laboratory 

experimentation. 

2 
High Sclwol Seniors' Instructional 

Experiences in Science and Mathematics 

• Both science and math teachers should make regular use of group 

discussions formats for "thinking out loud" about how to define and solve 

problems. 

• Teachers should emphasize the connections between mathematics and science and 

problems of everyday life, rather than teaching the subjects as specializations that are 

pursued for their own sakes. 

• Teachers should incorporate the technologies of calculators in mathematics and computerbased data analysis in science, emphasizing the utility of these tools for solving problems. 

The aim of these recommendations is to improve the learning outcomes of students in science and 

mathematics classes by making the subjects more engaging and challenging. While the present report 

cannot address the value judgments involved in these recommendations, it can address the empirical 

questions of how widely and under which conditions the recommendations are being pursued, and whether 

students whose teachers claim to follow the recommendations are actually achieving at higher levels than 

students whose teachers claim to do otherwise. 

While the reform platforms emphasize the importance of improving classroom instruction, 

advocates in both subject areas also stress the importance of larger systemic reforms to that effort. Two 

areas that are key to the reforms are curriculum design and teacher professional development. The 

proposed curriculum changes in both fields represent sharp breaks from the past. One side of curriculum 

reform is the redesign of thematic content and sequences across all grade levels. This has coincided with 

formulation of standards as to what should be taught and what students need to know. Another important 

side is the assignment of teachers and students to classes. The traditional practices of ability grouping and 

ability-correlated curriculum differentiation are seen by many as impediments to student engagement 

because it is believed that students in lower groups invest less effort and are held to lower expectations 

by teachers. 

As might be expected, the teacher professional associations want these changes to come mainly 

from the ranks of the teachers themselves. Thus, alongside curriculum and instructional reform, they also 

advocate expanded inservice-training opportunities, increased preparation time, and greater opportunities 

for teachers to develop and coordinate their lessons with other teachers in their schools and professional 

communities (NCTM, 1991; NSTA, 1992). 

A possible problem with these reform proposals concerns the role of incentives and sanctions. 

The professional associations view teachers' behavior as guided by their knowledge base and the time and 

resources available to them to learn more. The associations believe that given the opportunity, teachers 

will develop better instruction and student performance will concomitantly improve. These critical 

opportunities, however, will probably cost more money because of the increased teaching staff needed to 

allow more planning and problem-solving sessions. In other words, the incentive to improve is there; what 

is lacking are the means. Critics of the proposals tend to believe that efforts to reform will accomplish 

little unless the goals have teeth and good work is rewarded (Hanushek, 1994). Unless schools and 

students are held accountable and rewarded for achieving specific objectives, reform will be half-hearted 

and often misdirected. Some claim that the costs of building strong incentive systems can be met by 

reallocating existing funds, rather than increasing expenditures (Hanushek, 1994). 

3 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

A related policy issue concerns the means of assessing student and school perfonnance. Many 

fear that when perfonnance is only assessed by multiple-choice test items, the incentives shift away from 

"teaching for understanding" to coverage of what is tested and repetitive drill (Newmann, 1992). This may 

discourage teachers from trying new instructional methods which promise to increase student engagement 

and which may promote deeper thinking and understanding (Sizer, 1984). This problem confronts the 

entire curriculum, for advanced students are subject to standards set by the SAT and ACT tests, while 

slower students are often subject to minimum competency tests. 

It is important to recognize that many teachers may in fact prefer "teaching to the test" and the 

concomitant drill, even when external accountability pressures are not present. The mathematics 

curriculum developed by John Saxon, for example, is used in many schools and has its share of strong 

supporters (Diegmueller, 1995). The argument can be made that student engagement increases with 

mastery, and that mastery is more accessible when tasks are highly structured and feedback unambiguous. 

Research on the Effects of Schools and Schooling. The theoretical interest stems from work 

over the past several decades on factors related to student achievement differences. Initial large-scale 

research proceeded from the hypothesis that differences among schools in the kinds and levels of resources 

they made available could account for a large share of the differences among students. The Coleman 

study of 1966 (Coleman, et al., 1966) showed, however, that about 80 percent of the overall variability 

in student test scores was among students enrolled in the same schools. Furthennore, if one factored out 

the impact of students' family background differences on the 20 percent of the variance that lies among 

schools, it turns out that only around 10 percent of overall test-score variance can be attributed to 

differences in what schools as units actually do. Essentially the same pattern that Coleman discovered 

has been found in other national smveys spanning the last 30 years (Jencks & Brown, 1975; Hauser, 

Sewell, & Alwin, 1976; Hotchkiss, 1984). 

While differences among schools are thus relatively small compared to the overall variability in 

test scores, this does not mean that schools do not have much effect on student learning. Studies that have 

examined the effects of whether and how long students are enrolled in school show that students learn 

very little when they are not attending school over the summer (Heyns, 1978; Entwisle & Alexander, 

1992) or if they drop out of school (Gamoran, 1987). Furthennore-and more to the point of the present 

study, there is substantial evidence that differences in students' schooling experiences have a large impact 

on their achievement outcomes. The research on the effects of ability grouping and curriculum tracking 

(Alexander & McDill, 1976; Gamoran & Mare, 1989; Hoffer, 1992) is one body of evidence here, while 

another is the research on classroom effects. While the teacher and classroom data have thus far been 

largely limited to smaller-scale, local samples, the evidence suggests that large differences in learning are 

found among classes (Hanushek, 1972; Murnane, 1975; Pauly, 1991). 

The mechanisms producing the observed achievement level and classroom differences, however, 

have not been clearly identified. Oak.es (1985) documents that the instructional goals, methods, and 

quality of classes varies by class achievement level, but does not attempt to relate these differences to the 

achievement gaps. Hoffer and Gamoran (1994) find some support for Oak.es' hypotheses, but show that 

large portions of ability group differences in eighth-grade mathematics and science achievement remain 

unexplained. There is thus a need to extend this research in order to gain a better understanding of why 

achievement differences arise and how outcomes for lower-achievers can be improved. 

4 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Which Aspects of Instruction are Important, and Why? 

A schematic representation of the conceptual model guiding this study is shown in Figure 1.1. 

This diagram is essentially a rough answer to the question, "Why do students differ in how much they 

learn over the course of high school?" The ovals represent the main sets of variables drawn upon in this 

report. The connecting lines indicate paths of influence or causation. Our main interest is in 

understanding the role of instructional differences among classes in generating achievement differences 

among students. 

What is meant by "achievement" is of course important to clarify. As used here, achievement 

refers to mastery of content and skills that are generally recognized as important goals of the secondary 

school science and mathematics curricula. These are operationalized in the NELS:88 survey in terms of 

multiple-choice items, but these items cluster into sets which measure both simple recall and more 

complex reasoning. This is important because some of the instructional and school policy factors we 

consider may lead to positive results on recall items but negative effects on problem-solving. In the 

analysis presented in Chapter V, we thus examine the effects of the instructional variables on the different 

types of achievement outcomes in both subject areas. 

The diagram shows that student learning is most directly affected by instructional opportunities. 

Instructional variables are themselves affected by various factors included under the rubric of teacher 

characteristics, and also by school and subject-department policies and practices, and the ability group of 

the class. School policies and practices are shaped by community characteristics such as commitment to 

education and financial support for schools. Individual student background differences are shown here 

as having an impact on their ability group placements. Background includes parental education and 

socioeconomic status, as well as actual involvement of the parents in their child's education. While the 

path is not shown in the diagram, individual background can also be considered to influence the kinds of 

communities in which students live, in the sense that family income, parental occupation, and educational 

preferences affect where families reside. Conversely, communities can also affect some aspects of 

individual background, as when community institutions facilitate greater parental involvement (Coleman 

and Hoffer, 1987). Also potentially important but not shown here are direct paths from family and 

community background to achievement outcomes. While we suspect that most of what students learn of 

mathematics and science during high school is learned in high school classrooms, students certainly can 

learn from parents, outside readings, museums, and television. 

5 
O'I 

Figure 1.1: 

Schematic Diagram of Factors Hypothesized to Affect 

High School Students' Achievement Score Gains 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Instructional opportunities. Instructional variables include the substantive content of the course, 

the quantity of time devoted to instruction, and the methods used to teach the content. The conception 

of course content used here refers to the general kinds of skills that the teacher aims to instill, rather than 

the specific skills such as algebraically solving for an unknown or balancing a chemical equation. 

Theoretically, the main distinction in the general skill objectives -of mathematics and science classes is 

between reasoning and recall. Many observers have claimed that American high schools tend to 

emphasize recall and routine application of skills to solve typicalproblems, at the expense of an emphasis 

on original thinking and devising and applying problem-solving strategies (Goodlad, 1984; Sizer, 1984; 

Powell, Farrar, and Cohen, 1985). If the critics are correct, students should perform better on tests 

requiring reasoning and problem solving when their teachers emphasize thinking over recall. On the other 

hand, students whose teachers emphasize recall may perform better on tests of factual knowledge and 

simple operations. 

A second general skill dimension along which we anticipate class content will differ is the 

emphasis teachers place on practical applications and the importance of math and science in everyday life. 

The science and mathematics teachers associations are both recommending that teachers present these 

subjects as practical activities rather than as abstract pursuits with littl~ relevance to life outside the 

classroom. The rationale for this is that it will improve student engagement in the subject matter. We 

thus expect to find that, other things being equal, teachers who emphasize practical applications will 

realize better achievement outcomes among their students. In practice, however, other things may be 

difficult to keep equal, because teachers who allocate time to emphasize practical applications may be 

taking time away from covering material or working on problem-solving skills. 

The quantity of instruction simply refers to the amount of time devoted to instruction. One of the 

more influential hypotheses of educational research over the past 30 years has been Carroll's (1963) idea 

that learning differences are affected by the amounts of time devoted to coverage of materials. Research 

has operationalized "time on task" in various ways, some ways being more error-prone (e.g., the length 

of the school year) than others (e.g., measures derived from detailed classroom observations of how time 

is actually spent). Predictably, the more fine-grained studies have found strong associations between time 

devoted to instructional tasks and students' learning of the content in question (Fisher, et al., 1978). 

The third aspect of classroom instruction, the methods of instruction, is the most difficult for 

which to formulate grounded hypotheses. Are lectures more effective than discussions? Is dividing the 

class into small work teams that work out solutions to problems more effective than teacher-centered 

whole class methods? Any answer to these questions seems to depend on many conditions. A 

thoughtfully-articulated lecture from a well-educated adult is likely to be more informative than even the 

most earnest discussion among 17-year olds. But a careless lecture may be much less effective than a 

good discussion. And even the best lecture may fail to stimulate reflection among many students, while 

the discussion forum may carry some compulsion for the same students to use their intellects. 

Factors affecting instruction. Why might classes vary in the kinds of instruction provided to 

students? Teachers traditionally have had considerable control over how to teach their classes, and some 

control over the content, as well (Lortie, 1975). The personal preferences of teachers are thus allowed 

some expression, and instructional differences may be quite unsystematic. Systematic variations may still 

arise, however, from both direct and indirect mechanisms. 

One influence may be the educational background of the teacher. Teachers with undergraduate 

and graduate specializations in science and mathematics should have better understandings of their subjects 

and thus should be able to explain ideas more intelligently. Little evidence of positive effects of teacher 

7 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

credentials on student achievement exists (Hanushek, 1989; Hedges, Laine, & Greenwald, 1994), but the 

expectation of positive effects is sufficiently strong to warrant the further analysis we undertake here. 

Teachers also differ in their years of experience. More experience should lead to greater effectiveness in 

classroom management as well as a deeper understanding of the substantive material. On the negative 

side, more experience may result in the teacher's knowledge base and methods of classroom management 

being more outdated. A mix of positive and negative effects would be consistent with the evidence from 

past research, for the effects of experience are usually found to be positive but inconsistent and small 

(Hanushek, 1989) 

Instructional opportunities are also likely to be affected by the composition of the class, 

particularly the achievement or ability level of the students. Some observers have claimed that the most 

effective teachers are often assigned to the highest ability levels (Oakes, 1990). This path is indicated in 

Figure 1.1 by the arrow from ability group to teacher characteristics. A large literature also suggests that 

ability group placement affects the instructional goals and methods of all teachers, regardless of the 

teachers' professional backgrounds and personal preferences (Raudenbush, Rowan, & Cheong, 1993; see 

Gamoran and Berends, 1987 for a review). Students in higher-ability groups are more attentive to teachers 

and engaged in school, and their teachers are thus able to use whole-class instructional methods more 

frequently and to assign more homework. Higher-group teachers may also be able to adapt more easily 

the open-ended inquiry methods recommended by the professional associations. 

Although most high school teachers are members ofsubject-area departments, research on the roles 

departments play and their influence over their members is only beginning to appear (Bidwell & Bryk, 

1994; Little & McLaughlin, 1993). Exploratory research by Talbert and McLaughlin (1994a, 1994b) on 

a sample of 16 high schools shows that departmental policies and practices affecting teacher professional 

orientation vary significantly from school to school. Some of the variability is likely to depend on how 

much autonomy departments have. In some schools, departments choose textbooks and supporting 

materials. Departments may also set guidelines on what their members should cover and even how it 

should be covered. Less formal exchanges of information and opinions are also likely to be important 

functions of departments. 

School policies allocate students and teachers to classes, and thus can affect instruction through 

those mechanisms. Students' time on task may vary because of differences in school and district policies 

regarding the length of the school year and class periods (Wiley, 1976) and the number of courses students 

must pass to graduate (Wilson & Rossman, 1993). Time on task differences may also result from different 

amounts of time needed to discharge administrative duties and to administer tests required by the school. 

School policies can also directly affect the definition of instructional goals and the methods used. 

This can happen through informal channels, as when teachers are influenced by unwritten norms about 

what to teach and how (Kilgore, 1993). As noted above, one important path of technical and normative 

information is the teacher's dlscussions with other teachers in the school, particularly within the same 

subject-area department. School policies affecting the professional collegiality have not received much 

research attention, but we speculate that schools which delegate curricular responsibilities to subject-area 

departments and allocate time to fulfill those responsibilities will have greater collegial involvement in 

instructional issues. We also suspect that school policies which directly address student learning goals 

will have an impact on teachers' instructional decisions. Some schools evaluate principals and teachers 

partly on the basis of measured achievement levels, and there thus can be a strong incentive to find and 

implement more effective goals and methods (Schneider, Plank, and Wang, 1994). 

8 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Effects of student and school background characteristics. The final (left) tier of variables in 

Figure 1.1 is hypothesized to affect school policy and practice. Numerous studies have shown that student 

background variables of gender, race-ethnicity, and parental socioeconomic status are associated with 

instructional experiences in science and mathematics. Transcript studies show that females complete about 

the same numbers of math and science courses during high school, but are still less likely to take the most 

advanced courses, particularly in science. These lower rates of participation hold even when males and 

females at the same achievement levels are compared. Instructional inequalities associated with student 

SES and race-ethnicity can arise both from segregation between classes within schools as well as 

segregation between schools. Within schools, lower-SES and minority students are usually found to be 

disproportionately enrolled in lower-level classes. Between schools, Oakes (1990) showed that schools 

where lower-SES and minority youth are concentrated tend to offer classes which have less-well-educated 

teachers than their more affluent counterparts. 

School background characteristics include geographic location, type of control ( whether the school 

is public, Catholic, or other private), school size (which could also be viewed as a policy variable), and 

average socioeconomic status (also affected by policy). Traditionally, students in the Midwest and 

Northeast states have scored better on standardized achievement tests than students in the South and West 

(NSF, 1993, p. 26). Similarly, students in suburban high schools usually score higher on average than 

urban and rural students. 

School control type is also associated with outcome differences, and the effects are not completely 

accounted for by sector differences in the students' backgrounds (Coleman and Hoffer, 1987). Whether 

by virtue of selectivity (Murnane, 1984), market-driven competition (Chubb and Moe, 1990), or closer 

student-faculty ties (Bryk, Lee, and Holland, 1993), Catholic schools tend to place greater academic 

demands on their students. 

School enrollment size has long been considered an important influence on school organization 

and climate. The trend throughout most of this century has been toward consolidating smaller schools into 

larger units which could realize various economies of scale and provide a greater range and depth of 

courses. However, larger schools are usually considered to be more impersonal and less able to exert 

informal social control over students. As far as instruction is concerned, this could lead to less use of 

methods which require independent work by students, such as small group projects and homework. 

Because of the challenges larger size schools encounter in their control over students, research suggests 

they tend to be more formalized and less demanding (Lee, Bryk, & Smith, 1993). 

School SES composition is also associated with average school achievement, but once individual 

SES is taken into account, the research record does not generally indicate large independent effects on 

individual student learning (Gamoran, 1987; Mayer & Jencks, 1989). In other words, low-SES and highSES students do about the same whether they are in high-SES or low-SES schools. Nonetheless, some 

studies have found that instructional resources and practices are better in higher-SES schools (Oakes, 1990; 

Hom, Hafner, and Owings, 1992). From the standpoint of equality of opportunity, it is thus useful to 

examine instructional differences among high- and low-SES schools. 

Research Questions 

The conceptual framework diagrammed in Figure 1.1 shows how we have organized our ideas 

about the causes and consequences of instructional differences. Each of the paths represents a hypothesis 

or set of hypotheses that we will address in various ways throughout this report. Our focus, however, will 

be a relatively small set of questions that can be formulated as follows: 

9 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

(1) How equal are instructional opportunities, and, what are the sources of inequalities? Since 

our main concern is with the allocation of opportunities to classrooms rather than 

individuals, ine.qualities must be conceptualized as generated tiu;ough the processes which 

allocate students, teachers, and other resources to classes. This implies that we should 

first examine how instruction varies among types of classes, and then tum to the question 

of whether relationships can be found between students' social background and the kinds 

of instruction they receive in high school. Three subquestions can thus be identified: 

(a) What are the main dimensions along which learning opportunities vary within 

high schools? Some research suggests that the main source of differences is 

ability grouping: Students in the higher ability, more accelerated classes are 

allocated the most resources and receive the best instruction. Other researchers 

have emphasized. the importance of differences among teachers in background 

preparation, motivation, and pedagogical skill. 

(b) To what extent do instructional opportunities vary from school to school? Some 

research suggests that most of the variability is found within, rather than between, 

schools, but this has not been systematically tested with large-scale survey data. 

Insofar as differences are found, we will try to identify particular aspects of the 

schools which may account for them. 

(c) What sorts of relationships can be found between students' social background and 

the kinds of instruction they receive in high school? A number of previous 

studies have argued that low-SES and minority youth receive poorer instruction. 

In addressing this question, we make an effort to place whatever inequalities we 

may find among students in the contexts of the types of classes and schools in 

which the students are enrolled. 

(2) Are there any indications that differences in students' instructional experiences are related 

to differences in achievement? While the NELS:88 design does not allow a definitive 

answer to this question, we may find some positive support for certain practices. We will 

address this question in two steps: 

(a) What are the overall effects of instructional differences on achievement growth 

over the last two years of high school? 

(b) Are the effects essentially the same for all students, or are they different for 

students with different backgrounds? To what extent can good instruction 

compensate for a disadvantaged background? 

Limitations of the Present Study 

For several reasons, the present study is best regarded as heuristic and partial with respect to the 

larger issues of improving student achievement. First, the NELS:88 survey is the first national study to 

collect detailed information on the goals and conduct of high school classes. We thus lack comparable 

data from High School and. Beyond, and therefore cannot make inferences about trends in high school 

science and mathematics instruction. Second, the NELS:88 survey design limits the effort to estimate the 

effects of classroom differences on student outcomes. The NELS:88 data do not allow a direct link of 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

instructional variables to achievement growth, since the instructional variables refer to particular one-year 

or even one-semester classes, while achievement was only measured every two years. We thus do not 

have a complete account of the instruction students have received over the learning period, and causal 

inferences about the effects of instruction on learning must be tentative. Third, the focus on 12th graders 

enrolled in science and mathematics implies that the inferences we draw apply to a somewhat select group 

of students. While enrollments in these subjects among seniors has increased significantly in recent years, 

only 48 percent of seniors took science, and only 66 percent took mathematics. As we shall see, though, 

these students come from a wide variety of academic and social backgrounds, and were enrolled in courses 

ranging from the most basic to the most advanced. 

Despite these limitations, careful examination of the NELS:88 data are warranted because current 

discussions about reducing inequalities in students' "opportunities to learn" are often based on anecdotal 

information about how classrooms are organized and function. The NELS:88 files contain the best 

available nationally-representative information on high school instructional practices in science and 

mathematics and should prove useful in refining the focus of current policy pursuits. And although our 

ability to estimate the effects of the instructional variables on student learning is limited, it is still possible 

to gain some important clues about the relative significance of different instructional factors for learning 

over the last two years of high school. 

1992 Seniors: The NELS:88 Second Follow-Up Sample 

The data analyzed in this report are drawn primarily from the NELS:88 second (1992) follow-up 

surveys of students and their teachers. NELS:88 began in 1988 with a national sample of about 24,000 

eighth-graders selected from 1,052 public and private schools. The study collected questionnaire and 

cognitive achievement data from the students in 1988, 1990, and 1992, and followed the student beyond 

high school with mail questionnaires and phone interviews in 1994. While the students were in middle 

and high school, data were also collected from their teachers, principals, and parents. The high school 

transcripts of the students were also collected after the 1991-1992 school year. Participants who dropped 

out of high school were followed up in 1990 and 1992. In 1992, 12 percent of the 1988 eighth-grade 

cohort were classified as dropouts in the NELS:88 survey (McMillan, Kaufman, & Whitener, 1994, Table 

18). 

About 15,100 of the original sampled students were enrolled as seniors in high schools where 

NELS:88 surveyed the science and mathematics teachers in 1992. Ninety percent of the targeted teachers 

completed questionnaires, providing data for 9,634 of the 10,603 NELS:88 seniors enrolled in math and 

science (see Appendix B.1 for a detailed description of the study design). 

It is important to keep in mind at all points of this study that (a) many 12th graders do not take 

science and math, and (b) the 12th graders who do take these subjects are on average higher achievers and 

thus not a representative sample of the larger grade or age cohorts. Nonetheless, it is not the case that 

only the most advanced students take science and mathematics during their senior years. As will soon 

be evident, students from a wide range of ability levels and social backgrounds take these courses. 

11 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The result of the NELS:88 second follow-up design is that the sample of students, properly 

weighted, is representative of 1991-1992 school year seniors.1 Further, the subsamples with teachersupplied information on science and mathematics courses are representative of seniors who took those 

courses. However, because the study included only one set of teacher data per eligible student, the 

proportions of students who have science or mathematics teacher data are substantially lower than the 

proportions who actually took science or mathematics as seniors. To obtain an estimate of the latter, one 

must tum to the transcript data. Transcripts were collected for 13,862 of the 15,105 seniors (92 percent). 

These students are used in the analyses of senior-year enrollments presented in the next section of this 

chapter and in Chapters III and IV. 

Twelfth Grade Mathematics and Science Course Enrollment Patterns 

Drawing on the transcript data, we constructed indicators of whether the student took courses in 

science and mathematics during the 1991-92 school year, and, if so, the number and types of courses. 

The weighted percentages of students taking each of the main mathematics and science subjects in 12th 

grade are shown in Table 1.1. These estimates are derived from the transcript data.2 Two-thirds (66 

percent) of the 1992 seniors completed a mathematics course. The mathematics courses with the highest 

enrollment of seniors (25 percent) are those classified here as "advanced." These are mostly trigonometry 

courses, but also include analytic geometry, pre-calculus, and statistics. At the top of the mathematics 

course-taking hierarchy, 10 percent of the seniors completed a course in calculus. While 12th grade 

mathematics enrollments are heavily tilted toward the more advanced levels, substantial numbers of 

students are enrolled in geometry (5 percent), algebra 2 (10 percent), algebra 1 (3 percent), and applied 

or basic (13 percent combined) courses. 

1 The design of the NELS:88 sample includes clusters of students within schools. This means that the sample as a whole 

is not as comprehensive with respect to the population being represented as a simple random sample of the same size would be. 

Most statistical packages base their estimates of standard errors on the assumption of simple random sampling, but these 

underestimate the standard errors and thus exaggerate the statistical significance of results. To correct for the NELS:88 departures 

from simple random sampling, we used the SUDAAN package to estimate all standard errors reported and used for statistical 

significance tests. 

2 We used the course-level data in the NELS:88 transcript files to construct these indicators. We used the subsample of 

courses completed during the 1991-92 school year. Math and science courses were identified by the standard Classification of 

Secondary School Courses (CSSC) codes. Since many senior-year science and math courses are single-semester courses, many 

students had more than one course listed in one or both subjects. Moreover, a small number of students take two science courses 

or two math courses concurrently. In order to characterize the students' levels of course-work in such cases, we ranked the courses 

in the order listed in Table 1.1 and assigned the highest level taken to each student. 

12 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.1. Percentage of Seniors Enrolled in Different Types of Mathematics and Science 

Courses, 1991-1992 School Year. 

Type of Course 

Percent 

Enrolled 

Mathematics: 

No math course 34 

Basic, general, & pre-algebra 4 

Applied math 9 

Algebra 1 3 

Geometry 5 

Algebra 2 10 

Advanced: Trigonometry, Analysis, Pre-calculus, & Statistics 25 

Calculus 10 

Total 100 

I Sample Size I 13,862 

Science: 

No science course 52 

Basic (survey, biology, chemistry, or physics) 11 

Biology - regular level 5 

Chemistry - regular level 5 

Physics - regular level 10 

Specialized (survey, biology, chemistry, or physics) 9 

Advanced (biology, chemistry, or physics) 8 

Total 100 

I Sample Size I 13,862 I 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), 1992 High School Transcripts file. 

I 

13 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

A majority of seniors (52 percent) took no science at all. As was true in mathematics, the most 

popular 12th grade science courses were the more advanced subjects. First-year physics enrolled 10 

percent of seniors, followed by specialized topics (9 percent), and second year or AP biology, chemistry, 

and physics (8 percent). At the same time, a substantial number of seniors were enrolled in low-level 

introductory classes: 11 percent were in designated basic courses, and another 5 percent took a regular 

biology course. 

Measures of Instruction: Course Content 

Course content differences are not confined to the subject matter areas summarized in Table 1. 1. 

Nominally identical courses may vary considerably in terms of the subjects covered as well as the 

cognitive goals pursued through those subjects. The NELS:88 second follow-up teacher survey included 

several questions about subject matter and learning objectives. The subject-matter questions are shown in 

Tables 1.2 to 1.5. These data are primarily useful as an alternative, or possibly an adjunct, to the 

transcript data as a means of identifying the classes within the conventional schema of mathematics and 

science courses. The teachers were asked "Have you taught or reviewed the following topics in this (math, 

biology, chemistry, physics) class this year?" and were given five response options: 

1= Yes, I taught it as new content. 

2= Yes, but I reviewed it only. 

3= No, but it was taught previously. 

4= No, but I will teach or review it later this school year. 

5= No, topic is beyond the scope of this course. 

For present purposes, we collapsed responses 1-4 into a single category indicating whether the 

student has been or will be exposed to the topic, either in the present class or in one taken in a previous 

term. From Table 1.2, it is clear that the great majority of students who took senior-year mathematics will 

graduate with some exposure to basic algebra (linear equations and polynomials) and geometry (patterns 

and functions, properties of geometric figures, and coordinate geometry). Proofs are somewhat less widely 

taught than other traditional geometric topics, suggesting that some of the geometry classes are adopting 

an informal approach. 

14 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.2. Percentage of Twelfth-Grade Mathematics Students Whose Teachers Report 

Different Topics Covered: 1991-1992 School Year. 

Have you taught or reviewed the following topics in this math class during this year? 

Taught, reviewed, or assumed prior knowledge of: Percent 

Sample 

Size 

Integers 95 5,658 

Patterns and functions 90 5,640 

Linear equations 92 5,653 

Polynomials 88 5,645 

Properties of geometric figures 88 5,644 

Coordinate geometry 85 5,647 

Proofs 78 5,632 

Trigonometry 68 5,643 

Statistics 48 5,625 

Probability 55 5,632 

Calculus 29 5,632 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

The questions about topical coverage in science differed, depending on whether the course was 

in biology, chemistry, or physics. Because of this screening mechanism, the percentages of students with 

exposure to the topics tend to be higher than in mathematics, and indeed exceed 90 percent in most cases. 

Exceptions are human biology, ecology, and evolution in the biology classes; organic, nuclear, life process, 

and environmental chemistry; and molecular or nuclear physics. 

15 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.3. Percentage of Twelfth-Grade Biology Students Whose Teachers Report Different 

Topics Covered: 1991-1992 School Year. 

Have you taught or reviewed the following topics in this biology class during this year? 

Taught, reviewed, or assumed prior knowledge of: Percent 

Sample 

Size 

Cell structure and function 95 994 

Genetics 94 989 

Diversity of life 91 994 

Metabolism and regulation of the organism 93 991 

Behavior of the organism 90 992 

Reproduction and development of the organism 96 991 

Human biology 83 992 

Evolution 87 990 

Ecology 87 992 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

16 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.4. Percentage of Twelfth-Grade Chemistry Students Whose Teachers Report Different 

Topics Covered: 1991-1992 School Year. 

Have you taught or reviewed the following topics in this chemistry class during this year? 

Taught, reviewed, or assumed prior knowledge of: Percent 

Sample 

Size 

Atomic and molecular structure 97 871 

Properties and changes in matter 98 871 

The periodic system 96 859 

Energy relationships 93 861 

Reactions 96 858 

Inorganic chemistry 94 857 

Organic chemistry 72 858 

Environmental chemistry 70 853 

Chemistry of life processes 56 852 

Nuclear chemistry 68 858 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

17 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.5. Percentage of Twelfth-Grade Physics Students Whose Teachers Report Different 

Topics Covered: 1991-1992 School Year. 

Have you taught or reviewed the following topics in this physics class during this year? 

Taught, reviewed, or assumed prior knowledge of: Percent 

Sample 

Size 

Fonns and sources of energy 98 1,500 

Forces, time, motion 96 1,504 

Molecular/nuclear physics 72 1,503 

Energy /matter transfonnations 90 1,503 

Sound and vibrations 92 1,510 

Light 93 1,501 

Electricity and magnetism 91 1,509 

Solids/fluids/gases 90 1,504 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

Instructional emphases. Course content also includes the sorts o'f skills teachers try to develop 

among their charges. NELS:88 asked teachers to indicate the relative emphasis (with response options 

"none," "minor," "moderate," and "major") they placed on a number of different skills that cut across 

subject areas and are widely considered to be important. 

As Table 1.6 makes clear, most seniors are in math classes with at least moderate emphases on 

each of the objectives included in the NELS:88 questionnaire. Consistent with the recommendations of 

the National Council of Teachers of Mathematics (NCTM), a large majority of students have teachers who 

emphasize representing problems in multiple ways (86 percent "moderate" or "major"), integrating 

different branches of mathematics (81 percent), conceiving multiple approaches to problems (84 percent), 

and raising questions and formulating conjectures (81 percent). 

18 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.6. Percentage of Twelfth-Grade Mathematics Takers Whose Teachers Report Various 

Emphases: 1991-1992 School Year 

In this math class, how 

much emphasis do you 

give to the following 

objectives: None Minor Moderate Major 

Sample 

Size 

Understanding the nature 

of proofs 25 39 25 10 5,657 

Memorizing facts, rules, 

and steps 3 27 48 22 5,658 

Representing problems in 

multiple ways 2 11 38 48 5,659 

Integrating different 

branches of math 5 14 34 47 5,647 

Conceiving multiple 

approaches to problems I 14 42 42 5,653 

Perfonning calculations 

with speed and accuracy 5 27 41 27 5,643 

Showing the importance 

of math in everyday life 2 22 40 37 5,657 

Solving equations 2 14 35 49 5,636 

Raising questions and 

fonnulating conjectures 2 17 47 34 5,645 

Increasing students' 

interest in math/science 0 8 46 46 5,643 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

19 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The distributions of three items which tap key dimensions of the mathematics refonn proposals 

are shown in Figure 1.2. The first variable is a practice which refonners are trying to de-emphasize: 

having students memorize facts, rules, and steps. Despite the refonn proposals, 22 percent of the seniors 

are in classes where the teacher reports a major emphasis on this objective, and another 48 percent are in 

classes where the teacher reports a moderate emphasis on memorization. The middle chart shows that a 

much higher percentage, 42 percent, of the seniors are in classes where the teachers emphasizes conceiving 

multiple approaches to problems. Also consistent with the NCTM recommendations, a large percentage 

(37 percent) of students are also in classes where the teacher emphasizes the importance of mathematics 

in everyday life. These charts indicate that while the objectives advocated by the refonn proposals are 

given greater emphasis than memorization, substantial numbers of seniors are still in classes where 

memorization is a major objective. 

20 
Figure 1.2. 

Percentage of 12th-Grade Mathematics Students 

Whose Teachers Report Various Emphases: 1992 

60% 

50 % 

40% 

30% 

20% 

10% 

0% 

- - - - - - - - - - - - _48.% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

42% 42% 

------------

- - - - - - -

- - - - - - -

14% 

. . . . . . . . . . . ·-<· . 

1% -:•-:-:•-:-:·-:-:•-:= 

·:. ·: • •_•• ·: ■• 

Memorizing facts, Conceiving multiple 

rules, and steps approaches to problems 

(•None E3Minor ~Moderate rnIIIlMajor J 

- - - - - - - - - - - - - - - - - - - - - - - - - - - - -

40% 

22% 

Showing the importance of 

math in everyday life 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Some of these items shown in Table 1.6 appear to measure common dimensions. To see whether 

a smaller number of underlying factors could be identified, we estimated a factor model. Three factors 

emerged: (1) an emphasis on "higher-order" thinking skills, (2) an emphasis on "relevance," and (3) an 

emphasis on mechanical operations. To simplify the presentation of results, we combined the grouped 

items into three scales, giving each item an equal weight (see Appendix B.3 for details on the items 

included in the scales). In the rest of this report, the composite variables are used in place of the 

individual items presented in Table 1.6. 

The science class emphases also tend to be strongly skewed toward the moderate-to-major end of 

the scale. The full set of items is included in Table 1.7; Figure 1.3 shows the distributions of three items 

which seem especially germane to current reform discussions. The objectives with the highest emphases 

are "increasing students' interest in science" (96 percent "moderate" or "major") and "developing problemsolving/inquiry skills" (92 percent). Objectives with the lowest emphases are "learning about applications 

of science to environmental issues" (64 percent "moderate" or "major") and "memorizing facts, principles, 

and rules" (69 percent). The strong emphasis on problem-solving and inquiry skills and the lower 

emphasis on memorization are consistent with recent reform recommendations from the National Science 

Teachers Association. 

22 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.7. Percentage of Twelfth-Grade Science Takers Whose Teachers Report Various 

Emphases: 1991-1992 School Year. 

In this science class, 

how much emphasis do 

you give to the 

following objectives: None Minor Moderate Major 

Sample 

Size 

Increasing students' 

interest in science 0 4 36 60 3,615 

Memorizing scientific 

facts, principles, and 

rules 

1 29 49 20 3,602 

Learning scientific 

methods 0 14 46 39 3,593 

Preparing students for 

further study in science 1 10 34 55 3,598 

Developing problemsolving/ inquiry skills 0 8 26 66 3,603 

Developing skills in lab 

techniques 6 16 43 34 3,596 

Learning about . 

applications of science to 

environmental issues 

3 32 36 28 3,598 

Showing the importance 

of science in everyday 

life 

1 13 36 50 3,596 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of1988 (NELS:88), Second Follow-Up survey. 

23 
- - - - - - - - - - - - - - - - - - -

Figure 1.3. 

Percentage of 12th-Grade Science Students 

Whose Teachers Report Various Emphases: 1992 

70% 

60% 

50% 

40% 

30% 

20% 

10% 

0% 

'O 

Developing problem-solving/ Showing the importance of 

inquiry skills science in everyday life 

_,..,.............,.....,, 

29% - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - 26% 

13% 

- - - - - - - - - - - - _8_% _ 

O% \\ifi:if l:if i} --------~ ~- !!i!!i!fi!l.l 

Memorizing scientific facts, 

principles, and rules 

49% 50%

- - - - - - - - - - - - - - - -36 %-

(•None [l]Minor ~Moderate [Illl]]Major ) 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Factor analysis of these items shows two underlying factors: an emphasis on the importance of 

science in everyday life, and an emphasis on higher-order thinking or "inquiry" skills. The item asking 

about memorization of facts, principles, and rules did not group with any other items and is used as a 

single-item indicator in subsequent analyses. The other items are combined as equally-weighted 

components of their respective scales; these scales are used in the rest of this report in place of the I 

individual items. 

Measures of Instruction: Quantity of Instruction 

Quantity of instruction refers simply to students' exposure to instruction in whatever qualitative 

form it might assume. The measures available in the NELS:88 second follow-up include the length of 

the school year (from the school survey), the number of minutes the class meets each week, and the 

teacher's estimate of how much time is devoted to instruction as opposed to maintaining order, 

administrative duties, and testing. The amount of homework a student completes can also be considered 

under this rubric. 

The average 12th grade math student is in class for 235 minutes per week, or about 45 minutes 

per day. The science teachers were asked to separate lab periods from their time reports, and their average 

class time is slightly lower, at 222 minutes per week. In addition to this allocation, the average 12th grade 

science student spends 56 minutes per week in labs. While the variability around these means is not great, 

the class times of the 12th grade students do differ. 

Average daily homework assignments reported by the teachers are slightly higher in mathematics 

than in science, with 34 versus 31 minutes (Table 1.8). Considerable variability in the amounts assigned 

are found in both subjects. About 14 percent of the math students are in classes where the teacher assigns 

50 minutes or more each day, while 27 percent have less that 30 minutes a day. Science students are 

assigned less homework than math students. About 12 percent of the science students are assigned 50 

minutes or more daily, and 39 percent are assigned less than 30 minutes. 

25 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.8. Percentage of 12th Grade Math and Science Students with Different Average 

Amounts of Daily Homework Assigned: 1991-92 School Year. 

Minutes per Day of Homework Mathematics Science 

None 3.5 2.9 

10-19 7.8 15.1 

20-29 15.7 21.4 

30-39 38.9 33.5 

40-49 20.0 15.0 

50-59 1.6 1.7 

60-69 10.6 7.6 

70+ 1.9 2.8 

Total 100 100 

Mean 34. 31 

Sample Size 5,698 3,758 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

Quantity of instruction was also measured with a set of questions asking the teachers to estimate 

the percent of class time they spent on various activities (Table 1.9). About 56 percent of the senior mathtakers were in classes which devoted at least half of their time to whole-class instruction. Work in small 

groups and individualized instruction are relatively rare in both mathematics and science. 

26 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.9. Percentage of 12th Grade Math Students Whose Teachers Report Spending Different 

Amounts of Time on Various Activities: 1991-1992 School Year. 

What percent of 

class time is spent 

in a typical week 

doing each of the 

following with this 

class? 

Percent of class time 

0 1-10% 10-24% 25-49% 50-74% 75-100% 

unw. 

N 

Providing 

instruction to the 

class as a whole 

0.5 2 11 31 43 12 5,264 

Providing 

instruction to small 

groups of students 

11 42 31 13 3 0.5 5,178 

Providing 

instruction to 

individual students 

4 41 37 12 4 2 5,224 

Maintaining order/ 

disciplining 

students 

37 53 5 2 1 2 5,205 

Administering tests 

or quizzes I 35 58 4 I 0.5 5,260 

Performing routine 

administrative tasks 9 87 3 0 0 0 5,227 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

27 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.10. Percentage of 12th Grade Science Students Whose Teachers Report Spending 

Different Amounts of Time on Various Activities: 1991-1992 School Year. 

What percent of 

class time is spent 

in a typical week 

doing each of the 

following with this 

class? 

Percent of class time 

0 1-10% 10-24% 25-49% 50-74% 75-100% 

unw. 

N 

Providing instruction 

to the class as a 

whole 

1 3 11 27 41 17 3,472 

Providing instruction 

to small groups of 

students 

8 38 38 10 4 1 3,406 

Providing instruction 

to individual students 6 56 30 4 2 2 3,411 

Maintaining order/ 

disciplining students 38 52 6 2 1 1 3,446 

Administering tests 

or quizzes 1 43 51 4 0 0 3,460 

Performing routine 

administrative tasks 10 84 5 0.5 0 0 3,456 

Conducting lab 

periods 8 11 50 24 6 1 3,424 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

28 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Measures of Instruction: Quality of Instruction 

Quality of instruction refers to how the material is presented and is measured mainly by the 

teachers' reports of their instructional methods. The methods are listed in Table 1.11 along with the 

percentages of students whose teachers reported using them at each level of frequency. Lectures and 

recitation (i.e., "students respond orally to questions on subject matter") are the most common ways of 

using class time and are presented in Figures 1.4 and 1.5. In mathematics, fully 85 percent of the students 

were in classes which had daily or almost daily lectures, and 85 percent were in classes which used 

recitation on a daily or almost daily basis. 

29 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 1.11. Percentage of seniors with mathematics or science teachers reporting different 

frequencies of using various instructional methods: 1992 

How often do you use the 

following teaching methods or 

media? Never 

1-2 times/ 

mth 

1-2 times/ 

week 

Almost 

Daily Daily 

unw. 

N 

Lecture math 3 3 9 64 21 5,268 

science 3 5 33 52 6 3,482 

Students respond 

orally to questions 

on subject matter 

math 1 3 12 51 34 5,278 

science 3 7 24 48 19 3,502 

Teacher-led whole 

group discussions 

math 19 16 23 34 8 5,223 

science 14 23 36 24 4 3,484 

Student-led 

whole-group 

discussions 

math 61 21 12 4 2 5,233 

science 57. 27 12 4 0 3,468 

Students work 

together in 

cooperative 

groups 

math 11 29 32 23 5 5,274 

science 6 22 52 16 3 3,505 

Students complete 

individual written 

assignments or 

worksheets in 

class 

math 14 20 28 26 12 5,277 

science 16 24 42 15 3 3,511 

Students give oral 

reports 

math 83 13 2 2 0 5,251 

science 72 25 2 0.5 0 3,490 

Computers math 69 19 7 3 2 5,238 

science 65 24 8 2 0 3,445 

Audio-visual 

material 

math 41 24 14 16 6 5,207 

science 10 40 33 14 3 3,487 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

30 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Figure 1.4 

Percentage of Seniors With Mathematics Teachers Reporting 

Different Frequencies of Using Various Instructional Methods: 1992 

70% 

64% 

60% 

51% 

50% 

40% 

4% 32% 

29% 

30% 

1% 

20% 

10% 

0% 

Students work together in 

cooperative groups 

9% 

Lecture Students respond orally to 

questions on subject matter 

(•Never 1-2 Times/Month ~1-2 Times/Week IIIIlJAlmost Daily ~Daily J 

Figure 1.5 

Percentage of Seniors With Science Teachers Reporting 

Different Frequencies of Using Various Instructional Methods: 1992 

60% 

50% 

40% 

30% 

20% 

10% 

0% 

52% 52% 

· · · · - - · · · · · · · 

· · · · · - - · · 

Lecture Students respond orally to 

questions on subject matter 

Students work together in 

cooperative groups 

(•Never 01-2 Times/Month ~1-2 Times/Week IIIITIAlmost Daily ~Daily) 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up Survey. 

31 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The reliance on lectures and recitation has been widely criticized in recent years, and many reform 

proposals advocate greater use of cooperative learning and "authentic" discussions. Authentic discussion 

refers to situations where participants are trying to define or solve a novel problem; that is, a problem to 

which the answer is not known in advance. While "teacher-led whole-group discussions" and "student-led 

whole-group discussions" are not necessarily authentic discussions, the numbers in Table 1.11 can be taken 

as upper bounds on the prevalence of authentic discussions. Teacher-led discussions were fairly common, 

with about two-thirds of the students in classes which used them at least once a week. Student-led 

discussions were much less frequently used. Most students were in classes which never used them, and 

less than 20 percent in either subject had them once a week or more. Oral reports by students are even 

rarer: 83 percent of the mathematics students and 72 percent for the science students were in classes that 

never used them. 

Over 60 percent of the students were in math and science classes which used cooperative methods 

at least once a week, and only 11 percent in math and 6 percent in science had teachers who never had 

the students work in cooperative groups. Work in cooperative groups is actually reported to about as 

common as "seatwork," the practice of having students complete individual written assignments or 

worksheets in class. 

Despite calls for a greater role of computers in the classroom, Table 1.11 shows their use to be 

relatively rare in senior-year math and science. Sixty-nine percent of the math students and 65 percent 

of the science students never use computers. It should be noted that many math educators believe that 

wider introduction of hand calculators is even more important than use of computers. Unfortunately, the 

NELS:88 teacher survey did not include any questions asking whether calculators were used in the classes, 

and we thus do not pursue this topic.3 

Data Quality Issues 

How reliable and valid are the variables introduced in this chapter as measures of classroom 

instruction? We have noted ambiguity around some of the items, but there is a general question here 

about how well any of the items measure specific orientations and practices of teachers and their classes. 

Perhaps the best way to answer the validity question· would be to compare questionnaire data with 

observational reports from teacher classrooms. Unfortunately, observational data were not collected in the 

NELS:88 study, and we thus cannot clearly gauge the validity of these questionnaire items. Nor have 

there been any other systematic studies of the issue that can be drawn upon for guidance. 

The reliability issue refers to the extent to which the questions would elicit the same responses 

from the teachers if asked again some short time later. Again, we cannot address this question directly, 

because the teachers were not resurveyed. For some of the constructs, however, the teachers were asked 

a number of similar questions. This redundancy can be measured and, if present, utilized to build 

composite measures. We ran factor analyses on all of the emphasis, time allocation, teaching methods, 

and science class activity variables described in this chapter and in Appendix B.3. There is some 

redundancy in the items, and composite measures are justified in many cases. The drawback of using 

composites which cut across the batteries is that the metric of the composites are not interpretable in terms 

of any concrete time referents. The emphasis items range from l=none to 4=major, and thus have no 

concrete referent in the first place. We therefore used composites for the emphasis items which factored 

3 The 1992 student questionnaire did, however, ask the extent to which calculators were used in the students most recent 

math course. 

32 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

together, after introducing the individual items in Chapter 1. However, we did not combine the time and 

strategy variables until we did the regression analyses, and did so there only in science. The additional 

science instruction composite variables we constructed measure the extents to which computers and student 

presentations are used. 

Summary 

This chapter has set forth the principal research problems addressed in the pages that follow. 

While our larger objective is to identify instructional variables which contribute to positive outcomes for 

students, most of our efforts in this study are directed toward identifying factors related to differences in 

the 1992 seniors' mathematics and science instructional experiences. The next three chapters address this 

problem from three different angles: the impact of curriculum differentiation, the role of family 

background, and the role of schools as larger organizations. The final chapter returns to the issue of 

instructional effects on outcomes, examining the impact of selected instructional variables on student 

academic achievement and attitudes toward science and mathematics. 

33 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Chapter II 

Types of Courses and Instruction 

The conceptual framework set forth in Chapter 1 indicates that students' instructional experiences 

are likely to differ partly as a result of the type of courses in which they are enrolled. Figure 1.1 shows 

that the average student ability or achievement level of a course is hypothesized to be associated with 

instructional differences in a direct way, and also indirectly, because of the tendency of at least some 

schools to assign teachers with higher background qualifications to the higher-achievement-level courses. 

Different types of courses within the science or mathematics curriculum are likely to vary in 

several aspects of instruction. One reason for this is that the students in different courses typically have 

different levels of interest in the subject and prior achievement. Teachers might thus be expected to adapt 

instruction to students' different needs and interests. Some critics of curriculum differentiation have 

argued that student diversity does not in itself call forth instructional differences; what it does call forth 

are different teacher expectations. That issue aside, another reason instruction may vary is the subject 

matter itself: some subjects call for different objectives and methods, even when students are comparable 

(Stodolsky & Grossman, 1995). There are thus two dimensions of courses that we suspect are important 

to instruction: the ability level of the students and the content. Unfortunately, the information on course 

content cannot be linked to the information collected from the teachers for about 20 percent of the 

students. We thus rely on teacher reports on the achievement level of the classes in order to assess 

instructional differences (see Appendix C for a full discussion of the procedures used to categorize the 

classes). 

The distribution of students across the different class-achievement levels is shown in Figure 2.1. 

Most of the twelfth graders are in average-level or higher classes in both subjects. Twelfth-grade science 

appears to be somewhat more selective than mathematics. About 57 percent of the science students were 

in classes which their teachers classified as "advanced placement" or "above-average," compared to 43 

percent of the mathematics students. 

35 
Figure 2.1. 

Percentage of Grade 12 Mathematics and Science Students 

Enrolled in Classes at Each Class Achievement Level: 1992 

l,.) 

0\ 

Remedial 4.0% 

Advanced Placement 8.7% 

Above-Average 34.2% 

Mathematics 

Average 35.2% 

Low 8.1%

Above-Average 47.1% Advanced Placement 9.7% 

Science 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Class Achievement Levels and Instructional Emphases 

The achievement level of the students' classes is associated with the emphases their teachers place 

on different objectives. Using the composite measures of instructional emphases described in Chapter I 

and Appendix B.3, Figures 2.2 and 2.3 show that the average emphasis on "higher-order" skills increases 

as tl1e average achievement level of the class increases (see Appendix tables A2.2 and A2.3 for the 

numbers upon which these figures are based and the standard errors of the estimates). Conversely, 

emphases on the everyday relevance of math and science decrease as the achievement levels rise. While 

these trends are evident, it is also important to note that the absolute differences among the different types 

of classes are not great. The scale of the items used in these tables is l=none, 2=minor, 3=moderate, and 

4=major. Classes with the lowest average emphasis (levels of 2.8 and 2.9) thus still have "moderate" 

emphases on the skills in question. Moreover, the standard deviations on these variables are not very 

large, indicating that the variability around the means is not great. Virtually all students, then, are in 

classes where these objectives receive at least some attention. 

37 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Figure 2.2 

Average Emphasis Math Teachers of 12th-Grade Students 

Place on Different Objective, by Achievement Level of the Class: 1992 

Major= 4 

3.54 

Moderate=3 

Minor= 2 

None= 1 

-' 

- ' 

.....-· ,, 

- . Learning Mee anical 

Operations 

ES!Overall •Remedial Ellil!ILow 

Average 9High ll:l!IAP 

Figure 2.3 

Average Emphasis Science Teachers of 12th-Grade Students 

Place on Different Objective, by Achievement Level of the Class: 1992 

Major= 4 

Moderate =3 

Minor=2 

None= 1 

Developing Inquiry 

Skills 

jESJOverall IILow lii!Average High ll:l!IAP 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up Survey. 

38 
- High School Seniors' Instructional 

Experiences in Science and Mathematics 

Class Achievement Levels and Instructional Time 

Students in the different achievement levels show some large differences in the ways their teachers 

allocate class time. While the total amount of time the students spend in class does not differ across class 

achievement levels (not tabulated here), the way the time is used and the amount of additional time 

demanded in the form of homework differ significantly. The time devoted to science labs is greater in 

the higher classes (Figure 2.4). AP students spend 76 minutes in lab on average compared to 50 for 

average and 40 for low group students. 

39 
100 

80 

60 

40 

20 

0 

Figure 2.4. 

Average Minutes Per Week Allocated for Science Labs, 

by Achievement Level of Student's Class: 1992 

- - - - - - - - - 5_7_ - - - - - - - - - - - - - - - - - - - -

50 

-16 - - - --

61 ,0~,0~,0 

!1!!1:_'.!l!l.ll!!l.!J:.!1.:!11!1~1:!l ~ ' 1\1 ~~_..,,.. ...,,.. ...,... W,, .. \I I l~,I 11 , •r , 'I! ,. •• ' \I I' , 0 ''I ' " ' •r 'pl\, in 'j'o 1'0' I ~,Ill i,"a ■, o "'o ■ • ' I 

11 I 'I,~,•, ■ 1 I' 11 ■ ,< II' "I I ',. •r-,. ' I 11• 1 ',,.. ''p, • : 'II• , .W' .I'' •• I ' I~ 'l 'II._ W,,J, 11 i' 11,,,1 11 I , , ,,r,- ,•,-'I\,- W,, o '0 ,1 

111 '.,,.. .,... i,,• w• w,. I" -. .,,.. ',._,, ' w• - .. - - - 'II!~, •r, ••• ,,. 'II,,," ~J, W' " I ~ 

"" p, •,11' ,'lo ''p/1 ,In, 'lo ,,l'I ,, ' ' r,. \I l ·~.- II I '" ,I •r, ~ ",f',. 'I! .. Iii,, ,I ilo I" ,,11, i'lo ,"'pl'o' \,0, I 1, I, I••, ■ "r," ,,., 

W,, j lj ,I ', I 1 ' '' ! ",f', 1 \, W,, • ~ I 'II I I ! 

,-.:,•• w•,11• ,,w•• •.,... •• 11 ,,,,, ,,, 

' ' ' "',. ' ■ " I' ~ I '~,I lo I ,r,. I,. "If 'I, ~ 

1111111111111111111111111111111111111111111111111111111111111111 :,:i:ii?:i:ii::i3:'.'i}i;:::i/:i/:i:~i:•:/i ·~:~:~: •• ·' ••••••••••• ,• •• •• :O"<)"'I: 

••••• •• • • •• ••• ••• • •••• •••••••• •• ••• •• ••• •• • • •• ••• •• •• ~),"().-,C),l\(,;,,.-,c) "<~~t~ 

:: .:-::-:. -::-:: .' ·.'."·.: ............ ~t~t~;~t~~~t~t~t~~"C ~"C - ... '• . . .... ~~~,~f~•~~~,~f~•~=~=~,~

••:.'•:.'•:.'• ••: I Iii\, '1:-r~~~•:.;.•:,.'~:'.w~ 1"0~,jl~!';:~~:.;. •',•,' ,',•,' ,', ,~t.;.';,~~~J,1~1 .. ~,',1,~r-.~::~ 1

~'01''.'",:'._~•~~I • ' • ' • ' • ' ' 11 I ' , ~ ~ ', , "I~ 'W i' ,.~ '" I ~ I ~,- •i,,- •~ 

:.•.••• .... •.•:••.• ..... • .. •••,• • "Oil" ',• l"'I'" ~•"o,_wo:,111 \II"\" • ~ ,. 'If ,. I,, J ~ ,I 'II I I , 11 'lo It , • • ,. '"I, 0 W ~ '. 

I'' I~ "'ol• •~: 'II' : J,10, W' ,JII "0 ,~ ~o ~, 

W I II I •~, •1 • ,. "'!''" •~ ~ W,, 0 ', I ' 11 I "'!' 

Achievement Level of Class 

.. ' • "• "' •, I I"• I" •,... /h ,WO ,,WO,• I 

I , , Y, 'i I' "I,' 'I j 11 1 It I •r, "'!',. ",c I 

I'- ,,in, I~ 'I~•~' /h' 'pl' 'WO ,111 ill '1 'plO 

lj ' ~ ' 'l , lj I ' I •r • "' 0 "'!'' ' 'lo O , II 

E88Overall •Low •Average E2lHigh ~AP 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The amount of homework assigned by teachers is strongly related to the level of the classes 

(Figure 2.5). Remedial math students are assigned 23 minutes per day on average, rising to 50 minutes 

per day for AP pupils. The low group-AP difference works out to over 2 hours of homework per week 

and 85 hours for a 38 week school year. The high group - AP difference is less than half of that but is 

still a full hour per week. Comparable inequalities are apparent for science. 

41 
Figure 2.5. 

Average Minutes Per Day of Homework Assigned by 

Teachers of 12th Grade Math and Science Students 

by Achievement Level of the Class: 1992 

60 

50 

-c 

cu 

= 40 ~ 

~-~ ('I.) Q l:'I.) -<('I.) 

<l) ~ 

..... s. 30 = 0 .5 ~ 

~ s 20 

0 

= 

10 

0 

50 

31 

.., (," __, 

., ., ~II ■ .. 

Math Classes Science Classes 

~Overall •Remedial •Low [I]Average ~High ~AP 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 

50 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The way class time is used varies with the achievement level of the class. The teachers' responses 

to the questions about the percentages of time they spend on different fonns of instruction as well as 

maintaining order are shown in Figures 2.6 and 2. 7 (see Appendix Tables A2.4 and A2.5 for the 

supporting numbers).4 In both subjects, the achievement level of the class is related to two activities: 

use of whole-class instruction and time spent on discipline. In mathematics, AP and remedial classes 

differ by 23 percentage points on the portions of class time devoted to whole-class instruction. For a 50 

minute period, this translates into about 18 minutes of whole-class instruction in remedial classes versus 

29 minutes in the average AP class. The differences are much smaller between average, above average, 

and AP classes. 

4 The questionnaire response options for the questions asking about the percentages of time devoted to various practices 

are the percentile ranges described in Appendix B.3. The mean percentages reported here and in subsequent figures and tables were 

derived by coding the ranges to their respective percentage-scale midpoints. 

43 
------------------------------------------------------------------

-- - - -- - --- - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

Figure 2.6. 

Average Percentage of Class Time Spent on Various Activities, 

As Reported by Teachers of 12th Grade Math Students, 

by Achievement Level of the Class: 1992 

100 

80 

.5 58- aJ 6 0 

Eir,J 

-

~ 

u 40 - - - - - - - - - - - - - - - - - - 321-- - - - - - - - - - - - - - - - - - - - - - - - - - - - - -

~ 

20 

0 Whole-Class Small-Group Individualized Maintain 

Instruction Instruction Instruction Order 

!~Remedial •Low •Average EJHigh ~AP 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 
------------------------------------------------------------------

Figure 2.7. 

Average Percentage of Science Class Time Spent on Various Activities, 

As Reported by Teachers of 12th Grade Science Students, 

by Achievement Level of the Class: 1992 

100 

80 

w 

·-

~ 

= 60 

tr.l 

tr.l 

u - 40 ~ 

20 

0 

Small-Group Individualized Maintain Lab 

Instruction Instruction Order Periods 

,~Low •Average •High EmAP 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 

.p.. 

Whole-Class 

Instruction 

VI 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

In tenns of discipline, remedial and low math students have about 10 percent of their class time 

spent on maintaining order, compared to only 1 or 2 percent of the time in AP classes. Comparable 

differentials are apparent among students in the different science classes. 

Across all types of classes, Figures 2.6 and 2.7 show that most of the time not used for wholegroup instruction is devoted to small-group work, individualized study, administering tests and quizzes, 

and, in science, laboratory work. As might be expected, remedial math classes use much more 

individualized study than other types of classes. Students in AP and above average-level science classes 

have slightly more time devoted to laboratories than low-level science students. Otherwise, without 

exception, the time devoted to these activities is nearly equal for students at the different levels. 

Class Achievement Level and Instructional Methods 

Despite the differences among classes in the percentage of time devoted to different activities, the 

kinds of activities pursued in the different classes tum out to differ very little. To summarize the 

relationships, we calculated gamma coefficients between the class achievement variables and the teacher 

reports of the extents to which they use various instructional methods. The gamma coefficient was 

developed to measure direct association between two ordinal variables, and ranges from a minimum of -

1.0 to +1.0. Table 2.1 shows the correlations between the class achievement level and the teachers' use 

of lectures, discussions, computers, cooperative groups, and other methods. The variable showing the 

strongest association with the level of the student's class is the frequency of having students complete 

written assignments in class ("seatwork"). This is used less often the higher the achievement level of the 

class. Other significant associations are found between the achievement level of the class and the use of 

lectures and recitation in science, and the use of computers in both subjects. 

46 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 2.1. Correlations8 between the teacher's report of the achievement level of the student's 

class and the teacher-reported frequency of using various instructional methods 

(standard errors in parentheses): 1992 

Instructional methodb Mathematics Science 

Lecture .069 .169* 

(.040) (.048) 

Students respond orally to questions on subject 

matter 

-.046 .117* 

(.036) (.044) 

Teacher-led whole group discussions .003 -.008 

(.032) (.042) 

Student-led whole group discussions .041 .065 

(.038) (.050) 

Students work together in cooperative groups .036 .063 

(.032) (.048) 

Students complete individual written assignments 

or worksheets in class 

-.203* -.267* 

(.030) (.042) 

Students give oral reports -.039 -.059 

(.054) (.060) 

Use computers .160* .206* 

(.042) (.054) 

Use audio-visual material .010 -.053 

(.032) (.044) 

* p(-y=0) < .05. 

a Correlation is measured by the gamma (y) coefficient, which is used for ordinal variables. Values can 

range from -1.0 (perfect negative correlation) to 1.0 (perfect positive correlation). The standard errors 

of the gamma coefficients are adjusted for an assumed design effect of 2.0, by doubling the simple 

random sample standard errors calculated by the statistical program used for this table. 

b Instructional methods are measured ordinally. Values range from l=never or rarely, 2=1-2 times a 

month, 3=1-2 times a week, 4=almost every day, 5=every day. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

47 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

One reason for the disparities in the use of seatwmk may be the greater difficulty of getting 

students in lower-level classes to complete homework. Most would agree that individual efforts to solve 

problems are necessary to learning. If obtaining that effort through homework is difficult, then the teacher 

would reasonably set aside more time in class. Another explanation may be the greater difficulty of 

maintaining order in lower-level classes. Seatwork is a relatively easy way to control a class and may be 

given more as busywork than as a genuine pedagogical tool. Deciding which of these alternative 

explanations is more valid is difficult with survey data. Much depends on the quality of the work assigned 

in the class and how the teacher conducts class while the students are working on their assignments. 

These were not measured in the NELS:88 study, and thus we cannot draw any clear conclusions from 

these differences. 

Teacher Credentials and Instructional Practice 

The ability level of the class is one reason why instruction varies from class to class; another 

reason may be the orientation of the teacher. Of the many factors that shape one's professional decisions, 

one's educational background is likely to loom large. To assess the impact of teacher educational 

background on the instructional variables, we classified the students according to their teacher's highest 

specialization and then compared the distribution of instructional differences across the degree categories. 

The typology of educational degrees we constructed has five categories defined by the cross-classification 

of undergraduaie and graduate specialization fields: 

1 Undergraduate and graduate major in field 

2 Undergraduate m: graduate major in field, and graduate or undergraduate minor in field. 

3 Undergraduate or graduate major in field, but no minor. 

4 Undergraduate and/or graduate minor in field. 

5 No major or minor at either the undergraduate or graduate level. 

The students for whom we have 12th grade teacher data showed the following distributions: 

Teacher degree category: Mathematics Science 

1 (major/major) 20.2 28.8 

2 (major/minor) 11.5 11.6 

3 (major/none) 42.2 36.4 

4 (minor) 16.3 13.4 

5 (none/none) 9.8 9.8 

100% 100% 

Credentials are somewhat higher on average among the 12th graders' science teachers, but large majorities 

of the students in both subjects have teachers with a field specialty at either the undergraduate or graduate 

level. At the low end, about 10 percent of the math and science students have teachers without either a 

major or minor in their respective subjects. 

For present purposes, we collapsed the highest two degree categories and the lowest two to make 

a three-level indicator. This is cross-classified by the achievement level of the students' classes in Figures 

2.8 and 2.9. As one might expect, the students in the higher ability groups are assigned the teachers with 

the highest credentials. For example, 63 percent of the students in AP science had teachers in the highest 

category (a major with graduate coursework), compared to 29 percent of the students in low-level science, 

40 percent of the students in average-level science, and 41 percent of the students in higher-level science. 

48 
Figure 2.8. 

Percent of 12th Grade Math Students Whose Teachers 

Had Different Levels of Educational Credentials, 

by Achievement Level of the Class: 1992 

100 

r:l:l

..... 80 

=

Cl.) 

"'C 60 ..... = 

rJJ. 60 

..=..... 

~ 

~ 40 ~ 

0 

~ 20 

0 

Remedial Low Average Above Average AP

ls8aMajor With Graduate Courses 

•Major Only 

EmNo Major 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 
0 

Figure 2.9. UI 

Percent of 12th Grade Science Students Whose Teachers 

Had Different Levels of Educational Credentials, 

by Achievement Level of the Class: 1992 

100 

r,J 

...... 

= 80 

"C 

~ 

63 ...... = 

00. 60 ~ 

= 

~ 

·-~ 40 

00. 

;+,.. 

0 

~ 20 

0 

Low AP 

Source: U.S. Department of Education, National Center for Education 

Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up Survey. 

44 40 41 

Average Above Average 

8 

~Major With Graduate Courses 

•Major Only 

l2JNo Major 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The association between achievement level of the class and teacher credentials suggests that 

credentials are also associated with the instructional variables, because instructional differences are also 

associated with achievement level of the class. The question, then, is whether teachers with different 

educational backgrounds do different things with students at comparable ability levels. To answer this 

question, we used the technique of ordinary least squares linear regression to calculate the unique 

associations of teacher educational background and the achievement level of the class with selected 

instructional variables. 

The regression model specifies that the students' values on the instructional variables depend on 

their teachers' educational background and the achievement level of the class. As the conceptual model 

represented in Figure 1.1 suggests, the regression model is probably an oversimplification, for it ignores 

the role of student background and school variables.5 However, the model does give a compact summary 

of the relationships at issue, even while one must be careful not to draw causal conclusions on this basis. 

The main message of these regressions is that the instruction students receive along these selected 

dimensions depends much on the achievement level of their class and relatively little on their teachers' 

educational credentials. Despite the relative weakness of teacher credentials, several significant 

relationships with instruction are shown in Table 2.2. In mathematics, there is some indication that 

teachers with higher credentials place more emphasis on higher-order thinking skills, devote more time 

to whole-class instruction, and devote less time to maintaining order. It should be emphasized that these 

statistical associations are adjusted for the correlations between the achievement level of the class, teacher 

education level, and the dependent instruction variable. 

5 We have simplified the model even further, for teacher educational background and class achievement level are tteated 

as continuous variables with no interactions with one another. The benefit of these simplifications is that they result in single 

summary coefficients of the relationships between the independent and dependent variables. Those benefits are illusory, of course, 

if the simplications result in misrepresentations of the actual relationships. We are confident that the results in Table 2.2 are 

appropriate representations, because results of less restrictive analyses essentially corroborated the findings. Specifically, we 

estimated two-way analysis of variance models which specified the independent variables as categorical and which included 

interactions between the independent variables. These models fit the data only slightly better, and showed that the ordinal class 

achievement variable can indeed be properly treated as a continuous variable. The effects of teacher education on insttuction are 

not as consistent, and would probably be better treated as a categorical variable with respect to som(i aspects of insttuction. In these 

cases, what seems significant is simply whether the teacher has at least a minor in his or her field. Since none of the exceptions 

proved substantively very large, we opted for the models presented in Table 2.2. 

51 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 2.2. Multiple regression estimates of the relationships of teacher education level and the 

achievement level of the class with selected instructional variables (t-values in 

parentheses): 1992. 

I 

Dependent 

Instructional 

Variables 

Effect of class 

achievement 

level 

Effect of 

teacher 

education 

level 

Model R2 Sample size 

I Mathematics 

Emphasis on higher-order 

thinking 

.28 

(10.02) 

.10 

(4.12) 

.11 5,246 

Homework assigned 

(minutes/day) 

.38 

(13.47) 

.02 

(1.11) 

.15 5,234 

% Class time in whole-group 

instruction 

.20 

(6.16) 

.06 

(2.20) 

.05 5,185 

% Class time maintaining 

order 

-.18 

(-10.00) 

-.09 

(-3.39) 

.10 5,130 

I Science I 

Emphasis on inquiry .32 

(8.22) 

.02 

(0.01) 

.08 3,478 

Homework assigned 

(minutes/day) 

.38 

(11.17) 

.08 

(2.62) 

.16 3,409 

% Class time in whole-group 

instruction 

.09 

(2.70) 

.05 

(1.11) 

.01 3,433 

% Class time maintaining 

order 

-.16 

(-8.05) 

-.04 

(-2.27) 

.08 3,407 

Time in labs (minutes/week) .18 

(4.64) 

.12 

(3.29) 

.05 3,430 

Use of computers .10 

(3.10) 

.02 

(0.21) 

.01 3,497 

Use of student presentations .03 

(1.01) 

.01 

(0.03) 

.01 3,502 

NOTE: The coefficients are standardized betas. The ordinal measures of teacher education level and achievement 

level of the class are treated here as continuous independent variables. The coefficients reported in the 

table thus indicate proportions of a standard deviation unit on the dependent variable that are associated 

with a change of one standard deviation unit on the independent variable, holding constant the other 

independent variable. See Appendix Tables Al.2 and Al.3 for descriptive statistics on the variables used 

in these regressions. 

SOURCE: US. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

52 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The regressions of the science instructional variables also show that teachers' educational level 

is generally less strongly associated with the instructional variables than is the achievement level of the 

class. As with mathematics, teacher education is significantly related to some aspects of instruction. 

Teachers with higher credentials tend to assign more homework and devote more time to laboratories, and 

devote less time to maintaining order. 

Summary 

This chapter has shown that the instruction seniors receive in their science and mathematics classes 

is strongly associated with the average achievement level of their classes. Students in the higher classes 

experience a greater emphasis on developing higher-order thinking skills. Their science lab experiences, 

as measured by the time variable, are also much greater, as are the homework demands of their teachers. 

Finally, teachers manage their classes differently depending on the achievement level of the class. 

Students in lower-level classes receive less whole-class instruction and have a greater share of their class 

time consumed by efforts to maintain order. 

Another aspect of classes that correlates with instructional differences is the educational level of 

the teacher. The pattern of associations is generally consistent with the ability-level differences in 

instruction. However, when instructional differences between teacher degree levels are compared within 

ability groups, the associations between teacher credentials and instruction largely disappear. Exceptions 

to this in science are found in higher amounts of homework assigned and the greater use of laboratories 

associated with higher-credential teachers. In mathematics, the exceptions are that teachers with higher 

credentials place more emphasis on higher-order thinking, devote higher proportions of class time to 

whole-group instruction, and spend less time on discipline. Even these differences should be treated 

cautiously, for the students we have grouped into our achievement-level tracks are often quite 

heterogeneous. It could be the case, for example, that teachers with higher credentials tend to be 

concentrated in higher-SES schools. These schools may require or encourage teachers to devote more time 

to laboratories for their lower-achieving classes. Higher-SES students may also be more tractable, and 

this could account for the lower amounts of time which more-educated teachers report devoting to 

discipline. In order to address these competing explanations, it is necessary to take account of the role 

of student background differences in the instructional differences we have observed thus far. 

53 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Chapter III 

Instruction and Student Background 

The previous chapter showed that the achievement level of the seniors' math and science classes 

is associated with the types of instruction they receive. What other factors might affect instructional 

experiences? As the research review in Chapter I (schematized in Figure 1.1) noted, student background 

is likely to be associated with instructional experiences for several reasons. One is that student 

background variables are almost always found to be strongly related to the achievement level of the class 

in which one is enrolled. Family background may also make a difference even among students at the 

same class level. This would occur, for example, if teachers held lower expectations for classes composed 

mainly of lower-SES pupils. Expectations, in turn, could be lower either because of prejudicial biases or 

because of a reasoned adaptation to reality. 

This chapter examines the relationship of student background with instructional experiences 

(research question #le on p. 10). As used here, background includes parental SES, race-ethnicity, gender, 

and students' prior achievement levels (as measured in 1990, when most were sophomores).6 We 

examine bivariate relationships of the instructional variables with student background variables, and then 

move on to assess the relationships within the curriculum levels examined in the last chapter. 

Student Background and Course Enrollment 

The bivariate relationships of student background and enrollment in science and mathematics 

courses are shown in Figure 3.1. The information on courses used here comes from the transcript data, 

and the samples thus include all of the students who were enrolled, whether or not data from their teachers 

were collected. Looking first at simply whether or not students are enrolled in a 12th grade course, males 

are more likely than females to take mathematics in 12th grade. Asians are more likely than whites and 

Hispanics to take mathematics, and more likely to take science than whites, blacks, and Hispanics. None 

of the apparent differences among whites, blacks, and Hispanics are statistically significant. Coming from 

an above-average-SES household is associated with higher rates of course-taking. The last chart in Figure 

3.1 shows that academic achievement has a strong association with course-taking. Students in the highest 

achievement quartiles of the 1990 (sophomore year) NELS:88 mathematics and science test score 

distributions were, respectively, 29 percent and 30 percentage points more likely than students in the 

lowest quartiles to take mathematics and science in 12th grade. 

6 The sample of students used for the cross-classifications of senior coursework and instructional experiences by 1990 

achievement scores excludes the 264 seniors who were added to the study in 1992 in order to make the NELS:88 sample 

representative of 1992 seniors across the U.S. This means that this subsample is not exactly representative of seniors nationally, 

but this is probably a minor deviation. 

55 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Figure 3.1 

Percentage of 12th-Graders Taking Mathematics and Science Courses, 

by Student Background Characteristics: 1992 

By Sex 

100 

"O 80 --Q

= "' 

~ 60 r,J 

·-"' Q 

= 

~ 40

rl.l 

c..,. 

Q 

~ 20 

0 

100 

"O 80 

-

~ 69 - 65 e 

~ 

= 60 r,J 

·-= 

"'Q 

~ 40 

rl.l 

~ 

Q 

~ 20 

0 

Math Science 

(,5 

-.1 ... , ..,...,, .. , ,.,,... ,.. ,.,.,. .,,.n.,,,..,.,,1

.. ,.. ,,.,..,,.,., ,., "''''""''"''"''~ ........... , ......... ,.. ,,., "''"''"''"''"''

..... ,....,.. ,. ::::::::::a 

... ,..............,.. 

Math Science 

I~Males •Females 

By Race-Ethnicity 

- - - - 76- - - - - - - - - - - - - - - - - - - -- - - - - - - - - - - - - - - - - - - - - - - - - - - -- - - -- - - - - - -

1?28Asian •Hispanic •mack CJWhite [;§Am. Indian 

56 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Figure 3.1 

Percentage of 12th-Graders Taking Mathematics and Science Courses, 

by Student Background Characteristics: 1992 

(Continued) 

By SES Quartiles 100 

'O 80 - - - - - - - - - - - - - - - - -- - - - - - - --7-5 - - - - - - - - - - - -- . - - . --- -- - - - - - - - - - - - - - - - --

-

e 

<I>

- 61 

~ 

C 60 !:ll 

i.. 

·-0 

C 

<I> 40

C'I.) 

c... 

0 

~ 20

0 

Math Science I~Lowest •Low-Middle lmllHigh-Middle Highest I 

67 

,,o -,----1 

.Ji) 

By 1990 Test Score Quartiles 

100 

79 

'O 80 ~ 

Q 

C 

i.. 60 ~ 

!:ll 

·-

C 

i.. 

0 40 

<I> 

C'I.) 

c... 

0 20 ~ 

0 

Math Science 

I~Lowest •Low-Middle IIIIIIHigh-Middle Highest 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up Survey. 

57 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Among the students enrolled in 12th grade math and science, the demographic compositions of 

the classes in which the seniors were enrolled vary significantly by the teacher's rating of the class's 

average achievement level. Restricting the sample back to the students for whom teacher data were 

collected, Figures 3.2 and 3.3 show these distributions. Gender differences tend to be insignificant at all 

levels of coursework. However, racial-ethnic differences are more pronounced. Black students are 

underrepresented at the AP level. Asians, in contrast, are much more likely than any other group to be 

enrolled in the AP math and science courses. The largest differentials in Figures 3.2 and 3.3 are found 

among the SES and 10th grade achievement quartile groups. 

58 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Figure 3.2 

Percentage of 12th-Graders Mathematics Students Enrolled in Classes With 

Different Achievement Levels, by Student Background Characteristics: 1992 

By Sex 

60 

43 

0 

Remedial Low Average Above Average AP 

I~Males •Females 

By Race-Ethnicity 

60 

r.,J

.... 

= 

~ 40 

:::::l

.... 

r,r.; 

.c:

..... 

= 

~ 

~ 20 

~ 

0 

35 

- -- - - - - · · - · - - - - - -

Remedial Low Average Above Average AP 

I~Asian •Hispanic lillllBlack CJWhite 

59 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Figure 3.2 

Percentage of 12th-Graders Mathematics Students Enrolled in Classes With 

Different Achievement Levels, by Student Background Characteristics: 1992 

(Continued) 

By SES Quartiles 60 

0 

45 44 

- - - - - - - - - - - - - - - - - - - - -

iiI-..... 

Remedial Low Average Above Average AP 

IESaLowest •Low-Middle llllllllllHigh-Middle Highest I 

By 1990 Test Score Quartiles 

60 

[ll

-f 40 'C 

-

= 

r:.f.) 

.c... 

~ 

~ 20 ~ 

0 

~ 

0 

Remedial Low Average Above Average AP 

ESaLowest •Low-Middle EllllllllHigh-Middle Highest 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up Survey. 

60 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Figure 3.3 

Percentage of 12th-Graders Science Students Enrolled in Classes With 

Different Achievement Levels, by Student Background Characteristics: 1992 

By Sex 

60 

49 

Low Average Above Average AP 

I~Males •Females 

By Race-Ethnicity 

60 

48 r,:i 45 46 -

=

QJ 42

"g 40 JS 

00-

QJ 

,:,J 

= aJ ·,:,J 

-

~ 20 

0 

~ iO 

0 

Low Average Above Average AP 

I~Asian •Hispanic IIIIIIBlack White 

61 
- -

High School Seniors' Instructional 

Experiences in Science and Mathematics 

Figure 3.3 

Percentage of 12th-Graders Science Students Enrolled in Cla~s With 

Different Achievement Levels, by Student Background Characteristics: 1992 

(Continued) 

By SES Quartiles 

60 54 

0 

Average Above Average AP 

48 

28 

- - - - - - - - - - - - - -16-

Low 

9 :;.t;.l;J I I 

j 

~Lowest •Low-Middle IIIBIHigh-Middle Highest 

By 1990 Test Score Quartiles 

60 

____________ .18__ _ 

1 

Low Average Above Average AP 

!~Lowest •Low-Middle lllllHigh-Middle Highest I 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up Survey. 

62 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Background and Instruction 

The relationships between the background and instructional variables are shown in Tables 3.1 and 

3.2. The subpopulation differences evident in these tables are consistent with what one would expect from 

the relationships between background and group placement (Figures 3.2 and 3.3), and group placement 

and instruction (Chapter II). Gender differences in the instruction students receive are negligible in both 

subjects. SES and race-ethnicity differences in instruction are evident at several points. SES differences 

in mathematics are found in the time-allocation variables: high SES students have less class time devoted 

to small-group and individualized instruction and to maintaining order than low SES students. Race and 

ethnicity differences in math instruction are evident on two variables. Black seniors have more of their 

class time devoted to maintaining order than Asians. Further, blacks and whites have less homework 

assigned to them than Asians, and blacks have less than Hispanics. 

In science, high-SES students are assigned more homework than low-SES students. There are no 

significant SES differences in the number of minutes per week devoted to additional lab sessions or the 

teacher responses to the question asking them to estimate the percentage of time devoted to laboratories. 

Black and Hispanic youth have about the same amounts of laboratory experience as non-Hispanic whites 

by either method of reckoning, and are assigned about the same amounts of homework. 

63 
Table 3.1. Means of math instructional variables reported by the teachers of 12th-grade math students, by student background 

characteristics: 1991-92 School year. 

IVariable I 

Gender Socio-Economic Quartile Race/Ethnicity 

Males Females Low Mid-low Mid-high High Asian Hispanic Black White 

Instructing whole class(% class time) 51.4 51.4 48.1 52.8 50.9 52.5 51.7 48.8 53.6 51.4 

Instructing small groups(% class time) 14.9 13.5 17.1 14.1 14.6 12.5 12.0 15.8 14.7 14.1 

Instructing individuals (% class time) 16.8 16.5 20.2 18.3 15.7 14.2 14.4 21.8 16.3 16.0 

Maintaining order(% class time) 6.6 5.9 8.1 6.2 7.4 4.3 3.9 7.5 10.4 5.5 

Administering tests (% class time) 14.6 13.7 13.9 14.9 14.0 14.1 12.9 14.0 15.8 14.1 

Administrative tasks (% class time) 5.5 5.3 5.6 5.6 5.7 4.9 5.5 6.5 6.2 5.1 

Conducting lab periods(% class time) 1.7 1.1 2.9 1.0 1.4 1.0 1.3 1.5 0.7 1.6 

Lecture (use: l=never/rarely to 

5=every day) 3.96 3.99 3.95 3.99 3.99 3.98 3.95 3.98 3.98 3.98 

Use computers (use) 1.50 1.51 1.60 1.46 1.49 1.52 1.56 1.57 1.38 1.52 

Use audio-visual materials (use) 2.19 2.24 2.41 2.27 2.19 2.10 2.29 2.13 2.34 2.20 

Use teacher-led discussion (use) 2.94 3.02 2.96 2.88 2.95 3.08 3.04 3.02 3.06 2.95 

Recitation (use) 4.13 4.14 4.15 4.12 4.12 4.15 4.12 4.04 4.27 4.12 

Use student-led discussion (use) 1.61 1.70 1.61 1.59 1.65 1.71 1.59 1.69 1.78 1.63 

Cooperative groups (use) 2.79 2.84 2.94 2.72 2.78 2.85 2.66 3.11 2.79 2.79 

Seatwork (use) 2.98 3.08 3.34 3.14 2.94 2.83 2.88 3.23 3.26 2.96 

Student oral reports (use) 1.23 1.22 1.27 1.19 1.15 1.30 1.17 1.34 1.25 1.21 

Homework (minutes/day) 32.8 35.3 31.5 30.9 34.4 37.3 37.7 36.8 31.7 33.7 

Emphasis: Problem-solving 

(l=none to 4=major) 3.21 3.26 3.10 3.19 3.25 3.34 3.28 3.19 3.26 3.24 

Emphasis: Applications 

(l=none to 4=major) 3.22 3;26 3.34 3.22 3.24 3.19 3.13 3.30 3.38 3.21 

Emphasis: Mechanics 

(l=none to 4=major) 3.04 3.02 3.03 3.05 3.05 3.00 2.97 3.01 3.14 3.02 

SOURCE: US. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up survey. 
Table 3.2. Means of science instructional variables reported by the teachers of 12th-grade science students, by student background 

characteristics: 1991-92 School year. 

IVariable I 

Gender Socio-Economic Quartile Race/Ethnicity 

Male Female Low Mid-low Mid-high High Asian Hispanic Black White 

Instructing whole class (% class time) 51.5 53.3 51.7 51.6 51.4 53.7 51.2 50.9 53.4 53.0 

Instructing small groups (% class time) 15.4 15.3 18.5 13.9 16.2 14.2 12.5 22.6 15.0 14.9 

Instructing individuals (% class time) 12.0 11.8 12.9 11.2 12.2 11.7 13.0 13.4 10.5 11.2 

Maintaining order(% class time) 5.1 5.4 7.2 5.5 5.2 4.5 4.2 6.4 7.4 4.6 

Administering tests (% class time) 12.2 13.1 12.9 12.1 11.9 13.3 12.6 12.2 12.6 12.5 

Administrative tasks (% class time) 5.5 5.6 6.0 5.8 5.7 5.2 5.4 6.4 5.6 5.5 

Conducting lab periods (% class time) 21.5 23.0 19.1 21.3 23.0 23.6 22.5 21.2 20.9 22.7 

Lecture (use: l=never to 5=every day) 3.55 3.52 3.46 3.57 3.46 3.59 3.45 3.54 3.50 3.56 

Use computers (use) 1.49 1.47 1.40 1.43 1.56 1.48 1.52 1.43 1.79 1.45 

Use audio-visual materials (use) 2.56 2.64 2.68 2.44 2.61 2.64 2.68 2.70 2.53 2.60 

Use teacher-led discussion (use) 2.83 2.80 2.89 2.79 2.88 2.75 2.84 2.95 2.95 2.79 

Recitation (use) 3.69 3.77 3.63 3.76 3.63 3.81 3.63 3.59 3.67 3.75 

Use student-led discussion (use) 1.62 1.63 1.59 1.57 1.70 1.62 1.51 1.63 1.90 1.59 

Cooperative groups (use) 2.89 2.85 2.81 2.90 2.88 2.87 2.71 2.89 2.79 2.89 

Seatwork (use) 2.72 2.62 2.91 2.80 2.68 2.50 2.56 2.76 2.70 2.66 

Student oral reports (use) 1.30 1.34 1.34 1.27 1.34 1.32 1.31 1.34 1.42 1.31 

Homework (minutes/day) 31.2 31.6 27.6 29.8 30.3 34.1 38.0 34.8 31.9 30.3 

Laboratory (minutes/week) 56.2 57.4 54.3 55.1 56.5 59.2 63.1 57.4 60.0 56.1 

Emphasis: Inquiry 

(l=none to 4= major) 3.33 3.33 3.17 3.34 3.36 3.35 3.32 3.28 3.34 3.33 

Emphasis: Science & Society 

(l=none to 4=major) 3.11 3.15 3.20 3.14 3.21 3.04 2.96 3.22 3.23 3.11 

Emphasis: Memorizing Facts 

(l=none to 4=major) 2.88 2.87 2.90 2.85 2.84 2.91 2.81 2.96 2.90 2.87 

Composite frequency of computer use 

(l=never to 5=every day) 1.40 1.37 1.29 1.35 1.43 1.40 1.42 1.30 1.52 1.38 

Composite frequency of student 

presentations (l=never to 5=every day) 1.40 1.42 1.40 1.36 1.44 1.41 1.36 1.45 1.53 1.39 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The background variable that is most consistently associated with instructional differences thus 

appears to be socioeconomic status. One explanation for this is that SES is related to the achievement 

level of the students' classes, and Figures 3.2 and 3.3 indeed show that socioeconomic background 

differences are strongly associated with the class achievement level. But it is also possible that SES is 

associated with instructional differences even among students at the same achievement level. To assess 

this possibility, we confined our attention to the instructional variables which showed SES differentials 

in Tables 3.1 and 3.2; these were also found in the last chapter to be associated with the class achievement 

levels. These instructional variables included the shares of class time devoted to whole-class instruction 

and discipline, the amount of homework assigned, the amount of lab time (in science), and the teacher's 

emphasis on developing higher-order thinking skills. In science, we added to this set the frequency of 

computer use and student presentations. 

The relationships can be efficiently summarized using ordinary least squares (OLS) regression 

techniques. Regressing each of the instructional variables on the individual background indicators gives 

estimates of the independent effects of background on instruction. Adding measures of the achievement 

level of the class to the model shows the extent to which the overall effects are mediated by class 

achievement level. 

Since this is not an experimental study, many of the explanatory variables we examine are 

intercorrelated. Multivariate statistical methods are thus needed to identify the independent associations, 

or "effects," of the variables on the outcomes of interest. Effects imply "other things equal," and it is 

important to emphasize that this always must be interpreted in terms of the specific set of variables 

included in the model. As initial formulations, the regression equations included in this report are 

simplifications, and almost certainly leave out some variables that affect the outcomes. Further research 

is needed to pursue alternative specifications and to assess the extent to which those modifications alter 

the results reported here. The inferences drawn here should thus be viewed as preliminary statements, 

rather than definitive distillations from extensive model-building efforts. The occasional use of causal 

imagery in this report should be understood in this light. And, as is always the case in social science, 

causatioq even under the best of circumstances is a probabilistic rather than a deterministic notion. 

With these caveats in mind, Table 3.3 shows the coefficients from regressions of the math 

instruction variables on background and class achievement level. The full regression model estimates are 

included in Appendix D. The right-most column of the table shows the R2 statistics for the models. 

These are proportions of the total variance in the dependent variables that are explained by the models. 

The statistics are "adjusted" for the sample sizes. The first point to make about these regressions is that 

the student background variables alone (Model 1) account for very little of the variability among students 

on any of the dependent instructional variables. While a number of the coefficients are significant, it is 

important to recognize that even when the achievement level of the class is added (Model 2), the variance 

explained ranges from a high of .174 (homework assignments) to a low of .053 (time on discipline). Most 

of the variability in the instructional variables is thus accounted for by factors not included in these simple 

models. The results for mathematics indicate significantly more minutes of homework assigned and 

greater teacher's emphasis on developing higher-order thinking skills for females. When the controls for 

the achievement level of the class are added to the model, these gender differences diminish, and neither 

is statistically significant. 

66 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 3.3. Regression coefficients for selected student background variables from regressions of 

mathematics instructional variables: 1992. 

Gender Race-Ethnicity SES 

Composit 

e 

R2 

Dependent Variable: Model Female Asian Hispanic Black 

% class time for wholeclass instruction 1 0.025 0.600 -1.054 3.191 1.783 .006 

2 -0.654 -0.259 0.010 4.470** 0.724 .060 

% class time for 

discipline 

1 -0.752 -1.676* 1.051 4.203* -1.238** .021 

2 -0.271 -0.901 0.872 3.680 -0.697** .053 

Homework minutes/day 1 2.671** 4.196** 5.620** -0.199 3.696** .038 

2 1.567 1.770 6.219** 1.387 2.095** .174 

Higher-order skills 1 0.059* 0.060 0.038 0.078 0.124** .027 

2 0.032 0.020 0.065 0.127** 0.085** .110 

Key: Model 1: student background variables only. 

Model 2: student background variables plus achievement level of the class. 

*: p $; 0.05; **: p $; 0.01 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up s111vey. 

Significant racial and ethnic differences are apparent in time spent on discipline, where Asians are 

in classes with less time spent maintaining order, and blacks tend to be in classes where more time is 

spent on classroom control. In terms of homework, Asians and Hispanics have teachers who report higher 

homework loads. The greater proportion of time spent on discipline in the classes of black youth 

decreases to insignificance with the addition of the class achievement level. The greater homework load 

for Hispanics actually increases when class achievement level is added, while the Asian-white difference 

diminishes to insignificance. The elevation of the Hispanic effect occurs because Hispanics tend to be 

underrepresented in the higher-achievement-level classes, whose teachers generally tend to assign more 

homework. For the same reason, the teachers' emphasis on higher-order skills becomes significantly 

greater for blacks when the class achievement level is added. 

Socioeconomic differences among students are significant in the areas of homework assignments, 

class time spent on discipline, and the teacher's emphasis on higher-order thinking. These effects diminish 

with the additional controls, but still remain strongly significant. 

The coefficients from the regressions of the science instruction variables on background and class 

achievement level are shown in Table 3.4. The variance-explained statistic, R2. is also small for each of 

these models. The Model 1 equations uniformly account for less than 5 percent of the variance, and the 

Model 2 elaborations only reach 10 percent for the homework assignments and inquiry-skill emphasis 

variables. Again, the point to note is that the social background variables used here and the classachievement level variable account for only a small part of the overall variability among seniors in their 

instructional experiences. Gender differences are not apparent on any of the science class variables. 

67 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 3.4. Regression coefficients for selected student background variables from regressions of science 

instructional variables: 1992. 

Gender Race-Ethnicity SES 

Composit 

e 

R2 

Dependent Variable: Model Female Asian Hispanic Black 

% class time for wholeclass instruction 1 2.288 -1.646 -2.401 1.012 0.978 .022 

2 1.955 -2.606 -2.616 0.736 -0.056 .031 

% class time for 

discipline 

1 0.019 -0.330 0.871 2.105 -1.186** .049 

2 0.252 0.175 1.042 2.216 -0.572* .071 

Homework minutes/day 1 0.814 7.440** 6.177* 3.771* 3.868** .038 

2 0.115 4.186* 4.856* 3.423 1.062 .181 

Lab minutes/week 1 1.402 6.847 5.315 5.755 3.298* .004 

2 1.137 3.088 0.306 4.853 -0.310 .040 

Emphasis on inquiry 

skills 

1 0.001 -0.011 0.005 0.049 0.071** .010 

2 -0.026 -0.043 -0.022 0.040 0.017 .109 

Use of computers 1 -0.026 0.034 -0.017 0.175* 0.068** .014 

2 -0.029 0.025 -0.018 0.178* 0.051* .021 

Use of student 

presentations 

1 0.019 -0.031 0.061 0.160** 0.027 .010 

2 0.020 -0.045 0.061 0.160** 0.021 .013 

Key: Model 1: student background variables only. 

Model 2: student background variables plus achievement level of the class. 

*: p ~ 0.05; **: p ~ 0.01 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up survey. 

Racial-ethnic differences are significant in the amount of homework assigned, the extent of 

computer use, and the frequency of student presentations. Asian, Hispanic, and black students have 

teachers who report assigning larger amounts of homework than the teachers of white students. With the 

addition of the controls for the achievement level of the class, the larger homework loads for Asians and 

Hispanics are diminished but are still significant. The science teachers of black youth are significantly 

more likely than the science teachers of white youth to use computers and student presentations. This 

tendency is not explained by class-achievement level differences, because the racial gap remains 

unchanged and is still significant with the additional controls. 

68 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Finally, socioeconomic differences among students are significant in several areas: higher SES 

students tend to be in classes where less time is spent on discipline, more homework is assigned, more 

lab time is allotted, more emphasis is placed on developing inquiry skills, and computers are used more 

frequently. However, with the addition of the controls, the SES effect remains significant only for the 

amount of time spent maintaining order and for the use of computers. 

Summary 

Social background differences among the 1992 seniors are associated with the types of science 

and math classes they take and thus affect their instructional experiences. But we have also found aspects 

of instruction which differ along the lines of student background even after taking account of the ability 

levels of the classes. 

Gender differences are very small both in rates and types of course enrollments and in the teacher 

reports of instructional practices. Race and ethnic differences are evident but mainly reflect socioeconomic 

differences among the groups. Even after taking account of the ability level of the classes, the 

mathematics teachers of higher-SES students assign more homework, spend less time on discipline, and 

place a greater emphasis on higher-order thinking skills. In science, higher-SES students have teachers 

who report less class time spent on maintaining order and more frequent use of computers for research 

purposes than their lower-SES peers of equal ability. 

69 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Chapter IV 

Instruction and School Characteristics 

Thus far we have seen that seniors' instructional experiences are related to the level of their course 

and, at least indirectly, to their social backgrounds. Course enrollment patterns and student background 

both vary from school to school, and thus which school one attends is associated with the kind of 

instruction one receives. But schools are complex entities that differ from one another in hundreds of 

ways--a large proportion of which were measured by the NELS:88 surveys of principals, teachers, and 

students. Which aspects of schools influence the content and form of classroom instruction? A large body 

of research conducted over the past 15 years offers many suggestions, but few clear answers. 

While by no means exhaustive of the possibilities, the school variables we examine here do 

include indicators used by many previous studies. Two measures refer to school geographic location, and 

are included for simple comparative purposes rather than for any particular theoretical reasons. Of greater 

interest are the variables which in various ways reflect policy decisions, including the school's social class 

composition, enrollment size, whether the school is under public or private control, and the school's 

organizational characteristics. This chapter assesses whether instruction systematically varies between 

schools along each ofthese dimensions. To begin with, we return to the question of who takes senior year 

mathematics and science courses. Beyond that, we will try to determine the extent to which these school 

differences are associated with the instructional variables, and whether those aspects of schools which do 

correlate with instructional differences maintain any association once student background variables are 

controlled.7 

School Characteristics and Course Enrollments 

For a number of reasons, course enrollments in senior-year science and math are likely to vary 

among states, local districts, and schools within districts. First, enrollments vary because of 

socioeconomic-related differences in individual demand for the courses, because average socioeconomic 

status differs among states, districts, and schools. Individual differences are not the whole story, though, 

for policy differences that cut across socioeconomic lines are also found. Most to the point, policies on 

graduation requirements differ to some extent between states, and local districts and schools are usually 

able to enact policies more stringent than those of their state. Less directly, state and local university 

systems differ in their entrance requirements, and one would expect high school enrollment patterns also 

to respond to these variations. 

7 The multilevel nature of the NELS:88 data, where students are nested within schools, suggests that mixed or hierarchical 

models would be appropriate for estimating the relationships of interest here (see Bryk and Raudenbush, 1992 for an exposition of 

this methodology). Using these models is impractical with the NELS:88 second follow-up data, because school sample weights are 

not available. If weights were available, mixed models would be primarily useful for improving estimates of the standard errors. 

However, proper estimation of standard errors does not require mixed model methodology, but is instead solvable with use of the 

Taylor series approximation method as implemented in SUDAAN (Shah, et al., 1992) and other software packages. The large degree 

of dispersion of the original 8th grade sample as the students moved into high school means that the students are not likely to be 

accurate representative samples of the students in their particular high schools. The mixed model methodology would thus not be 

useful for estimating between- and within-school variance components, or for estimating cross-level interactions as random effects. 

Anticipating these problems, NELS:88 augmented the within-school samples of a subset of about 230 high schools and surveyed 

and tested these students i,md their teachers in 1990 and 1992. These data, referred to as the High School Effects Study, will be 

available in 1995. 

71 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

To assess the contributions of these different factors, we rely on logistic regression techniques. 

This method gives results that are analogous to ordinary regression, and it is appropriate for multivariate 

models when the dependent variable is dichotomous. In the present case, the dependent variables are 

whether the student was enrolled in mathematics and science courses during the senior year. Controlling 

for individual background differences in SES, gender, and race-ethnicity, the logistic regression equation 

estimates the effects of a unit change in each of the measures of school characteristics on the likelihood 

of course enrollment. For present purposes, the effects are presented as ratios of the odds of course 

enrollment for students who differ by one unit on the school variables. If the odds are equal, the odds 

ratio equals one. If the comparison group is less likely to be enrolled than the reference group, the odds 

ratio is less than one; if more likely, then the ratio exceeds one. 

We estimated two logistic models for each subject-area enrollment outcome. The first (Model 1) 

includes variables which are usually outside the control oflocal school policy makers, such as the school's 

geographic location, SES enrollment, and sector (public versus private). The second model (Model 2) 

adds a number of variables which, in contrast, tend to be subject to some local influence. These include 

the number of students enrolled in the school, the importance of test scores in how the principal is 

evaluated, whether the school has minimum competency requirements in math or science for graduation, 

and the number of math or science courses students are required to complete for graduation. 

The odds ratios shown in Model 1 of Table 4.1 indicate that whether a school is urban, rural, or 

suburban is not related to mathematics or science enrollments. A few significant regional differences exist 

(the reference of these comparisons are students in the Northeast): students in the West are less likely to 

take math, and students in the Midwest and South are less likely to take science. The South-Northeast 

difference is reduced somewhat but is not explained away when the additional variables included in Model 

2 are added. One possibility is that colleges in the Northeast tend to require more coursework in science 

and math. Another is that the economic bases of the regions differ so that even students not planning on 

college are encouraged to take more courses in these areas. 

The measure of the socioeconomic composition of the students' schools used here is the principal' s 

report of the percentage of students eligible for the free and reduced price federal lunch program. 

Controlling for individual SES, the results for Model 1 show that students in schools where 21 to 50 

percent of the students are poor are more likely to take senior science than students in schools where 0 

to 5 percent are poor, but no significant effects are found for any of the other levels of poverty 

enrollments. When the policy variables are added, in Model 2, that effect is no longer significant, but a 

significant effect emerges in mathematics. Generally, though, the effects of school-level SES appear to 

be minimal. Individual SES, in contrast, is the single strongest predictor of senior-year enrollment in 

science and math (see Appendix Table A4. l). 

72 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 4.1. Adjusted odds ratio~ of students taking mathematics and science in 1991-1992 school 

year, by school characteristics 

Variable Mathematics Science 

(Model 1) (Model 2) (Model 1) (Model 2) 

I Urbanicity I 

urban vs. suburban 1.090 1.110 1.234 1.010 

rural vs. suburban 1.005 1.030 0.997 0.932 

I Region of U.S. I 

midwest vs. northeast 0.853 0.957 0.743** 0.791 

south vs northeast 0.941 0.962 0.564** 0.591 ** 

west vs. northeast 0.666** 0.738* 0.828 0.913 

Percent students eligible for subsidized lunch 

6-20% vs. 0-5% 0.940 0.847 1.067 1.105 

21-50% vs. 0-5% 0.860 0.719** 1.251 * 1.239 

51 %+ vs. 0-5% 1.052 0.865 1.337 1.175 

I School control type I 

Catholic vs public 1.581 * 1.262 1.510* 1.485 

NAIS vs. public 3.512** 2.502* 4.538** 2.833** 

Other private vs. public 1.078 0.571 1.057 0.677 

73 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 4.1. Adjusted odds ratios8 ofstudents taking mathematics and science in 1991-1992 school 

year, by school characteristics (Continued) 

I 

Variable Mathematics Mathematics Science Science 

(Model 1) (Model 2) (Model 1) (Model 2) 

I School organizational variables 

12th grade enrollment 

size (natural log) 

-- 1.051 -- 1.061 

Importance of test scores 

in evaluation of principal 

-- 1.037 -- 1.011 

School rewarded for high 

achievement vs. not 

-- 0.949 -- 0.997 

School has min. 

competency requirement 

for math/science vs. not 

-- 0.894 -- 0.751** 

Years of math/science 

required for graduation 

-- 1.237** -- 1.246** 

a Odds ratios are estimated from logistic regressions of whether the students took math or science on the 

variables listed in the table plus controls for SES, gender, and race-ethnicity. See Appendix for full 

regression equations. 

-- Not included in Model 1. 

NOTE: * indicates the effect of the variable on the odds of taking the indicated course is statistically 

significant at the .05 level; ** indicates significance at the .01 level. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

As one would expect from the results of the High School and Beyond analyses of sector 

differences (Coleman and Hoffer, 1987), students in Catholic schools are more likely than their public 

school counterparts to take mathematics and science in their final year of high school. The unadjusted 

proportions enrolled in mathematics are 79 percent in Catholic schools versus 64 percent in the public 

schools; in science, 63 percent of the Catholic school seniors are enrolled versus 46 percent of the public 

school seniors. In contrast to HS&B, NELS:88 distinguishes non-Catholic private schools into two 

categories: schools that are members of the National Association of Independent Schools (NAIS) and 

others. NAIS private schools tend to be the most exclusive in terms of tuitiqn costs and academic 

entrance requirements, and come the closest to the stereotype of the elite private school. Ninety-two 

percent of the NAIS school seniors take mathematics while 88 percent take science. 

74 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Non-public high schools tend to enroll students from more advantaged socioeconomic 

backgrounds, however, and it is likely that some if not all of the unadjusted differences are due to the 

different student backgrounds. When background differences among students are taken into account, Table 

4.1 shows that the Catholic-public and NAIS-public enrollment differences are still significant. The 

Catholic advantages are not significant in Model 2, but students in the NAIS schools are still much more 

likely to take senior-year math and science than public school students. Other private school seniors, in 

contrast, do not significantly differ from public school seniors in either Model 1 or Model 2. 

Larger high schools might be expected to maintain higher enrollments because of their ability to 

offer more classes. Working against this is the possibility that larger schools tend to have weaker control 

over their students, and it may be easier for their students to avoid pressures to enroll in more demanding 

courses. In any case, the results in Table 4.1 show that size is not related to course-taking. Further work 

might usefully examine whether there is a lower threshold level below which enrollment falls due to 

insufficient numbers of students to make classes, and perhaps an upper threshold over which enrollment 

also drops due to weaker social control. 

The remaining school variables in Table 4.1 refer to specific organizational practices and policies. 

The rationale for including these measures is that all of them index policies that are designed to increase 

student achievement levels, and which may be expected to raise rates of participation in grade 12 

mathematics and science courses as a means to that end. Two of the questions ask whether the school 

is accountable (the principal's report of how much influence the performance of the school's students on 

standardized tests has on how the principal is evaluated by his or her superiors) or somehow rewarded for 

higher academic achievement (the principal's report of whether or not the state or local district offers a 

financial award or recognition to schools for raising student achievement levels). Neither of these 

measures proves to be associated with senior year course enrollments. One reason for this may be that 

the principals are judged on the basis of test results from grade levels other than grade 12, and thus do 

not try to change grade 12 course enrollments. Another possible explanation is that the principals try other 

methods to raise achievement than increasing senior enrollments in math and science. 

The other two questions address whether the school has standards which the students are obliged 

to maintain, specifically in the areas of science and mathematics. The first of these asks whether the 

school has minimum competency requirements for math and science in order for students to graduate. 

This proves to have a negative impact on 12th grade enrollments in science. This result is 

counterintuitive, but may be explained by a tendency of students who have passed the exams (often first 

offered in the freshman year) to become more complacent about their skill levels. Alternatively, the 

mechanism may be organizational if, for example, schools with minimum competency requirements tend 

to discourage further participation of some students once they have passed the requirements. 

The organizational policy which has a clear positive effect on enrollments is the number of courses 

required for graduation. Whether students learn much from the courses is an interesting question for 

further research. Other studies have shown that high school achievement growth is strongly related to 

the numbers and types of courses students take (Rock and Pollack, 1995; Hoffer, Rasinski, and Moore, 

1995), but additional research could usefully examine whether that general pattern holds when the 

additional courses are required versus voluntary. 

School Characteristics and Classroom Instruction 

In order to estimate the independent effects of school characteristics on classroom instruction 

variables, we relied on OLS regressions. For each of the instruction variables analyzed in the last two 

75 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

chapters, we estimated the effects of the school variables controlling for the individual student's SES, 

gender, and race-ethnicity. Controls for the achievement levels of the classes are not included in this 

analysis, because our interest here is in the total effects of the school variables rather than the effects that 

are not mediated by the achievement level of the student's class. As Figure 1.1 illustrated, school 

variables can affect a student's chances of being in a higher versus a lower ability group. For example, 

students in Catholic schools may be more likely to be enrolled in above-average classes, and that could 

account for the greater proportion of time their teachers spend on whole-class instruction. Controlling for 

the achievement level of the student's class, it would then look like Catholic school attendance has no 

effect on how much whole-class instruction one receives. But this would be an incorrect inference, 

because Catholic schools do have an effect, albeit one mediated by the effect of Catholic school attendance 

on the achievement level of the student's class. We suspect that some part of the total effects of the 

school variables presented here are so mediated, but tracing out those paths of influence is beyond the 

scope of this analysis. 

In addition to the school variables included in Table 4.1, the following analysis includes several 

measures derived from the NELS:88 1992 survey of mathematics and science teachers. Prior research on 

differences among effective and ineffective schools suggests that instruction is affected by the professional 

culture of the school. Lee, Bryk, and Smith (1993) argue that the extent to which teachers assume 

responsibility for student outcomes is particularly important. Responsibility is not something that is easily 

mandated, because standardized methods for achieving results are largely unavailable. What schools can 

do instead is to identify problems and facilitate problem-solving initiatives among teachers. If teachers 

have influence over instructional decisions and opportunities to discuss issues with one another, then ideas 

about what works and what does not will be refined and practice will improve. To begin to assess these 

ideas, we included measures of (a) the principal's leadership in setting goals and obtaining resources, (b) 

the extent to which teachers have influence over instructional methods, (c) the extent of teacher influence 

over instructional content, (d) the extent to which teachers coordinate the content of their courses, and (e) 

the extent to which teachers discuss instructional content issues with other teachers. These five measures 

are scales constructed from multiple items which we grouped together on the basis of common factor 

analysis. The items used to construct these scales are described in Appendix B.3. 

The regression results for mathematics are shown in Table 4.2. Although several statistically 

significant coefficients are evident in this table, the R2 values indicate that the school variables coupled 

with the controls for individual background explain relatively little of the overall variability in any of the 

instruction variables. The geographic location variables show some significant effects, but no clear 

patterns are evident across the different outcomes, and there is little consistency between the results for 

mathematics and those for science. Among the students taking mathematics, students in the Northeast (the 

reference category) have significantly lower amounts of homework assigned and have significantly more 

time devoted to whole-class instruction. Neither set of results holds in science, though. 

76 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 4.2. Estimated effects of school variables on mathematics instruction variables, from OLS 

regressions: 1992 

Independent 

Variables 

Higherorder 

thinking 

Emphasis: 

practical 

applictns 

Emphasis: 

mechanical 

operations 

Minutes/ 

day of 

homework 

assigned 

Time 

devoted to 

whole-class 

Time 

devoted to 

discipline 

I Urbanicity (vs. Suburb) I 

Urban 0.08 0.03 -0.02 1.44 -2.95 2.65 

Rural -0.04 -0.01 -0.04 -1.73 -1.72 -0.11 

I Region (vs. Northwest) I 

Midwest 0.02 -0.06 -OJ)() 4.83** -6.87** -0.58 

South 0.07 0.12* 0.15** 2.74 -5.40* 0.54 

West -0.08 -0.00 -0.02 4.48** -11.78** 1.79 

I Sector (vs. Public) I 

Catholic -0.03 -0.23* -0.07 -0.07 14.67** -1.92 

NAIS -0.12 -0.10 -0.27* 4.20 16.91 ** -2.31 

Other Private -0.02 -0.20 -0.10 4.36 15.77** 1.71 

I % Students Receiving Federal Lunch (vs. 0-S%) I 

6-20% -0.02 0.01 0.04 -1.18 3.84* 0.37 

21-50% 0.00 0.10 0.13** -1.64 6.10** 0.40 

51% + 0.14 -0.07 0.12 -0.54 10.17** 5.65 

I Number 12th Graders Enrolled in the School 

I Ln(size) I -0.02 -0.09** I -0.03 -1.12 3.28** I 0.04 I I I I 

Accountability of Principals for Achievement Outcomes 

Principal evaluated 

by test scores 0.04 0.02 0.00 0.93 -0.83 -1.37 

Effective schools 

recognized (0-1) -0.10* -0.02 -0.00 1.37 0.26 1.14 

I Graduation Requirement I 

Must pass math 

min. competency 

(0-1) 

0.04 0.00 0.00 -0.38 4.53** 1.11 

Years of math 

required 0.02 0.00 -0.00 -0.74 -2.77** -0.45 

I 

77 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 4.2. Estimated effects of school variables on mathematics instruction variables, from OLS 

regressions: 1992 (Continued) 

Independent 

Variables 

Higherorder 

thinking 

Emphasis: 

practical 

applictns 

Emphasis: 

mechanical 

operations 

Minutes/ 

day of 

homework 

assigned 

Time 

devoted to 

whole-class 

Time 

devoted to 

discipline 

School Organization Characteristics 

Principal' s leadership -0.07 0.02 0.02 0.79 -0.44 0.53 

Teachers influence: 

methods 0.03 0.06 0.02 0.16 2.16 -1.13** 

Teachers influence: 

curriculum 0.04** 0.03* -0.00 0.49 0.68 -0.22 

Teachers coordinate 

content 0.16** 0.10** 0.03 0.81 0.11 -0.65 

Teachers discuss 

content 0.28** 0.24** 0.09* 2.46 0.05 0.20 

R2 .144 0.10 .049 .083 .076 .060 

Sample Size 3,823 3,823 3,825 3,807 3,807 3,760 

* p <== .05; ** p <== .01. 

NOTE: All models include controls for individual student SES, race/ethnicity, and gender. See 

Appendix for full regression equations. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

Research from the High School and Beyond survey found several indications of instructional 

differences between public and Catholic schools (Bryk, Lee, and Holland, 1993; Coleman and Hoffer, 

1987). The general characterization that emerged was that Catholic high schools placed higher academic 

and disciplinary demands upon their students than public schools. Academic demands were measured by 

the numbers of academic courses the students completed and the amount of homework the students 

reported completing. Disciplinary demands were mainly measured by student reports of their own 

misbehavior, and teacher reports of the discipline climate in their schools. Neither set of measures thus 

ref erred to characteristics of specific courses or classes. What sorts of sector differences might one expect 

to find from the teacher-class reports in the NELS:88 data? Students in private schools can be expected 

to have teachers who assign more homework and spend less time on discipline. Emphasis on problemsolving and inquiry skills are also likely to be greater, reflecting the importance placed on academic rigor. 

The strong college-preparatory orientation of private schools may lead to lower emphases on practical 

applications. That orientation could also lead to more time devoted to whole-class instruction and less 

time on discussions and student presentations. The results in Table 4.2 give only limited support to these 

78 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

expectations, at least when one controls for student background and school organizational differences. 

Other things equal, students in the different types of private schools do not attend classes with greater 

emphasis on higher-order thinking skills, and are not assigned significantly more homework. School 

sector differences in mathematics instruction are found in the lower emphasis on practical applications in 

Catholic schools, and in the lower emphasis on mechanical skills in the NAIS schools. Students in all 

types of nonpublic schools receive more whole-class instruction in mathematics than students in public 

schools. 

For a variety of reasons, one would expect schools that enroll larger numbers of low-income 

students to confront special instructional challenges and to show instructional differences from more 

advantaged schools. However, Table 4.2 shows that school SES composition as measured here (the 

principal's report of the percentage of students receiving reduced-price lunch) generally has little effect 

on seniors' mathematics instructional experiences. The main exception to this is that students in schools 

with the greatest concentrations of poor students have teachers who use whole-class instruction more. 

School enrollment size, like school SES, has long been considered an important factor in school 

organization and climate. As discussed earlier, larger schools are usually considered to be more 

impersonal and less able to exert informal social control over students. As far as instruction is concerned, 

this could lead to less use of methods which require independent work by students, such as small group 

projects and homework. The results in Table 4.2 show that school size has no effect on homework, time 

devoted to maintaining discipline, or higher-order skills emphasis in math, but is negatively associated 

with emphases on practical applications. As might be predicted, students in larger schools receive 

relatively more whole-class instruction. These results thus give some support to the conception of larger 

schools as more formalized, but not to the view that they are also less demanding and more unruly. 

The school organizational variables have several significant effects on the mathematics instruction 

variables. One notable exception is that the instructional experiences of math students whose teachers see 

the principal as a strong leader do not differ from math students whose teachers give the principal lower 

ratings. 

The teacher influence over class content, the extent of coordination, and the extent of collegial 

discussions tend to be the strongest factors in predicting instructional differences in mathematics. All of 

these factors are positively associated with both an emphasis on higher-order thinking and on practical 

applications. In both cases, the strongest effect is from the extent of teacher discussions with colleagues 

about curriculum content issues. Greater collegial discussions also are associated with greater emphasis 

on computational skills. 

The results of comparable regressions for the science instruction variables are shown in Table 4.3. 

The instructional experiences ofurban, rural, and suburban (the reference) students significantly differ only 

on the teachers' emphasis on the role of science in society, which is greater in urban schools. Regional 

differences in science instruction show a few sizable differences on some instructional variables, but no 

clear pattern of advantage or disadvantage overall. Students in the Midwest and South experience a 

greater emphasis on learning facts and principles. Students in the West have teachers who make less use 

of computers as scientific research tools. Students in the South have teachers who make greater use of 

student presentations. 

79 
Table 4.3. Estimated effects of school variables on science instruction, from OLS regressions: 1992. 

I 

I 

I 

I 

I 

I 

I 

I 

Independent 

Variables 

Emphasis: 

inquiry 

learning 

Emphasis: 

practical 

applictns 

Emphasis: 

facts & 

principles 

Minutes/day 

of homework 

assigned 

Emphasis 

on lab work 

Time 

devoted to 

whole-class 

Time 

devoted to 

discipline 

Frequency 

of using 

computers 

Frequency 

of student 

oral reports 

I Urbanicity (vs. Suburban) 

Urban 0.07 0.21** -0.01 1.34 -0.02 2.85 -1.14 -0.04 0.05 

Rural 0.06 O.Ql 0.07 -0.27 0.03 -3.05 -0.48 -0.08 -0.02 

I Region (vs. Northeast) 

Midwest -0.01 -0.05 0.27** -1.96 -0.02 2.48 0.05 0.01 -0.04 

South 0.11 0.10 0.23** 0.88 -0.05 4.10 0.33 -0.06 0.13* 

West -0.05 -0.03 0.03 0.01 -0.09 -2.58 0.03 -0.16* 0.08 

I Sector (vs. Public) 

Catholic 0.10 -0.13 0.17 -1.53 0.06 3.11 1.09 -0.12 -0.16 

NAIS 0.24* -0.36* 0.13 9.08 0.39** 5.02 -0.70 0.19 -0.12 

Other private 0.10 -0.10 0.05 -1.74 -0.15 4.00 1.78 -0.25* 0.02 

I % Federal lunch (vs. 0-5%) 

6-20% 0.17** 0.13 0.08 -1.17 0.20** -3.67 -0.39 0.07 0.00 

21-50% 0.17** 0.18* -0.01 -0.53 0.22* -2.42 0.21 0.08 -0.06 

51%+ 0.17 0.08 -0.02 1.96 0.05 3.78 -0.98 0.06 -0.07 

I N. 12th Grade Students 

Ln( enrollment) I o.oi I -0.05 I 0.03 I -1.05 I 0.08* -0.20 0.16 0.04 -0.05 I I I I I 

I School Accountability 

Evaluated by test 

scores 0.08* -0.04 0.05 0.95 0.12** -1.86 0.31 0.02 -0.05* 

School recognition -0.02 0.04 0.04 -2.25 0.00 1.64 0.93 -0.07 -0.10* 

I Grad Requirements 

Science min. 

competency -0.02 0.09 0.07 2.06 -0.13 3.35 2.74* -0.03 0.07 

Science course units -0.09** 0.01 0.06 -2.27** -0.09* 0.19 0.66 -0.01 -0.01 
I 

Table 4.3. Estimated effects of school variables on science instruction, from OLS regressions: 1992. (Continued) 

Independent 

Variables 

Emphasis: 

inquiry 

learning 

Emphasis: 

practical 

applictns 

Emphasis: 

facts & 

principles 

Minutes/day 

of homework 

assigned 

Emphasis 

on lab work 

Time 

devoted to 

whole-class 

Time 

devoted to 

discipline 

Frequency 

of using 

computers 

Frequency 

of student 

oral reports 

I School Organization 

Principal' s leadership -0.08* -0.10 -0.04 -2.32 -0.08 -2.38 -0.22 -0.04 0.01 

Teacher influence: 

methods 0.06* 0.11* 0.01 0.83 0.02 3.38* -0.94* 0.00 0.02 

Teacher influence: 

curriculum 0.02 -0.00 0.01 0.52 0.04* -0.10 0.74** 0.06** 0.00 

Teacher coordination 0.04 0.15** 0.09 1.90 0.02 0.18 0.58 0.02 0.06 

Teachers discuss 

content 0.17** 0.27** -0.12 0.37 0.22** -4.62* -0.54 0.17** 0.22** 

R2 .102 .094 .044 .063 .094 .052 .055 · .072 .074 

Sample size 2,493 2,492 2,491 2,463 2,518 2,475 2,446 2,516 2,520 

* p <= .05; ** p <= .01. 

NOTE: All models include controls for individual student SES, race/ethnicity, and gender. See Appendix for full regression equations. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

NAIS school students tend to receive a greater emphasis on inquiry skills than public school 

students, and less emphasis on the role of science in everyday life. Catholic school students do not 

significantly differ from public school students on any of the science instructional measures. Other private 

students differ from public school students only in their lower use of computers. 

The consequences of school SES differences (measured by the principal' s report of the percentage 

of students receiving reduced-price lunches) for science instruction do not conform to what one might 

expect. Attending a poorer school does not appear to have a negative impact on instructional experiences 

as measured here, other things equal. The significant effects in Table 4.3, in fact, tend to show advantages 

for students in schools serving moderate (6 to 50%) percentages of poverty-level youth. The emphases 

on inquiry learning and lab work tend to be greater in schools with 6 to 50 percent of the students 

receiving federal lunch. The effects of SES on instruction that we saw in Chapter III appear to be largely 

differences among students within schools, rather than reflections of school-to-school differences arising 

from social class segregation. 

School enrollment size has a significant effect only on the use of lab work, which may reflect an 

economy of scale, in that larger schools are able to provide laboratory space and resources for more 

classes because of the larger absolute numbers of students they enroll in senior-year science. 

The school organizational variables also show mixed results in most cases. Students in schools 

where accountability mechanisms are tied to test performance might be expected to emphasize learning 

facts and principles, and downplay problem-solving and inquiry skills; spend more time in whole-class 

instructional settings; and have less time devoted to oral presentations. The reason for these predictions 

is that the tests typically used for accountability purposes tend to assess factual knowledge and routine 

applications rather than complex thinking and presentational skills (Madaus, et al., 1992; Glaser & Silver, 

1994). 

The results in Table 4.3 give mixed support for these predictions. Students in the schools where 

the principal is evaluated in part on student test scores actually experience greater emphasis on inquiry 

skills and had more time devoted to laboratories. However, these students also have fewer opportunities 

to give oral presentations in class. 

One might also predict that higher graduation requirements for students would also lead teachers 

away from inquiry learning and labs, toward more routinized instruction, because they may be likely to 

confront students who are less interested in science, who are talcing the classes in order to graduate. As 

shown in Table 4.1, senior-year science enrollments are strongly affected by school policy on the number 

of courses required for graduation, but not by the presence of minimum competency requirements. As 

predicted, students in schools with higher science graduation requirements do receive a lower emphasis 

on inquiry learning and lab work and have less homework assigned. Students in minimum competency 

schools significantly differ from nonminimum competency schools only in that students in the former have 

teachers who report spending more time on maintaining order. While these effects are not encouraging 

to advocates of these policies, it must be kept in mind that the net effects of the requirements may still 

be positive. Higher graduation requirements, for example, may lead to higher achievement because the 

positive effects of greater exposure to science offset the negative effects of lower instructional quality. 

The negative effects in Table 4.2 may be explained by students who would not otherwise talce science as 

seniors being enrolled in lower-level classes. Further, what looks to some like "lower instructional 

quality" may prove more effective in raising scores on standardized tests than the methods recommended 

by progressive advocates. 

82 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The principal leadership measure is negatively- associated with use of inquiry methods. The 

measure of teacher influence over instructional methods is positively related to the use of inquiry methods, 

emphasis on practical applications, and time devoted to whole-class instruction, and is negatively 

associated with the amount of time spent on discipline. These findings are complemented by the positive 

effect of greater teacher influence over instructional content on use of labs and computers, and the 

negative effect on time spent on discipline. This indicates that when teachers are free to implement what 

they judge best, they tend to adopt at least some practices that are consistent with reform 

recommendations. Weighing against this tendency is the lack of association of teacher influence and the 

use of student presentations. 

Students whose teachers report more content-related discussions with other teachers tend to align 

more closely with refonn recommendations. The strongest effects on science instruction tend to be 

associated with greater collegial discussions: the students whose teachers talk more with other teachers 

receive greater emphases on inquiry skill development, the role of science in society, and lab work. While 

their emphasis on facts and principles is not significantly lower, they spend less time in whole-class 

instructional settings and make much greater use of computers and student presentations. 

Summary 

This chapter has presented evidence of school effects both on the likelihood of taking mathematics 

and science and on the levels of the instructional variables in the NELS:88 data. School characteristics 

associated with higher probabilities that students take senior year mathematics and science include Catholic 

and NAIS affiliation and the number of years of science and math course-work required for graduation. 

School characteristics are also consequential when one examines the instructional experiences of 

the students who enrolled in these courses. Some differences among urban, suburban, and rural schools 

and among schools from different regions are found for the instructional variables. These are curious, but 

further infonnation on the underlying organizational differences which produce these results is needed 

before one should hazard interpreting them. The proportion of low-income students in the school is not 

clearly associated with instructional disadvantages along the lines examined here. 

We found little evidence of instructional differences between students in public and Catholic high 

schools, but the analysis conducted here is not quite appropriate for estimating sector effects. This is 

because school sector may affect the school policy variables which were also included in the regression 

equations. Further work that separated the analyses (as was done in Table 4.1) is thus needed to see 

whether sector effects on these aspects of instruction are present. 

The school characteristics that have the greatest effects on instruction are the organizational 

variables of teacher influence, coordination, and infonnational exchange. In both subjects, the evidence 

presented here indicates that stronger professional cultures lead to instruction that is closer to the ideals 

of the current reform movements in mathematics and science. These findings support the contentions of 

the professional associations that workplace conditions in the schools are key factors in the implementation 

of reform proposals (NCTM, 1991). 

83 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Chapter V 

Instruction and Student Achievement 

Thus far we have seen that instruction differences are related to student background, school 

characteristics, and the achievement levels of the classes. The backdrop for all of these analyses, however, 

was an assumption that differences in instructional experiences make a difference in students' educational 

outcomes. Most important of these from a public policy standpoint is the academic achievement of the 

seniors. This chapter returns to our original question, presenting an analysis of the relationships of 

instructional variables with standardized measures of student achievement in science and mathematics. 

The NELS:88 Achievement Tests 

During the base year, first follow-up, and second follow-up surveys, the NELS:88 study 

administered achievement tests in science, mathematics, reading comprehension, and social studies (history, 

civics, and geography). The students' responses were scored to create overall achievement scales in each 

subject, as well as a set of proficiency measures. The latter were defined in terms of classes of skills 

ranging from simple recall of definitions to complex problem-solving and deductive inference. The 

analyses presented in this chapter use both the overall, or "composite," measures and the proficiency 

measures for mathematics and science. 

The NELS:88 project followed a strategy of adaptive testing in order to produce achievement 

scores that would satisfy two objectives: (a) measuring student cognitive growth over the 1988-to-1992 

time span, and (b) minimizing "floor" and "ceiling" effects in the tests (see Rock & Pollack, 1995, for a 

comprehensive description of the NELS:88 testing program). In mathematics, this involved administering 

tests with three levels of difficulty during the 1990 and 1992 follow-up. Students were assigned to one 

of the three levels based on their level of performance on the previous cycle test. In science, NELS:88 

used only grade-level adaptive testing, varying the items from cycle to cycle but not using multiple forms 

within years. By adapting the tests in this way, NELS:88 was able to obtain more accurate assessments 

of the students' achievement levels and growth curves than if a single form had been used. 

The composite measures of mathematics and science achievement were constructed with Item 

Response Theory (IRT) methods. This methodology allows one to combine information from multiple 

forms, when the different forms contain subsets of common items. While the metric of the scores could 

be defined in several different ways, NELS:88 settled on the use of an "estimated number of items correct" 

scale for the composite scores. The scores on this metric represent IRT-derived estimates of how many 

of the total number of items NELS:88 administered across all three cycles that each student would have 

answered correctly, had he or she taken all the items at each cycle. This number must be estimated 

because the adaptive testing program involved having the students take at each time point only a subset 

of all the items used in the project. 

The proficiency subscales were developed to allow researchers to focus on more specific skills 

within the larger domains of mathematics, science, and reading comprehension. The subscales in 

mathematics and science are described in the NELS:88 codebook (Ingels, et al., 1994, p. H-34) as follows: 

Math Level 1: Simple arithmetical operations on whole numbers; essentially single step operations 

which rely on rote memory. 

Math Level 2: Simple operations with decimals, fractions, powers, and roots. 

85 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Math Level 3: Simple problem solving, requiring the understanding of low level mathematical 

concepts. 

Math Level 4: Understanding of intennediate level mathematical concepts and/or having the ability 

to fonnulate multi-step solutions to word problems. 

Math Level 5: Proficiency in solving complex multi-step word problems and/or the ability to 

demonstrate knowledge of mathematics material found in advanced mathematics 

courses. 

Science Level 1: Understanding of everyday science concepts; "common knowledge" that can be 

acquired in everyday life. 

Science Level 2: Understanding of fundamental science concepts upon which more complex science 

knowledge can be built. 

Science Level 3: Understanding of relatively complex scientific concepts; typically requiring an 

additional problem solving step. 

The math and science test items were grouped into sets corresponding to each level, and 

proficiency scores were calculated based on the response patterns. The proficiency measures we use are 

probabilities of mastery of each of these levels. It turns out that there was virtually no change from 10th 

to 12th grade on the proficiency at level 1, where nearly all students had attained proficiency by 10th 

grade, and at level 5, where virtually none were proficient as sophomores or seniors. 

Proficiency scores are available in two metrics. One is a dichotomous indicator of whether or not 

the student crossed the proficiency threshold, where the threshold is defined as correctly answering 75 

percent or better of the skill-area items. The other metric is a continuous "probability of proficiency" 

which ranges from zero to one and indicates how likely the student was to attain the proficiency threshold 

for the skill area in question. The regression analyses presented in Tables 5.5 and 5.6 use the probabilities 

of proficiency as the dependent variables. 

Research Questions and Analytic Strategy 

The strategy we follow involves three different analyses. The first analysis estimates the effects 

of the instructional variables on the composite achievement scores for all students. This gives a picture 

of the average impact of the instructional variables, but does not assess whether the effects are the same 

for all students. Returning to the research questions set forth in Chapter I, it is important to assess 

whether particular kinds of instruction are especially helpful for some students but not for others. In the 

second analysis, we address this issue by estimating separate equations for students who had attained 

different levels of mastery in the 10th grade. The third analysis also assesses whether the relationships 

of instructional variables with achievement differ, but extends the inquiry by asking whether the effects 

also depend on the level of the achievement outcomes. 

The method we use for these analyses is again ordinary least squares regression analysis. The 

regression equations include measures of student background and school characteristics that are associated 

with instructional variables and achievement, and thus help rule out some alternative explanations of 

whatever associations between instruction and learning we might discover. The regressions also control 

86 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

for the student's 1990 level of achievement. This means that the dependent variable is really the amount 

of change in achievement from 1990 to 1992, and that the coefficients for the independent variables should 

be interpreted as the amount of change in achievement over the two year span that is associated with a 

unit change on the respective independent variable. 

These analyses have limitations which should be noted from the outset. The main problem we 

face in drawing conclusions about the effects of the instructional variables is that the time span covered 

by the change in NELS:88 achievement test scores is two years (from sophomore to senior year), while 

the time span covered by the instructional variables is only the senior year. Since we do not know what 

instructional experiences, if any, the students had in 11th grade science and mathematics, we are 

measuring the students' instructional experiences with some error, the magnitude of which is unknown. 

In general, though, measurement error of this type results in underestimates of the effects of the errorprone variables. 

In this light, the best strategy is to downplay the importance of statistically insignificant results 

and look instead for any large (positive or negative) effects. With the proper statistical controls for 

differences among students' social and academic backgrounds, we can have more confidence in the 

validity of significant effects than of insignificant ones. 

Instruction and Overall Achievement Growth 

To assess the overall effects of the instruction variables on achievement growth, we estimated three 

OLS regressions for the composite measures of achievement in math and science. The first model 

regresses the 12th grade achievement score on the comparable tenth-grade achievement score plus the 

measures of social background, school demographic char:acteristics, and the achievement level of the 

student's senior year class. The second model adds the teacher education indicators to the set used in 

Model 1. The results indicate the extent to which differences in teacher background mediate the effects 

of ability group placement and independently contribute to learning differences within ability groups. The 

third model adds the instruction variables, giving estimates of the independent effects of instructional 

differences on achievement growth. 8 

The regression results for the overall mathematics scores are presented in Table 5.1. The estimates 

for Model 1 indicate strong effects of the achievement level of the students' classes on their growth from 

10th to 12th grade. Controlling for social background, school characteristics, and 10th grade level of 

achievement, students in AP classes learned the equivalent of about 2.7 test items more than their average 

group counterparts. Remedial-level students, in contrast, learned about 3.1 items less. How large are 

these differences? One widely-used standard is to express the effects as fractions of the test's standard 

deviation; this is referred to as an "effect size" (e.s.) metric. Researchers typically consider "treatment" 

(i.e., exposure versus nonexposure to some influence) effect sizes of .10 or greater to be substantively 

important. The standard deviation of the composite math test in the 1992 NELS:88 administration is 13.4, 

8 The sample used in the regressions presented in this chapter consist of students with complete data on all of the 

variables used in the analysis. Since the seniors that were added to the NELS:88 study in 1992 (the 264 "freshened" cases referred 

to in Appendix B) do not have 1990 test scores, they are excluded from the analysis. This technically means that the sample is not 

fully representative of the 1992 seniors. As a practical matter; though, the loss of these cases is a relatively small proportion of the 

total attrition from missing data. Of the nearly 5,700 math students with 1992 teacher data, some 4,100 have complete data and are 

included in the analysis. In science, about 2,600 of the 3,850 science students with 1992 teacher data have complete data on all the 

variables in the analysis. See Appendix Table Al.2 and Al.3 for descriptive statistics on variables used in the analyses of this 

chapter. 

87 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

and the effect sizes thus range from -.23 for the remedial versus average contrast to .09 for the aboveaverage versus average group comparison. 

Table 5.1. Effects of Class Achievement Level, Teacher Education, and Instructional Variables 

on Sophomore-to-Senior Achievement Growth in Mathematics, from OLS 

Regressions: 1992. 

Independent Variables 

Model 1 Model 2 Model3 

b s.e. b s.e. b s.e. 

I Class Achievement Level (vs. average) I 

AP 2.718** 0.607 2.739** 0.630 2.438** 0.733 

Above Average 1.161** 0.344 1.148** 0.364 0.934** 0.377 

Low -1.656** 0.428 -1.569** 0.441 -1.157** 0.469 

Remedial -3.129** 0.708 -3.018** 0.750 -2.509** 0.776 

I Teacher Education (vs. major in field) I 

College & graduate major 0.156 0.357 0.121 0.356 

Major and minor -0.514 0.390 -0.611 0.405 

Minor only -0.461 0.375 -0.435 0.376 

No major or minor -1.528** 0.457 -1.155** 0.439 

I Instructional Variables I 

% class time spent in whole 

group instruction 0.125 0.170 

% class time spent maintaining 

order -0.405** 0.157 

Minutes/day of homework 

assigned · 0.013 0.010 

Emphasis on higher-order 

thinking skills 0.732** 0.248 

Emphasis on practical skills -0.594* 0.272 

Emphasis on mechanical skills 0.041 0.259 

R2 0.86 0.86 0.86 

* p <= .05; ** p <= .01 

NOTE: All models include controls for individual and school SES, race/ethnicity, gender, sophomore 

math achievement, school urbanicity, region of the country, and school sector. See Appendix 

D for full regression equations. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

88 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The effects of class group placement are not much reduced when the indicators of teacher 

education are introduced in Model 2. The only significant teacher education effect is for students who 

had teachers with neither a major nor a minor in mathematics. These students learned substantially less 

(b=-1.53, e.s.=-.12) than the reference group, whose teachers had a major but no additional major or minor 

specializations in math. 

Measures of instructional variables are added to the regression equation in Model 3. The 

explanatory power of the model (indexed by R2

) does not perceptibly improve with the addition of these 

variables, though several show significant effects on achievement growth. Three of the variables-the 

percent of class time devoted to whole-group instruction, the amount of homework assigned each day, and 

the amount of emphasis the teacher gives to developing mechanical skills-have no effects on achievement 

growth. The effects of the other variables are in the expected directions. To gain a sense of the relative 

strength of these effects, one can multiply the coefficients by the standard deviation of the variable, and 

divide the product by the standard deviation of the 12th grade math test; this gives standardized effect size 

estimates. The largest effects of this set are the positive effect of emphasizing higher-order thinking skills 

(e.s.=.05) and the negative effects of maintaining order (e.s.=-.03) and emphasizing the importance of 

mathematics in everyday life (e.s.=-.04). None of these effects is large, but it must be remembered that 

the errors of measurement associated with using only the senior year instruction variables for the two-year 

growth analysis are likely to result in a downward bias. The true effects may be larger than these 

estimates. 

Table 5.2 summarizes the regressions of overall science achievement. The results for Model 

1 show large effects of the class-achievement level. As the standard deviation of the 1992 science test 

is 6.1 items, the regression coefficients represent effect sizes of .18 for the AP, .15 for above-average, and 

-.13 for below-average groups. The addition of the teacher education indicators in Model 2 does not 

significantly reduce the effects of class-achievement level, and none of the teacher education indicators 

has a significant effect on achievement growth in science. 

89 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 5.2. Estimated Effects of Class Achievement Level, Teacher Education, and Instructional 

Variables on Sophomore-to-Senior Achievement Growth in Science, from OLS 

Regressions: 1992. 

Independent Variables 

Model 1 Model 2 Model 3 

b s.e. b s.e. b s.e. 

I Class Achievement Level (vs. average) I 

AP 1.092** 0.347 .993** 0.378 .770* 0.423 

Above Average .917** 0.211 .900** 0.220 .913** 0.221 

Low -.813* 0.377 -.749* 0.393 -0.524 0.419 

I Teacher Education (vs. major in field) I 

College & graduate major 0.484 0.304 0.371 0.268 

Major and minor 0.122 0.296 0.239 0.300 

Minor only 0.032 0.267 0.006 0.259 

No major minor -0.092 0.272 -0.064 0.313 

I Instructional Variables I 

% class time spent in whole 

group instruction 0.054 0.095 

% class time spent maintaining 

order -0.009 0.152 

Minutes/day of homework 

assigned 0.002 0.007 

Emphasis on lab use -0.020 0.175 

Emphas!s on inquiry skills 0.246 0.221 

Emphasis on practical skills -0.351 ** 0.146 

Emphasis on scientific facts 0.063 0.135 

R2 0.67 0.67 0.68 

* p <= .05; ** p <= .01 

NOTE: All models include controls for individual and school SES, race/ethnicity, gender, sophomore 

science achievement, school urbanicity, region of the country, and school sector. See Appendix 

D for full regression equations. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

The addition of the instruction variables adds virtually no explanatory power to the science 

achievement model. The only variable with a significant effect is the teacher-reported emphasis on the 

role of science in everyday life. At face value, this suggests that students whose teachers opt for greater 

emphasis in this area are learning less of what the NELS:88 tests measure. 

90 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Effects of Instructional Variables for High- and Low-Achieving Students 

The effects of the instructional variables on learning may not be the same for all students. As 

we have noted at various points in this report, teachers may use different methods for different classes 

because they believe the effectiveness of a particular method depends on the level of the class. For 

example, an emphasis on higher-order thinking may work well among college-oriented, highly motivated 

students, but may fail with students mainly interested in completing a graduation requirement. 

To assess whether the instructional variables have variable effects on the composite achievement 

scores, we re-estimated the regressions presented in Tables 5.1 and 5.2 separately for three groups of 

students: those who scored in the lowest quartile as sophomores, those in the middle two quartiles, and 

those in the highest quartile. One could divide up the sample in other ways; for example, by the 

achievement level of the class, or student SES levels, race-ethnicity, or gender. We selected the grade 10 

achievement levels because the theoretical rationales for varying curriculum according to the students' 

initial achievement levels are the most compelling. Many teachers and parents believe that instructional 

approaches are appropriately varied by the achievement level of the students; few would argue that 

instruction should be modified on the basis of SES, racial-ethnic, or gender differences among classes. 

The results of this analysis are presented in Tables 5.3 and 5.4. While the statistical significance 

of the estimates is lower due to the smaller sample sizes, the pattern of effects tends to be consistent with 

the overall patterns seen in Tables 5.1 and 5.2. In mathematics, significant positive effects are found in 

all three groups for being in an above-average or AP-level class. A significant positive effect of the 

emphasis on developing higher-order thinking skills is only found for students in the middle two quartiles, 

but the signs and magnitudes of the coefficients in the other quartiles are consistent with the overall 

estimates. Significant negative effects are found for the time devoted to maintaining order in all but the 

highest quartile and a greater emphasis on showing the relevance of mathematics in the lowest quartile. 

91 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 5.3. Estimated effects of class-achievement level, teacher, and instruction variables on grade 12 

composite mathematics achievement, by grade 10 composite science achievement quartile, from 

OLS regressions: 1992. 

I 

I 

I 

Subsample: grade 10 achievement 

quartile 1 (lowest) 

grade 10 ach. quartile 

2 & 3 (middle) 

grade 10 achievement 

quartile 4 (highest) 

Coef SE Coef SE Coef SE 

I Achievement Level (vs. average) 

AP 3.387** 1.288 5.713* 2.416 3.568** 0.641 

Above Average 2.128** 0.803 1.007* 0.491 1.221** 0.438 

Low -0.761 0.552 -0.930 0.626 -0.129 1.010 

Remedial -1.392 0.832 -2.346 1.250 -3.648** 1.148 

I Teacher Education (vs. major in field) 

College & graduate major 0.559 0.924 0.242 0.508 -0.022 0.406 

Major and minor 0.559 0.983 -0.696 0.570 -0.591 0.418 

Minor only -0.534 0.646 -0.322 0.450 -0.475 0.572 

No major or minor -0.277 0.653 -1.511** 0.586 -0.820 0.604 

I Instructional Variables 

% class time spent 

in whole group 

instruction 

0.098 0.245 0.254 0.255 0.008 0.162 

% class time spent 

maintaining order -0.442* 0.206 -0.504* 0.200 -0.084 0.197 

Minutes/day of 

homework assigned 0.028 .017 .018 .014 -0.000 0.010 

Emphasis on higherorder thinking skills 0.409 0.429 0.737* 0.325 0.703 0.389 

Emphasis on 

practical skills -1.006* 0.514 -0.548 0.347 -0.330 0.270 

Emphasis on 

mechanical skills -0.069 0.469 -0.089 0.361 0.034 0.302 

R2 .39 .58 

Sample Size 536 2,009 I I I I 

.47 

1,565 I 

* p <= .05; ** p <= .01 

NOTE: All models include controls for individual and school SES, race/ethnicity, gender, sophomore math 

achievement, school urbanicity, region of the country, and school sector. See Appendix D for full 

regression equations. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up survey. 

92 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 5.4. Estimated effects of achievement level, teacher, and instruction variables on 

composite grade 12 science achievement, by grade 10 composite science achievement 

quartile, from OLS regressions: 1992. 

Subsample: grade 10 achievement 

quartile 1 

(lowest) 

grade 10 ach. 

quartiles 2 & 3 

(middle) 

grade 10 

achievement 

quartile 4 (highest) 

Coef SE Coef SE Coef SE 

Class Achievement Level (vs. average) I I 

AP 0.431 1.267 1.075* 0.513 0.867 0.537 

Above Average 0.998 0.646 0.983** 0.302 0.622* 0.315 

Low 0.696 0.840 -0.660 0.400 -1.986** 0.761 

I Teacher Education (vs. major in field) I 

College & graduate major 0.196 0.701 0.772** 0.311 0.190 0.375 

Major and minor 2.243** 0.775 -0.084 0.421 0.413 0.352 

Minor only 0.147 0.713 -0.367 0.325 0.664 0.385 

No major or minor 0.285 0.755 0.047 0.440 0.272 0.546 

I Instructional Variables I 

% class time spent in whole group 

instruction 0.124 0.226 -0.095 0.131 0.134 0.115 

% class time spent maintaining order -0.345 0.300 0.004 0.173 0.217 0.217 

Minutes/day of homework assigned 0.037** 0.012 0.004 0.008 -0.005 0.010 

Minutes/week of lab -0.003 0.362 -0.157 0.231 -0.029 0.258 

Emphasis on inquiry skills 0.608 0.558 -0.117 0.335 0.485 0.306 

Emphasis on practical skills -0.391 0.444 -0.510** 0.192 -0.078 0.185 

Emphasis on learning & memorizing 

facts, principals, & rules 0.566 0.342 -0.025 0.180 0.020 0.181 

Frequency of computer use -0.373 0.298 0.107 0.224 0.425 0.244 

Frequency of student presentations 0.035 0.447 0.355 0.239 -0.312 0.236 

R2 .34 .44 .23 

Sample Size 309 1,224 1,086 I I I I I 

* p <= .05; ** p <= .01 

NOTE: All models include controls for individual and school SES, race/ethnicity, gender, sophomore science 

achievement, school urbanicity, region of the country, and school sector. See Appendix for full regression 

equations. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up survey. 

93 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The effects of the instructional variables on science achievement gains shown in Table 5.4 are 

again weaker, but are also consistent with the findings of the full-sample analysis. Significant positive 

effects of AP and above-average class placements are apparent for the middle and upper quartile students, 

and students who scored high as sophomores but who enroll in low-level senior science courses learn 

significantly less than students enrolled in average-level classes. 

One variable which shows a significant effect in Table 5.4 but not in Table 5.2 is the amount 

of homework assigned. In Table 5.4, students who scored in the lowest quartile as sophomores score 

higher as seniors if they are assigned (and presumably do) more homework. 

Analysis of Proficiency Gains by Sophomore Achievement Levels 

The overall mathematics and science achievement scores summarize a number of different 

performances and are analogous to combined scores in sports like figure skating. Some of the items on 

the NELS:88 tests measure students' abilities to recall facts or perform simple calculations, while other 

items require relatively complex reasoning to answer correctly. It stands to reason that the different 

instructional experiences we have examined may have different effects depending on which type of 

performance one assesses.9 

A problem in following this reasoning, however, is that some students had already mastered one 

or more of the NELS:88 proficiency levels by the time they were sophomores. It would not be very 

informative to estimate the effects of instruction on skills that were already mastered. This implies that 

the samples should be restricted to students for whom the different proficiency scales are appropriate. 

How to decide what is appropriate? One strategy is to match the tests with class-achievement levels in 

some fashion. We might, for example, restrict the analysis of level 2 proficiency to remedial and belowaverage level students. A problem with this method is that the matching is necessarily based on certain 

normative criteria, since it in effect assumes what are appropriate goals for different groups. Some lowerlevel classes may pursue higher-level goals, and vice versa, but these would be arbitrarily excluded from 

that analysis. A strength of the method, though, is that the analyses are restricted to subsamples which 

correspond to conventional institutional categories ("remedial," "average group," "AP"). 

A less arbitrary strategy is to base the sample restriction on prior test performance. In addition 

to the probability of proficiency scores, the students were also coded into dichotomous "proficient /not 

proficient" categories when they were sophomores. Students were coded as proficient if they correctly 

answered the equivalent of 3 out of 4 items within a given proficiency level item set. For each 

proficiency level outcome, then, we can restrict the sample used in the regression to those students who 

were not proficient as sophomores. A deficiency of this method is that the subsamples thus generated do 

not correspond to clearly identifiable institutional categories, and the practical implications are thus 

somewhat murky. 

Table 5.5 summarizes the results of this analysis for mathematics. The columns of this table list 

the regression coefficients and standard errors for equations estimated for each of five mutually exclusive 

groups of students, categorized on the basis of their sophomore test results: (1) those who had not attained 

9 The articles by Kupermintz, et al. (in press) and Hamilton, et al. (in press) re-analyze the NELS:88 first follow-up 

test items and develop somewhat different subscales than the public-use file scales. They also analyze the relationships of 

instructional variables with achievement outcomes on the various tests they develop. 

94 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

proficiency level 1 as sophomores; (2) those who had attained level 1 but not level 2; (3) those who had 

attained level 2 but not 3; (4) those who had attained level 3 but not level 4; and (5) those who had 

attained level 4 but not 5. The dependent variable for group (1) is the probability of proficiency at level 

1; for group 2, the probability of proficiency at level 2; for group 3, the probability of proficiency at level 

3; and so on. 

95 
Table 5.5. Estimated effects of achievement level, teacher, and instruction variables on the probability of proficiency at different levelsa of grade 12 

mathematics: 1992. 

Dependent Variable: Probability of 

Profic.: Level 1 

Probability of 

Profic.: Level 2 

Probability of 

Profic.: Level 3 

Probability of 

Profic.: Level 4 

Probability of 

Profic.: Level 5 

Subsample: 

Grade 10 

profic.<Level 1 

(lowest) 

Grade 10 

profic.=Level 1 

Grade 10 

profic.=Level 2 

Grade 10 

profic.=Level 3 

Grade 10 

profic.=Level 4 

Coef SE Coef SE Coef SE Coef SE Coef SE 

I Class Achievement Level (vs. average) I 

AP -- -- 28.323** 6.739 -7.786 11.949 12.555** 4.330 20.701** 2.125 

Above Average 8.298** 2.688 3.112 3.540 .652 5.228 5.975* 2.610 5.704** 1.114 

Low -6.404* 3.120 -7.036 3.723 -15.869** 5.709 -6.115 4.635 2.775 3.050 

Remedial -17.839** 5.291 -15.053** 6.034 -20.669** 7.732 -2.729 10.393 4.797 3.963 

ITeacher Education (vs. major in field) I 

College & graduate 

major -.013 4.322 4.620 3.886 -6.509 4.792 1.802 3.524 1.124 1.606 

Major & minor 4.419 3.302 -.184 5.121 -3.510 6.600 -4.703* 3.142 -4.385** 1.721 

Minor only 2.277 3.599 0.033 3.873 -2.335 4.103 -3.289 2.275 -1.121 1.837 

No major or minor 0.667 3.276 -1.342 4.792 5.821 6.457 -11.722** 3.763 -6.098 4.383 

I Instructional Variables I 

% class time spent 

in whole group 

instruction 

-.019 1.287 1.372 1.703 -4.748* 2.273 .515 1.522 2.010* .934 

% class time spent 

maintaining order 1.276 1.500 -2.789* 1.374 -2.338 2.253 .600 1.357 -2.814** .726 

Minutes/day of 

homework assigned -.161* .080 .120 .086 .406** .141 .000 .082 -.045 .035 

Emphasis on higherorder thinking skills 4.723* 2.415 0.225 2.858 7.423* 3.252 9.201** 2.236 -.602 1.325 
Table S.S. Estimated effects of achievemeμt level, teacher, and instruction variables on the probability of proficiency at different levelsa of grade 12 

mathematics: 1992. (Continued) 

Dependent 

Variable: 

Probability of 

Profic.: Level 1 

Probability of 

Profic.: Level 2 

Probability of 

Profic.: Level 3 

Probability of 

Profic.: Level 4 

Probability of 

Profic.: Level 5 

Subsample: 

Grade 10 

profic.<Level 1 

(lowest) 

Grade 10 

profic.=Level 1 

Grade 10 

profic.=Level 2 

Grade 10 

profic.=Level 3 

Grade 10 

profic.=Level 4 

Coef SE Coef SE Coef SE Coef SE Coef SE 

I Instructional Variables (cont'd) I 

Emphasis on 

practical skills -4.359* 2.207 -5.695* 2.853 -4.517 3.286 -4.774* 1.975 .252 1.124 

Emphasis on 

mechanical skills -3.806 2.675 -.948 2.962 3.166 3.419 -1.501 2.529 -1.519 1.300 

R2 .57 .50 .42 .53 .50 

Sample Size 367 656 506 1,066 1,152 

* p <= .05; ** p <= .01 

a The levels of proficiency are described in the text of Chapter 5. 

NOTE: All models include controls for individual and school SES, race/ethnicity, gender, sophomore math achievement, school urbanicity, region of the 

country, and school sector. See Appendix D for full regression equations. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up survey. 
Table 5.6. Estimated effects of achievement level, teacher, and instruction variables on the probability of proficiency at different levelsa of grade 12 

science: 1992. 

I 

Dependent Variable: Probability of 

Proficiency: Level 1 

Probability of 

Proficiency: Level 2 

Probability of 

Proficiency: Level 3 

Probability of 

Proficiency: Level 4 

Subsample: Grade 10 

profic.<Level 1 

Grade 10 

profic.=Level 1 

Grade 10 

profic.=Level 2 

Grade 10 

profic.=Level 3 

Coef SE Coef SE Coef SE Coef SE 

I Class Achievement Level (vs. average) I 

AP -3.059 11.218 9.473 6.637 16.756** 5.475 13.132* 5.876 

Above Average 3.045 6.052 10.969** 3.062 7.613* 3.685 10.302* 4.764 

Low -1.386 6.912 -7.539* 3.610 -9.205 6.935 -19.509* 9.995 

I Teacher Education (vs. major in field) I 

College & graduate major 5.609 6.542 2.906 3.336 2.569 3.482 5.496 3.596 

Major & minor 13.435 7.267 -1.001 4.170 6.700 5.311 -.021 4.390 

Minor only -4.380 6.546 -5.213 3.382 -1.259 4.756 8.940 5.063 

No major or minor -9.088 10.625 -2.338 4.007 -.253 5.126 -4.288 8.092 

I Instructional Variables 

% class time spent in whole group 

instruction 5.186* 2.379 1.030 1.273 -1.806 1.558 .136 2.153 

% class time spent maintaining order -.350 3.122 -.253 1.744 -.027 1.941 3.680 2.311 

Minutes/day of homework assigned .176 .110 -.007 .080 .005 .066 -.168 .144 

Minutes/week of lab -.461 4.566 -.659 2.288 -1.879 2.615 -1.586 3.364 

Emphasis on inquiry skills 7.349 5.979 2.650 3.045 6.346 3.686 4.878 4.256 

Emphasis on practical skills 1.768 4.111 -2.578 1.932 -9.085** 2.128 1.868 2.278 
Table 5.6. Estimated effects of achievement level, teacher, and instruction variables on the probability of proficiency at different levelsa of grade 12 

science: 1992. (Continued) 

I 

* p <= .05; ** p <= .01 

a The levels of proficiency are described in the text of Chapter 5. 

NOTE: All models include controls for individual and school SES, race/ethnicity, gender, sophomore science achievement, school urbanicity, region of the 

country, and school sector. See Appendix D for full regression equations. 

Dependent Variable: Probability of 

Proficiency: Level 1 

Probability of 

Proficiency: Level 2 

Probability of 

Proficiency: Level 3 

Probability of 

Proficiency: Level 4 

Subsample: Grade 10 

profic.<Level 1 

Grade 10 

profic.=Level 1 

Grade 10 

profic.=Level 2 

Grade 10 

profic.=Level 3 

Coef SE Coef SE Coef SE Coef SE 

I Instructional Variables (cont'd) 

Emphasis on learning & memorizing 

facts, principals, & rules 

1.349 3.256 -.574 1.664 -3.670 2.255 .732 2.211 

Frequency of computer use -4.033 4.117 -1.650 2.377 1.695 2.709 5.161 3.043 

Frequency of student presentations -6.077 5.415 4.290 2.396 -1.698 3.007 3.899 3.169 

R2 

Sample Size I I 

.46 

283 I 

.48 

684 I 

.33 .36 

821 572 I I 

SOURCE: U.S. Depanment of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

The question we are trying to answer is whether the class and instructional variables have the same 

effects for students at different starting points. The answer, predictably, is that some do and some don't; 

but a number of interesting relationships are apparent. One is that the class achievement level makes a 

big difference at all levels where there are enough sampled students to make solid comparisons. Students 

in remedial and low-ability classes generally are less likely to reach the next proficiency level than 

otherwise comparable students in classes where the average achievement level matches that of the school 

as a whole. Conversely, students in above-average and AP classes generally are more likely to advance 

to the next proficiency level than otherwise comparable students in average-level classes. 

A second generalization is that teacher educational credentials are not good predictors of student 

success. We see some evidence that students whose teachers have no formal training in mathematics 

advance less. But whether a teacher has just a math minor as opposed to an undergraduate major or a 

graduate degree specialization seems to be inconsequential. 

Third, the instructional variables show few robust relations with achievement growth. Teachers 

who devote more time to whole-class instruction realize higher level-5 achievement among the top 

students, but students at lower levels do not seem to benefit from it. Heavier homework assignments are 

associated with greater success among middle-level students but not the rest. Greater emphasis on 

problem-solving has a significantly positive relation with learning at levels 1, 3 and 4. Greater emphasis 

on the significance of mathematics for everyday life is negatively associated with achievement for students 

starting below achievement levels 1, 2, and 4. Finally, greater emphasis on mechanical operations does 

not seem to help achievement even at the simplest level among the lowest achievers. 

Table 5.6 shows the results of the comparable analysis for science. The class achievement levels 

are not as closely tied to learning across the different levels in science. Students in below-average classes 

learn significantly less than average students who started at proficiency levels 1 or 3. Above average 

students show much higher growth than average-class students who started at proficiency levels 1, 2, or 

3. Large positive effects of AP class enrollment are found for students who started at proficiency levels 

2 or 3. The teacher credential effects on growth are erratic and insignificant 

The effects of the science instructional variables again prove to be almost uniformly negligible. 

The only exception to this is the large negative effect the "science and society" emphasis has on level 3 

growth for the students who were the highest achievers as sophomores. 

Summary 

This chapter addressed the issue of whether the differences in students' instructional experiences 

we have documented are related to learning outcomes in mathematics and science. We approached this 

problem in three ways. The first approach looked for effects of instructional differences on summary 

scores of mathematics and science achievement. The second examined whether the instructional variables 

have different effects depending on the students' initial levels of achievement. The third assessed whether 

the effects of instructional variables depend on the kinds of skills one examines within the domains of 

math and science. 

The strongest effects that emerge from the analysis are those associated with the students' class 

compositions, which we have referred to as their class achievement levels. Here we find that students in 

a higher achievement level class gained much more over the two year period on the NELS:88 math and 

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Experiences in Science and Mathematics 

science test scores than otherwise comparable students in lower achievement level classes. The results 

are more consistent in mathematics, but present in science as well. 

Several of the instructional measures we examined for mathematics show significant associations 

with learning. Controlling for sophomore achievement level, social background, school characteristics, 

achievement level, and teacher credentials, we still find that students whose teachers place greater 

emphasis on higher-order skills and lower emphasis on practical applications tend to score higher on 

NELS:88 tests. Higher levels of homework assignments are also beneficial, though the benefits appear 

to be confined to average-level students and in the domain of simple problem solving ("level 3" in the 

NELS:88 math hierarchy). Finally, students lose when their teachers have to spend more time maintaining 

order in the class. The problem of order and the benefits of maintaining it are not confined to lowerachieving students in the lower-level classes. When high-achievers are in classes where order is 

problematic, their achievement is also lower. 

The results from our analysis of science are not as strong as for math. While class-achievement 

level effects are again evident, the instructional variables do not show much connection with the variability 

in sophomore-to-senior achievement growth. The exception to this is the negative effect of greater 

emphasis on the role of science in society. The significance of this :finding is unclear, though. We 

suspect that many of the teachers who pursue this emphasis do so in the interest of attracting students to 

their classes and engaging them once there. De-emphasizing the everyday ramifications of science may 

thus lead not to higher achievement, but to lower enrollments in senior science. Resolution of the 

ambiguity around this finding requires taking better account of the role of student interest and choice in 

enrollment decisions and the allocation of effort among those enrolled. 

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Chapter VI 

Conclusions 

This report has addressed two general questions, both of which have a number of facets. At this 

point, it is useful to return to the original questions, summarize the main findings, draw out what we see 

as the main implications, and suggest some avenues for further research. 

Summary and Implications 

(1) How equal are instructional opportunities, and what are the sources of inequalities? 

A primary purpose of this report was to gain a better understanding of how and why high school 

mathematics and science classes differ along a number of dimensions that educational theorists and policy 

makers believe are important to student learning. We have conceptualized the main dimensions 

represented by the NELS:88 items as the content, the quantity, and the methods of instruction. The 

instruction students receive varies on each ofthese dimensions, so we first asked under what circumstances 

the differences arise, and examined three general hypotheses. The first is that students' instructional 

experiences vary according to the achievement levels of their math and science classes. The second 

hypothesis was that instructional experiences differ because of the social backgrounds ofthe students. The 

third hypothesis was that instruction differs because of school-level factors. 

(a) Are students' instructional experiences associated with the achievement level of their 

classes? 

The first point to emphasize is that many students do not take mathematics and science in their 

last year of high school: 34 percent did not take math and 52 percent did not take science. The seniors 

who take math and science are not enrolled strictly in advanced courses (see Table 1.1). About half of 

the enrolled mathematics students are in an advanced course (trigonometry, statistics, pre-calculus, or 

calculus), while 28 percent of the math enrollees are in algebra 1, applied, or basic math classes. In 

science, 56 percent of the enrollees are in regular physics, a specialized or interdisciplinary science 

offering, or an advanced-level biology, chemistry, or physics course. About 31 percent were at the other 

pole, enrolled in biology 1 or a basic-level (usually non-lab) science. 

What about the content and conduct of these classes? Since the specific topic inventories of the 

NELS:88 survey were defined in terms that, for the most part, did not discriminate very much (see Tables 

1.2 to 1.5), we focused instead on the teachers' reports of their emphases. The three main variables we 

examined were the emphasis on "higher-order" skills, learning facts, and learning about practical 

applications. Conduct of classes was also measured from teacher reports. The main dimensions are the 

use oflectures and whole-class instruction, small groups or student teams, student presentations, homework 

assignments, and time devoted to maintaining order. In science, we also considered the use of laboratories 

and computers. 

The results from Chapter II showed that several of the content and conduct variables are correlated 

with the achievement level of the seniors' classes. Higher-order thinking and inquiry skills receive greater 

emphasis in the higher-level classes, while the teachers' emphasis on the importance of math and science 

in everyday life is lower in the higher classes. The teachers' emphasis on memorizing scientific facts is 

also lower in the higher-level classes. 

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The conduct of the classes is also associated with the achievement levels of the classes. Higherlevel students have more homework assigned each day and spend more time in science laboratory sessions 

than their lower-level counterparts. Higher-level classes also use whole-class instruction more than lowerlevel classes, and spend less time maintaining order. Use of computers, cooperative groups, and student 

presentations show at most very small differences between higher- and lower-level classes. 

It is important to note that, on most measures, we do not find strong evidence that students in 

lower-level classes are on average receiving markedly inferior instruction in either science or mathematics. 

The instructional experiences of students in lower-level classes seem to be of most concern with respect 

to the emphasis on higher-order thinking in both subjects, and laboratory work in science. Altering these 

inequalities may prove difficult, in light of the evidence that discipline and order tend to be more of an 

issue in lower-level classes. 

From the perspective of refonn recommendations, even the highest-level classes are problematic 

in some respects. Students rarely are asked to make presentations to the class, and use of cooperative 

groups is not a prominent part of most classes. Instruction tends instead to follow the traditional model 

of the teacher lecturing and asking questions to the whole group. 

(b) What sorts of relationships can be found between student social background and the kinds 

of instruction they receive in high school? 

Do students from less-advantaged backgrounds receive different instructional experiences in 12th 

grade science and mathematics? We focused on three aspects of student background: SES, race-ethnicity, 

and gender. In tenns of simple course enrollments in senior-year science and math, gender and raceethnicity differences are fairly small (Figure 3.1). Females are less likely to take senior mathematics, but 

are as likely as males to take science. Asians arid blacks are more likely to take math than whites and 

Hispanics, and Asians are more likely than all other groups to take 12th grade science. Higher-SES 

students are more likely than lower-SES seniors to take both subjects. 

The race-ethnicity and SES differences are greater when students are compared in tenns of the 

achievement levels of their math and science classes (see Figures 3.2 and 3.3). Asians are more likely 

than whites, blacks, and Hispanics to take AP math and science; whites are more likely than blacks and 

Hispanics to take AP courses. Family SES is strongly correlated with class achievement levels in both 

subjects. 

Since class achievement levels are associated with student social background and instructional 

experiences, we used multivariate regression techniques to estimate the independent effects of background 

on instructional variables (see Tables 3.3 and 3.4). Controlling for the achievement levels of the students' 

classes, higher-SES students are assigned more homework in both subjects, have mathematics teachers who 

place greater emphasis on higher-order skill development, and use computers more in science classes. The 

regression analysis also shows that significant race-ethnicity effects on instruction tend to favor blacks and 

Hispanics, once SES is held constant 

The main conclusions from the analysis in Chapter III are that (a) the instructional experiences 

of students do vary according to race-ethnicity and SES, (b) these differences mainly arise from the effects 

of race-ethnicity and SES on the achievement levels of the students' classes, and (c) even controlling for 

class achievement level, lower-SES students have lower levels ofhomework, math instruction emphasizing 

higher-order thinking, and access to computers in science. 

104 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

(c) To what extent do instructional opportunities vary from school to school? 

How much do students' instructional experiences depend on the school in which they are enrolled? 

The school variables we examined in Chapter IV included measures of the school's location, proportion 

ofstudents from low-income households, public-versus-private control type, enrollment size, accountability 

structure, graduation requirements, administrative leadership, faculty influence over curriculum and 

teaching methods, and faculty collegiality. Our main focus was on the variables which are most directly 

subject to school or district policy decisions. Of those, the results indicate that students in schools with 

stronger teacher professional cultures are, other things equal, more likely to have teachers who emphasize 

higher-order thinking and practical applications. Those students are also more likely to have science 

teachers who incorporate the use of computers in their classes and who have students give oral 

presentations in class. 

(2) Are differences in students' instructional experiences related to differences in achievement? 

We used regression methods to estimate the relationships of the instruction variables and 

achievement growth from 10th to 12th grade. Since the instruction variables are correlated with students' 

social backgrounds and achievement level placements, we controlled for those variables in the analyses. 

We approached the problem in two ways, first looking for effects on composite, more general measures 

of learning in mathematics and science, and then looking at more fine-grained measures of the acquisition 

of specific proficiencies in each subject. 

(a) Which instructional variables have the strongest relationships with achievement growth 

over the last two years of high school? 

Several instructional variables have significant effects on mathematics achievement, but almost 

none were found to affect students' growth in science achievement from 10th to 12th grade. In both 

subjects, the instruction variables prove !o have weaker effects than the teacher's report of the achievement 

level of the classes. Students enrolled in higher-level classes learn more, even controlling for individual 

student's initial level of achievement and social background. This implies that the best strategy for 

improving achievement is to try to make lower-level classes more like higher-level ones. Part of the classachievement level effects on achievement growth are explained by instructional differences measured here, 

but most of the effects cannot be reduced to these variables. We suspect that the unexplained remainder 

can be attributed to more demanding content in the higher-level courses. A problem with increasing the 

demands placed upon students in the lower-level classes is that the students may not respond with greater 

effort. It may thus be necessary to also address the problem of incentives along with raising the demands. 

(b) Are the effects essentially the same for all students, or are they different for students with 

different backgrounds? 

The effects of the instructional variables could conceivably be quite different for different students. 

From a theoretical standpoint, the single most important background variable is the initial achievement 

level of the student. The main theoretical issue is whether teachers tend to adapt their instruction to what 

works best for the students in their classes, as opposed to adapting instruction to preconceived notions of 

what is appropriate. Ifthe effectiveness of methods depends on the achievement level of the students, one 

should find that the statistical associations between methods and outcomes varies by class level. If 

methods work about the same for all students, then the estimated relationships should be about equal in 

higher- and lower-level classes. 

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The results of the regression analyses presented in Tables 5.3 and 5.4 show that the effects are 

generally consistent when one analyzes students with low, average, and high levels of sophomore 

achievement separately. The analysis presented in Tables 5.5 and 5.6 indicates that the effects of the 

instructional variables are also generally consistent when the outcomes are proficiency scores and the 

analyses are stratified by students' sophomore levels of proficiency. 

Suggestions for Further Research 

This study has left aside a number of important issues for which the NELS:88 data can be usefully 

analyzed. Four topics in particular develop directly out of the work in this report. 

1. A comparison of instruction in grades 81 10, and 12. How highly correlated are the instruction 

variables across grade levels? If the variables are correlated, then some of the differences we have seen 

between students from different social backgrounds and in different achievement levels and schools would 

accumulate across grades to create larger inequalities than those found in a cross-sectional analysis. 

2. An analysis of the effects of schools on instruction using the NELS:88 High School Effects Study 

supplemental data. As noted in Chapter IV, the fact that the original NELS:88 students are not necessarily 

representative samples of their respective high school cohorts, coupled with the small numbers of sampled 

students enrolled in many of the high schools, makes certain types of school-level analyses problematic. 

Because of these shortcomings, NELS:88 developed the High School Effects Study by supplementing the 

student samples in 232 of the high schools so that representative samples of students in those schools were 

obtained. Multilevel data analysis would enable researchers to estimate the overall variation in students' 

instructional experiences and outcomes that lie between versus within high schools. That would give a 

better picture of the role of school policy in the overall variability we have documented in this report. 

Beyond that descriptive function; one could use the specialized multilevel data analysis techniques (see, 

for example, Bryk & Raudenbush, 1992) to obtain better estimates of the impacts of the school variables 

examined in this report, as well as others of interest. 

3. Analysis of the student reports of instructional experiences. In addition to the information 

collected from teachers analyzed in the present report, the NELS:88 second follow-up survey asked 

students a number of questions about their course work in science and mathematics. One purpose of such 

comparisons would be essentially methodological. The student and teacher data could be usefully 

compared to see whether their reports agree. Finding that the reports agree with one another would give 

analysts greater confidence in the validity of the reports. However, it is likely that disagreements will be 

found for many respondents. In that case, it may be possible to combine the information to produce better 

measures of what happens in classrooms. For example, one may find that student achievement is more 

responsive to an emphasis on higher-order thinking when students and teachers agree on such an emphasis 

than when the teacher says one thing and the student another. 

A second purpose is to see whether teacher decisions affect student perceptions. Students were 

asked to evaluate their science and math courses with respect to challenge, usefulness, and accessibility. 

Further research could look at the relationship of different instructional emphases and methods with the 

student evaluations. Do students find inquiry and problem-solving approaches more challenging? Do 

students find the increased ambiguity of the more open-ended approaches that many are now 

recommending to be stimulating or simply frustrating? The relationships between instructional practices 

and students' experiences may well vary from student to student, depending on such factors as their 

general interest in intellectual problems and future educational plans and career orientations. 

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High School Seniors' Instructional 

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4. Analysis of the effects of instructional differences on other outcomes, especially interest in science 

and math and persistence through high school and on into college. In the same vein, one usefully could 

explore the interactions of different instructional experiences and student background characteristics. We 

have addressed the question of whether certain types of instruction are particularly effective for students 

from less advantaged backgrounds from just one of several possible angles, and using just one type of 

outcome. 

Conclusion 

While much more can be usefully done with the NELS:88 data on classroom instruction, the main 

point to make is that the goal of identifying instructional practices closely associated with differences in 

learning outcomes remains elusive. Though elusive, this goal is still of critical importance. Substantial 

efforts at the national, state, and local levels have been made over the past decade to improve mathematics 

and science curricula, instruction, and outcomes. The curricula and outcomes are relatively well measured 

with the transcript and achievement test infonnation now available in the NELS:88 database, but work on 

the instructional side has lagged. This study and others ~fore it have shown that large learning gaps are 

found among students in different ability groups and achievement levels, even after adjusting for 

differences in the backgrounds of students. Lower-ability classes thus appear to be less effective, and it 

is critically important to understand why. If the answers given here are less than definitive, this study 

does make important contributions in raising the question of how the outcome differences arise and 

pointing the way toward gaining better answers in future data collections and research. 

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References 

Alexander, K.L. & McDill, E.L. (1976). Selection and allocation within schools: Some causes and 

consequences of curriculum placement. American Sociological Review, 41, 963-980. 

Baker, D.P. (1993). Compared to Japan, the U.S. is a low achiever ... really. Educational Researcher, 

22(3), 18-20. 

Bryk, A.S. & Raudenbush, S.W. (1992). Hierarchical linear models: Applications and data analysis 

methods. Newbury Park, CA. 

Bryk, A.S., Lee, V.E., & Holland, P.B. (1993). Catholic schools and the common good. Cambridge, MA: 

Harvard University Press. 

Carroll, J.B. (1963). "A model of school learning." Teachers College Record 64: 723-33. 

Chubb, J.E. & Moe, T.M. (1990). Politics, Markets, and American Schools. Washington, D.C.: The 

Brookings Institution. 

Coleman, J. S., Campbell, E. Q., Hobson, C. J., McPartland, J., Mood, A. M., Weinfeld, F., & York, R. 

L. (1966). Equality of educational opportunity. Washington, D. C.: Government Printing Office. 

Coleman, J.S. & Hoffer, T.B. (1987). Public and private high schools: The impact of community. New 

York: Basic Books. 

Diegmueller, K. (1995, January 25). Ga. proposal would ease state textbook control. Education Week, pp. 

7, 10. 

Entwisle, D.R. & Alexander, K.L. (1992). Summer setback: Race, poverty, school composition, and 

mathematics achievement in the first two years of school. American Sociological Review, 19, 72-

84. 

Fisher, C.W., Filby, N.N., Marliave, R.S., Cahen, L.S., Dishaw, M.M., Moore, J.E., & Berliner, D.C. 

(1978). Teaching behaviors, academic learning time, and student achievement: Final report of 

phase III-B. Technical Report V-1, Beginning Teacher Evaluation Study. San Francisco: Far West 

Laboratory of Educational Research and Development. 

Gamoran, A. (1987). The stratification of high school learning opportunities. Sociology ofEducation, 60, 

135-155. 

Gamoran, A. & Berends, M. (1987). The effects of stratification in secondary schools: Syntheses of 

survey and ethnographic research. Review of Educational Research, 57, 415-436. 

Gamoran, A. & Mare, R.D. (1989). Secondary school tracking and educational inequality: Compensation, 

reinforcement, or neutrality? American Journal of Sociology, 94, 1146-1183. 

109 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Glaser, R. & Silver, E. (1994). Assessment, testing, and instruction: Retrospect and prospect. In L. 

Darling-Hammond (Ed.). Review ofResearch in Education, 20 (pp. 393-419). Washington, D.C.: 

AERA Publications. 

Goodlad, J.L (1984). A place called school. New York: McGraw-Hill. 

Hamilton, L.S., Nussbaum, E.M., Kupermintz, H. Kerkhoven, J.I.M., & Snow, R.E. (in press). Enhancing 

the validity and usefulness of large-scale educational assessments: II. NELS:88 Science 

achievement. American Educational Research Journal. 

Hanushek, E.A. (1989). The impact of differential expenditures on school performance. Educational 

Researcher, 18, 45-51. 

Hanushek, E.A. (1972). Education and race: An analysis of the educational production process. 

Lexington, MA: D.C. Heath. 

Hanushek, E.A. (1994), Making schools work: Improving performance and controlling costs. 

Washington, D.C.: The Brookings Institution. 

Hauser, R.M., Sewell W.H., & Alwin, D.F. (1976). High school effects on achievement. In W.H. Sewell, 

R.M. Hauser, & D.L. Feathennan (Eds.). Schooling and achievement in American society (pp. 

309-342). New York: Academic Press. 

Hedges, L.V., Laihe, R.D., & Greenwald, R. (1994). Does money matter? A meta-analysis of studies of 

the effects of differential school inputs in student outcomes. Educational Researcher, 23, 5-14. 

Heyns, B. (1978). Summer learning and the effects of schooling. New York: Academic Press. 

Hoffer, T.B. (1992). Middle school ability grouping and student achievement in science and mathematics. 

Educational Evaluation and Policy Analysis, 14, 205-227. 

Hoffer, T.B. & Gamoran, A. (1994). Effects of instructional differences among ability groups on student 

achievement in middle-school science and mathematics. ERIC microfiche, ED 363 509. 

Hoffer, T.B., Rasinski, K., & Moore, W. (1995). Social background differences in math and science 

coursetaking and achievement. NCES 95-206. 

Hom, L., Hafner, A., & Owings, J. (1992). A profile ofAmerican eighth-grade mathematics and science 

instruction. Washington, D.C.: National Center for Education Statistics. 

Ingels, S.J., Dowd, K.L., Baldridge, J.D., Stipe, J.L., Bartot, V.H., & Frankel, M.R. (1995). NELS:88 

secondfollow-Up: Student component datafile user's manual. NCES 94-374. 

Ingels, S.J., Dowd, K.L., Taylor, J.R., Bartot, V.H., & Frankel, M.R. (1995). NELS:88 secondfollow-up: 

Transcript component datafile user's manual. NCES 94-377. 

Ingels, S.J., Thalji, L., Pulliam, P., Bartot, V.H., & Frankel, M.R. (1994). NELS:88 secondfollow-up: 

Teacher component datafile user's manual. NCES 94-379. 

110 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Jencks, C.S. & Brown, M.D. (1975). Effects of high schools on their students. Harvard Educationa.l 

Review, 45, 273-324. 

Kilgore, S.B. & Pendleton, W.W. (1993). The organizational context of learning: Framework. of 

understanding the acquisition of knowledge. Sociology ofEducation, 66, 66, 63-87. 

Kupennintz, H., Ennis, M.M., Hamilton, L.S., Talbert, J.E., & Snow, R.E. (in press). Enhancing the 

validity and usefulness of large-scale educational assessments: I. NELS:88 Mathematics 

Achievement. American Educational Research Journal. 

Lee, V.E., Bryk, A.S., & Smith, J.B. (1993). The organization of effective secondary schools. In L 

Darling-Hammond (ed.). Review ofResearch in Education, 19 (pp. 171-268). Washington, D.C.: 

AERA Publications. 

Legum, S., Caldwell, N., Goksel, H., Haynes, J., Hynson, C., Rust, K., & Blecher, N. (1993). The 1990 

high school transcript study tabulations: Comparative data on credits earned and demographics 

for 1990, 1987, and 1982 high school graduates. NCES 93-423. 

Lortie, D.C. (1975). Schoolteacher. Chicago: University of Chicago Press. 

Madaus, G.F., West, M.M, Hannon, M.C., Lomax, R.G., & Viator, K.A. (1992). The influence oftesting 

on teaching math and science in grades 4-12: Executive summary. (NSF Report No. SPA8954759). Chestnut Hill, MA: Center for the Study of Testing, Evaluation, and Educational 

Policy, Boston College. 

Mayer, S.E. & Jencks, C. (1989). Growing up in poor neighborhoods: How much does it matter? Science, 

243, 1441-1444. 

McKnight, C.C., Crosswhite, F.J., Dossey, J.A., Kifer, E., Swafford, J.O., Travers, K.J., and Cooney, T.J. 

(1987). The underachieving curriculum: Assessing u.S. School mathematics from an internationa.l 

perspective. Champaign, IL: Stipes Publishing Company. 

McMillen, M.M., Kaufman, P., & Whitener, S.D. (1994). Dropout rates in the United States: 1993. 

NCES 94-669. 

Mullis, I.V.S., Dossey, J.A., Owen, E.H., & Phillips, G.W. (1991). The state ofmathematics achievement: 

NAEP' s 1990 assessment of the nation and the trial assessment of the states. Washington, D.C.: 

National Center for Education Statistics. 

Murnane, R.J. (1975). The impact ofschool resources on the learning ofinner-city children. Cambridge, 

MA: Ballinger. 

Murnane, R.J. (1984). A review essay: Comparisons of public and private schools: Lessons from the 

uproar. Journa.l ofHuman Resources 19, 263-277. 

National Council of Teachers of Mathematics. (1989). Curriculum and evaluation standards for school 

mathematics. Reston, VA: National Council of Teachers of Mathematics. 

111 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

National Council of Teachers of Mathematics. (1991). Professional standards for teaching mathematics. 

Reston, VA: National Council of Teachers of Mathematics. 

National Science Foundation (NSF). 1993. Indicators ofscience and mathematics education 1992. Larry 

E. Suter (ed.). Washington D.C.: National Science Foundation (NSF 93-95). 

National Science Teachers Association. (1992). Scope, sequence, and coordination: Content Core. 

Washington, D.C.: NS':.'A. 

Oakes, J. (1985). Keeping track: How schools structure inequality. New Haven, CT: Yale University 

Press. 

Oakes, J. (1990). Multiplying inequalities. Santa Monica, CA: Rand Corporation. 

Pauly, E. (1991). The classroom crucible: What really works, what doesn't, and why. New York: Basic 

Books. 

Powell, A.G., Farrar, E., & Cohen, D.K. (1985). The shopping mall high school: Winners and losers in 

the educational marketplace. New York: Houghton Miflin. 

Raudenbush, S.W., Rowan, B., and Cheong, Y.F. (1993). Higher order instructional goals in secondary 

schools: Class, teacher, and school influences. American Journal ofEducational Research, 30, 

pp. 523-553. 

Schneider, B., Plank, S., & Wang, H. (1994). Output-driven systems: Reconsidering roles and incentives 

in schools. Paper presented at the annual meeting of the American Sociological Association. 

Shah, B.V., Barnwell, B.G., Hunt, P.N., and LaVange, L.M. (1992). SUDAAN User's Manual. Research 

Triangle Park, NC: Research Triangle Institute. 

Sizer, T. (1984). Horace's compromise: The dilemma ofthe American high school. New York: Houghton 

Miflin. 

Stedman, L.C. (1994). Incomplete explanations: The case of U.S. performance in the international 

assessments of education. Educational Researcher 23(7), 24-32. 

Stodolsky, S.S. & Grossman, P.L. (1995). The impact of subject matter on curricular activity: An analysis 

of five academic subjects. American Educational Research Journal, 32, 227-250. 

Talbert, J.E. & McLaughlin, M.W. (1994a). Teacher professionalism in local school contexts. American 

Journal ofEducation, 102, 123-153. 

Talbert, J.E. & McLaughlin, M.W. (1994b). Understanding teaching in context. In D.K. Cohen, M.W. 

McLaughlin, & J.E. Talbert (eds.) Teaching for understanding (pp. 167-206). San Francisco: 

Jossey-Bass. 

Westbury, I. (1992). Comparing American and Japanese achievement: Is the United States really a low 

achiever? Educational Researcher 21(5), 18-24. 

112 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Westbury, I. (1993). American and Japanese achievement ... again. Educational Researcher 22(3), 21-

25. 

Wiley, D. (1976). Another hour, another day: Quantity of schooling, a potent path for policy. In Sewell, 

W.H., Hauser, R.M., & Feathennan, D.L. (eds.) Schooling and Achievement in American Society 

(pp. 225-65). New York: Academic Press. 

Wilson, B.L. & Rossman, G.B. (1993). Mandating academic excellence: high school responses to state 

curriculum reform. New York: Teachers College Press. 

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Appendix A: 

Supplemental Descriptive Data 

and Standard Error Tables 

115 
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Experiences in Science and Mathematics 

Table Al.1 Descriptive statistics for student-level variables used in the analyses of 12th grade math and science· 

course enrollments, 1992. 

Variable I I N I Mean I Std Dev I Min. I Max. 

1991-92 senior year transcript record available (F2TRNFL) 15,105 0.912 0.284 0.000 1.000 

Enrolled in a math course senior year (from transcript) 13,862 1.342 0.474 1.000 2.000 

Enrolled in a science course senior year (from transcript) 13,862 1.523 0.499 1.000 2.000 

Socio-economic status composite (F2SES1) 14,945 0.048 0.769 -3.243 2.753 

Student is female (F2SEX) 15,105 0.493 0.500 0.000 1.000 

Student is Asian (F2RACE1) 15,067 0.044 0.205 0.000 1.000 

Student is Hispanic (F2RACE1) 15,067 0.101 0.301 0.000 1.000 

Student is Black (F2RACE1) 15,067 0.118 0.323 0.000 1.000 

Student is American Indian (F2RACE1) 15,067 0.011 0.105 0.000 1.000 

High school located in an urban area (Gl2URBN3) 15,105 0.274 0.446 0.000 1.000 

High school located in a rural area (G12URBN3) 15,105 0.303 0.459 0.000 1.000 

High school region: Midwest (G12REGON) .15,105 0.257 0.437 0.000 1.000 

High school region: South (G12REGON) 15,105 0.349 0.477 0.000 1.000 

High school region: West (G12REGON) 15,105 0.195 0.396 0.000 1.000 

High school sector: Catholic (Gl2CTRL2) 15,105 0.054 0.226 0.000 1.000 

High school sector: NAIS (Gl2CTRL2) 15,105 0.016 0.127 0.000 1.000 

High school sector: Other private (G12CTRL2) 15,105 0.024 0.154 0.000 1.000 

6-20% of students in school receive free or reduced-price lunch 

(F2C25A) 

15,105 0.303 0.459 0.000 1.000 

21-50% of students in school receive free or reduced-price lunch 

(F2C25A) 

15,105 0.276 0.447 0.000 1.000 

51%+ of students in school receive free or reduced-price lunch 

(F2C25A) 

15,105 0.094 0.292 0.000 1.000 

Ln of high school grade 12 enrollment (Gl2ENROL) 14,749 5.298 0.851 0.693 7.164 

Principal reports being rewarded for raising achievement levels 

(F1C89) 

11,735 0.167 0.373 0.000 1.000 

Principal report of influence of student standardized test scores on 

how he/she is evaluated (F2C62A) 

13,430 2.249 0.677 1.000 3.000 

High school has minimum competency math test for 12th graders 

(F2C45A) 

14,832 0.500 0.500 0.000 1.000 

High school has minimum competency science test for 12th 

graders (F2C45A) 

14,832 0.163 0.370 0.000 1.000 

Years of math required for high school graduation (F1C70B) 12,059 4.444 0.643 1.000 6.000 

Years of science required for high school graduation (F1C70C) 12,092 4.173 0.624 1.000 6.000 

NOTE: The names of the NELS:88 codebook variables are shown in parentheses. See Appendix B for complete descriptions 

of values and how variables were constructed. 

SOURCE: U.S, Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second 

Follow-Up survey. 

117 
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Experiences in Science and Mathematics 

Table Al.2. Descriptive statistics for student-level variables used in the analyses of 12th grade mathematics 

instruction: 1992. 

Variable N I Mean I Std Dev I Min. I Max. I I 

Socio-economic status composite (F2SES1) 6,286 0.100 0.778 -2.889 2.753 

Student is female (F2SEX) 6,337 0.456 0.498 0.000 1.000 

Student is Asian (F2RACE1) 6,320 0.046 0.209 0.000 1.000 

Student is Hispanic (F2RACE1) 6,320 0.106 0.308 0.000 1.000 

Student is Black (F2RACE1) 6,320 0.124 0.329 0.000 1.000 

Student is American Indian (F2RACE1) 6,320 0.008. 0.087 0.000 1.000 

Achievement level of class: AP (F2T2_3 & F2T2_ 4) 5,714 0.087 0.282 0.000 1.000 

Achievement level of class: above average (F2T2_3 & F2T2_4) 5,714 0.342 0.474 0.000 1.000 

Achievement level of class: below average (F2T2_3 & F2T2_ 4) 5,714 0.124 0.330 0.000 1.000 

Achievement level of class: remedial (F2T2_3 & F2T2_ 4) 5,714 0.040 0.196 0.000 1.000 

Teacher's math education: college and grad. major 5,343 0.207 0.405 0.000 1.000 

Teacher's math education: college or grad. major & minor 5,343 0.120 0.325 0.000 1.000 

Teacher's math education: minor only 5,343 0.164 0.370 0.000 1.000 

Teacher's math education: no major or minor 5,343 0.095 0.293 0.000 1.000 

6-20% of students in school receive free or reduced-price lunch 

(F2C25A) 

6,337 0.304 0.460 0.000 1.000 

21-50% of students in school receive free or reduced-price 

lunch (F2C25A) 

6,337 0.259 0.438 0.000 1.000 

51 %+ of students in school receive free or reduce<l-price lunch 

(F2C25A) 

6,337 0.092 0.289 0.000 1.000 

High school is located in an urban area (G12URBN3) 6,337 0.283 0.451 0.000 1.000 

High school is located in a rural area (Gl2URBN3) 6,337 0.281 0.449 0.000 1.000 

High school region: Midwest 

(G12REGON) 

6,337 0.228 0.420 0.000 1.000 

High school region: South (Gl2REGON) 6,337 0.390 0.488 0.000 1.000 

High school region: West (G12REGON) 6,337 0.177 0.382 0.000 1.000 

High school sector: Catholic (G12CTRL2) 6,337 0.063 0.242 0.000 1.000 

High school sector: NAIS (G12CTRL2) 6,337 0.Q25 0.156 0.000 1.000 

High school sector: Other private (Gl2CTRL2) 6,337 0.025 0.157 0.000 1.000 

Ln of high school grade 12 enrollment (G12ENROL) 6,271 5.320 0.814 0.693 7.164 

Number of years of math required for high school graduation 

(F1C70B) 

5,156 4.491 0.657 1.000 6.000 

118 
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Experiences in Science and Mathematics 

Table Al.2. Descriptive statistics for student-level variables used in the analyses of 12th grade mathematics 

instruction: 1992. (Continued) 

Variable I N I Mean IStd Dev I Min. I I Max. 

Principal reports being rewarded for raising achievement levels 

(F1C89) 

5,032 0.191 0.393 0.000 1.000 

Principal report of influence of student standardized test scores 

on how he/she is evaluated (F2C62A) 

5,775 2.266 0.685 1.000 3.000 

School has minimum competency math test (F2C45A) -6,306 0.508 0.500 0.000 1.000 

Extent of leadership & support from principal 5,261 2.778 0.405 1.333 4.000 

Extent of teacher influence: instructional methods 5,666 5.396 0.655 1.667 6.000 

Extent of teacher influence: course content 5,665 4.196 1.343 1.000 6.000 

Extent of content coordination in teacher's dept. 5,255 2.778 0.525 1.000 4.000 

Extent teacher discusses content w/ other teachers 5,250 2.110 0.367 1.000 3.000 

Degree of emphasis on higher-order skills 5,662 3.236 0.587 1.000 4.000 

Degree of emphasis on relevance of math 5,662 3.238 0.610 1.000 4.000 

Degree of emphasis on mechanical skills 5,666 3.032 0.549 1.000 4.000 

Minutes per day of homework for class (F2T2_8) 5,648 33.966 17.262 0.000 180.000 

% class time: whole class instruction (from F2T2_12A) 5,264 51.411 21.385 0.000 87.000 

Ordinal class time spent instructing whole. class (F2T2_12A) 5,264 4.518 0.933 1.000 6.000 

% class time: maintaining discipline (from F2T2_12D) 5,205 6.268 13.438 0.000 87.000 

Ordinal class time spent maintaining order (F2T2_12D) 5,205 1.812 0.904 1.000 6.000 

1990 mathematics !RT-estimated number right (F12XMIRR) 5,871 45.855 13.130 16.650 72.760 

1992 mathematics !RT-estimated number right (F22XMIRR) 5,553 50.863 13.574 17.690 78.100 

1990 math level 1: probability of proficiency (F12XMPP1) 5,871 0.941 0.149 0.030 1.000 

1990 Math level 2: probability of prof. (F12XMPP2) 5,871 0.707 0.403 0.000 1.000 

1990 Math level 3: probability of prof. (Fl2XMPP3) 5,871 0.506 0.457 0.000 1.000 

1990 Math level 4: probability of prof. (F12XMPP4) 5,871 0.232 0.343 0.000 1.000 

1990 Math level 5: probability of prof. (F12XMPP5) 5,871 0.004 0.024 0.000 0.380 

1992 Math level 1: probability of proficiency (F22XMPP1) 5,553 0.968 0.102 0.060 1.000 

1992 Math level 2: probability of prof. (F22XMPP2) 5,553 0.813 0.342 0.000 1.000 

1992 Math level 3: probability of prof. (F22XMPP3) 5,553 0.630 0.442 0.000 1.000 

1992 Math level 4: probability of prof. (F22XMPP4) 5,553 0.358 0.412 0.000 1.000 

1992 Math level 5: probability of prof. (F22XMPP5) 5,553 0.033 0.125 0.000 0.980 

NOTE: The names of the NELS:88 codebook variables are shown in parentheses. See Appendix B for complete descriptions 

of values and how variables were constructed. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second 

Follow-Up suney. 

119 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table Al.3. Descriptive statistics for student-level variables used in the analyses of 12th grade science instruction: 

1992. 

I Variable I N I Mean I Std Dev I Min. I Max. I 

Socio-economic status composite (F2SES1) 4,250 0.197 0.757 -3.243 1.970 

Student is female (F2SEX) 4,266 0.518 0.500 0.000 1.000 

Student is Asian (F2RACE1) 4,260 0.050 0.217 0.000 1.000 

Student is Hispanic (F2RACE1) 4,260 0.074 0.262 0.000 1.000 

Student is Black (F2RACE1) 4,260 0.111 0.314 0.000 1.000 

Student is American Indian (F2RACE1) 4,260 0.Q18 0.132 0.000 1.000 

Achievement level of class: AP (F2T2_3 & F2T2_ 4) 3,855 0.097 0.296 0.000 1.000 

Achievement level of class: above average (F2T2_3 & F2T2_ 4) 3,855 0.471 0.499 0.000 1.000 

Achievement level of class: below average (F2T2_3 & F2T2_ 4) -3,855 0.081 0.273 0.000 1.000 

Teacher's science education: college and grad. major & major 3,533 0.289 0.453 0.000 1.000 

Teacher's science education: college or grad. major & minor 3,533 0.129 0.335 0.000 1.000 

Teacher's science education: minor only 3,533 0.137 0.344 0.000 1.000 

Teacher's science education: no major or minor 3,533 0.079 0.270 0.000 1.000 

High school is located in an urban area (G12URBN3) 4,266 0.287 0.453 0.000 1.000 

High school is located in a rural area (Gl2URBN3) 4,266 0.310 0.463 0.000 1.000 

High school region: Midwest (G12REGON) 4,266 0.276 0.447 0.000 1.000 

High school region: South (G12REGON) 4,266 0.290 0.454 0.000 1.000 

High school region: West (G12REGON) 4,266 0.199 0.399 0.000 1.000 

High school sector: Catholic (G12CTRL2) 4,266 0.066 0.249 0.000 1.000 

High school sector: NAIS (G12CTRL2) 4,266 0.016 0.124 0.000 1.000 

High school sector: Other private (G12CTRL2) 4,266 0.029 0.168 0.000 1.000 

6-20% of students in school receive free or reduced-price lunch 4,266 0.303 0.460 0.000 1.000 

(F2C25A) 

21-50% of students in school receive free or reduced-price lunch 4,266 0.280 0.449 0.000 1.000 

(F2C25A) 

51 %+ of students in school receive free or reduced-price lunch 4,266 0.082 0.274 0.000 1.000 

(F2C25A) 

Ln of high school grade 12 enrollment (G12ENROL) 4,220 5.265 0.915 0.693 7.012 

Principal reports being rewarded for raising achievement levels 3,384 0.152 0.359 0.000 1.000 

(F1C89) 

Principal report of influence of student standardized test scores 3,831 2.226 0.674 1.000 3.000 

on how he/she is evaluated (F2C62A) 

High school has minimum competency science test for 12th 4,249 0.137 0.344 0.000 1.000 

graders (F2C45A) 

120 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table Al.3. Descriptive statistics for student-level variables used in the analyses of 12th grade science instruction: 

1992. (Cont'd) 

I Variable I N I Mean I Std Dev I Min. I Max. I 

Years of science required for high school graduation (F1C70C) 3,548 4.241 0.656 1.000 6.000 

Extent of leadership & support from principal 3,512 2.720 0.439 1.000 4.000 

Extent of teacher influence: instructional methods 3,843 5.333 0.695 1.000 6.000 

Extent of teacher influence: course content 3,844 4.812 1.160 1.000 6.000 

Extent of content coordination in teacher's dept. 3,497 2.520 0.612 1.000 4.000 

Extent teacher discusses content w/ other teachers 3,506 2.022 0.381 1.000 3.000 

Minutes per day of homework for class (F2T2_8) 3,758 31.397 18.531 0.000 180.000 

Minutes per week class meets for lab (F2T2_11) 3,471 56.858 46.517 0.000 350.000 

Degree of emphasis on lab science 3,848 2.816 0.665 1.000 4.750 

Degree of emphasis on scientific inquiry learning skills 3,608 3.328 0.510 1.000 4.000 

Degree of emphasis on relevance of science 3,605 3.131 0.699 1.000 4.000 

Degree of emphasis on memorizing scientific facts (F2T2_18B) 3,602 2.879 0.731 1.000 4.000 

Degree of emphasis on computer use in science 3,842 1.385 0.622 1.000 5.000 

Degree of emphasis on the use of student presentations in 3,847 1.410 0.539 1.000 5.000 

science 

% class time: whole class instruction (from F2T2_12A) 3,472 52.441 23.421 0.000 87.000 

Ordinal class time spent instructing whole class (F2T2_12A) 3,472 4.542 1.052 1.000 6.000 

% class time: maintaining discipline (from F2T2_12D) 3,446 5.249 10.054 0.000 87.000 

Ordinal class time spent maintaining order (F2T2_12D) 3,446 1.754 0.785 1.000 6.000 

1990 science !RT-estimated number right (F12XSIRR) 3,951 23.228 5.807 10.320 34.680 

1992 science !RT-estimated number right (F22XSIRR) 3,639 25.054 6.059 10.260 35.960 

1990 science level 1: probability of proficiency (F12XSPP1) 3,951 0.883 0.275 0.000 1.000 

1990 science level 2: probability of proficiency (F12XSPP2) 3,951 0.529 0.403 0.000 1.000 

1990 science level 3: probability of proficiency (F12XSPP3) 3,951 0.172 0.324 0.000 1.000 

1992 science level 1: probability of proficiency (F22XSPP1) 3,639 0.910 0.254 0.000 1.000 

1992 science level 2: probability of proficiency (F22XSPP2) 3,639 0.637 0.392 0.000 1.000 

1992 science level 3: probability of proficiency (F22XSPP3) 3,639 0.293 0.398 0.000 1.000 

NOTE: The names of the NELS:88 codebook variables are shown in parentheses. See Appendix B for complete descriptions 

of values and how variables were constructed. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second 

Follow-Up survey. 

121 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table A2.l: Numbers for Figure 2.1: Percentage of Grade 12 Mathematics and Science Students 

Enrolled in Classes by Achievement Level of the Class: 1991-1992 

Achievement Level 

Mathematics I 

Percent Standard 

Students Error 

II Science 

Percent Standard 

Students Error 

I 

Remedial 4.0 0.47 -- --

Below-Average 

Average 

12.4 

40.6 

1.08 

1.77 

8.1 

35.2 

0.76 

1.64 

Above-Average 

Advanced Placement 

Total 

34.2 

8.7 

100.0 

1.38 

0.75 

47.1 

9.7 

100.0 

1.86 

0.98 

NOTE: The achievement levels of the classes were identified by the teachers. Two percent of the grade 

12 science students were enrolled in remedial-level classes. These students were combined with 

"low" students in this report. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

122 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table A2.2. Numbers for Figure 2.2: Average emphasis math teachers of 12th-grade students place 

on different skills, by achievement level of the class: 1991-1992. 

Achievement Level of Students in the Class 

Emphasis on ... Total Remedial 

Below 

Average Average 

Above 

Average AP 

Developing higher-order 

thinking (mean of 4 

items) 

mean 3.24 2.80 2.92 3.21 3.36 3.54 

s.e. .02 .10 .04 .03 .02 .03 

unw.N 5,643 211 595 2,108 2,076 653 

Showing the importance 

of math in everyday life 

(mean of 2 items) 

mean 3.24 3.38 3.35 3.25 3.18 3.19 

s.e. .02 .07 .04 .04 .03 .06 

unw.N 5,643 211 595 2,109 2,075 653 

Leaming mechanical 

operations 

mean 3.03 2.92 2.91 

.06 

3.09 

.02 

3.05 2.93 

s.e. .02 .05 .02 .06 

unw.N 5,647 211 595 2,111 2,076 654 

Note: The emphasis and class achievement level are reported by the teachers. The scale of the emphasis 

items has four levels: 1 =none, 2 =some, 3 =moderate, 4 =major). 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

123 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table A2.3. Numbers for Figure 2.3: Average emphasis science teachers of 12th-grade students 

place on different skills, by Achievement Level of the class: 1991-1992. 

Achievement Levels of Students in Class 

Emphasis on ... Total 

Below 

Average Average 

Above 

Average AP 

Developing Inquiry skills 

(mean of 4 items) 

mean 3.33 2.94 3.20 3.45 3.50 

s.e. .02 .06 .03 .03 .04 

unw.N 3,591 280 1,214 1,661 436 

Memorizing scientific facts, 

principles, and rules 

mean 2.88 2.63 2.83 2.95 2.90 

s.e. .03 .07 .04 .03 .09 

unw.N 3,585 277 1,213 1,659 -436 

Showing the importance of 

science in everyday life (mean 

of 2 items) 

mean 3.13 3.30 3.24 3.05 2.98 

s.e. .03 .07 .04 .05 .06 

unw.N 3,588 281 1,212 1,659 436 

Note: The emphasis and class achievement level are reported by the teachers. The scale of the emphasis 

items has four levels: 1 =none, 2 =some, 3 =moderate, 4 =major). 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

124 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table A2.4: Numbers for Figures 2.4 & 2.5: Average Minutes Per Day of Homework Assigned by 

Teachers of 12th Grade Math and Science Students, and Average Minutes Per Week 

Allocated for Science Labs, by Achievement Level of the Class: 1992 

I 

I 

I 

Achievement Level 

Mathematics I II Science 

Mean Standard 

Errnr 

Mean Standard 

Error 

IMinutes per day of homework assigned 

Overall 34.0 0.56 I II I II 31.4 0.66 I 

Remedial 23.0 1.30 -- --

Below-Average 26.4 1.44 21.7 1.16 

Average 30.1 0.96 25.6 0.80 

Above-Average 38.5 0.76 33.7 0.92 

Advanced Placement 49.9 1.39 50.0 2.89 

Average minutes per week allocated for science labs 

Overall -- I I II 56.7 1.53 I 

Below-Average -- 40.3 4.17 

Average -- 49.7 2.79 

Above-Average -- 60.9 2.13 

Advanced Placement -- 76.4 7.25 

NOTE: The achievement levels of the classes were identified by the teachers. Two percent of the grade 

12 science students were enrolled in remedial-level classes. These students were combined with 

"low" students in this report. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study 

of 1988 (NELS:88), Second Follow-Up survey. 

I 

125 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table A2.5. Numbers for Figure 2.6: Average Use of Various Instructional Methods, As Reported 

by Teachers of 12-grade Math Students, by Achievement Level of Class: 1991-1992. 

Total Remedial 

Below 

Average Average 

Above 

Average AP 

Lecture mean 4.0 3.6 3.9 4.0 4.0 4.0 

s.e. .03 .12 .14 .04 .04 .06 

unw.N 5,253 186 561 1,943 1,948 615 

Computer mean 1.5 1.7 1.3 1.5 1.6 1.6 

s.e. .03 .14 .05 .06 .06 .08 

unw.N 5,215 186 562 1,924 1,933 610 

Audio-Visual 

Material 

mean 2.2 2.3 2.1 2.2 2.3 2.1 

s.e. .05 .14 .09 .09 .06 .14 

unw.N 5,184 185 559 1,923 1,916 601 

Whole Group 

Discussion 

mean 3.0 2.8 3.0 3.0 2.9 3.1 

s.e. .05 .13 .10 .10 .06 .12 

unw. N 5,200 186 558 1,920 1,930 606 

Oral Question Response mean 4.1 4.0 4.1 4.2 4.1 4.0 

s.e. .03 .08 .05 .05 .04 .08 

unw.N 5,255 186 567 1,941 1,954 607 

Student-Led Discussion mean 1.6 1.7 1.5 1.7 1.6 1.8 

s.e. .04 .12 .07 .09 .04 .10 

unw. N 5,217 184 558 1,923 1,943 609 

Coop Groups mean 2.8 2.9 2.7 2.8 2.8 2.9 

s.e. .04 .12 .08 .06 .05 .08 

unw.N 5,251 184 565 1,943 1,949 610 

Written Assignment mean 3.0 4.0 3.2 3.0 2.9 2.5 

s.e. .06 .12 .17 .10 .06 .13 

unw.N 5,255 187 564 1,950 1,941 613 

Oral Reports mean 1.2 1.2 1.2 1.3 1.2 1.3 

s.e. .03 .06 .06 .06 .02 .05 

unw.N 5,229 185 564 1,929 1,945 606 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), 

Second Follow-Up sur!ey. 

126 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table A2.6. Numbers for Figure 2.7: Average Use of Various Instructional Methods, As Reported by 

Teachers of 12th-grade Science Students, by Achievement Level of Class: 1991-1992. 

Total 

Below 

Average Average 

Above 

Average AP 

Lecture mean 3.5 3.2 3.5 3.6 3.6 

s.e. 0.4 .00 .06 .05 .07 

unw.N 3.466 275 1.169 1.600 422 

Computer mean 1.5 1.4 1.4 1.5 1.6 

s.e. .03 .06 .04 .05 .07 

unw.N 3.429 270 1.142 1,595 422 

Audio-Visual 

Material 

mean 2.6 2.8 2.6 2.6 2.6 

s.e. .04 .10 .05 .06 .10 

unw.N 3.471 275 1.171 1.601 424 

Whole Group Discussion mean 2.8 2.7 2.9 2.8 2.9 

s.e. .05 .15 .06 .08 .08 

unw.N 3.468 276 1.161 1,607 424 

Oral Question Response mean 3.7 3.6 3.7 3.7 3.8 

s.e. .04 .08 .04 .07 .12 

unw.N 3.486 275 1.173 1.614 424 

Student-Led Discussion mean 1.6 1.5 1.6 1.6 1.8 

s.e. .04 .07 .04 .06 .00 

unw.N 3.452 272 1,162 1599 419 

Coop Groups mean 2.9 2.8 2.8 2.9 2.7 

s.e. .03 .00 .05 .04 .11 

unw.N 3489 276 1.175 1614 424 

Written Assignment mean 2.7 3.1 2.8 2.6 2.1 

s.e. .05 .10 .06 .08 .10 

unw.N 3.495 274 1.179 1.618 424 

Oral Reports mean 1.3 1.3 1.3 1.3 1.4 

s.e. .02 .05 .03 .03 .06 

unw.N 3,474 273 1,167 1,610 424 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

127 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table A2.7. Numbers for Figures 2.8 and 2.9: Percentage distributions of 12th grade mathematics and 

science students, by achievement level of the class and teacher educational background: 1992. 

Class level and teacher education Mathematics Science 

Percent S.E. Percent S.E. 

Remedial Classes 

College & graduate major in field 11.5 3.54 -- --

College or graduate major plus a minor in field 5.0 1.76 -- --

College or graduate major but no minor in field 33.4 5.08 -- --

College or graduate minor in field 22.9 7.31 -- --

No major or minor in field 27.1 4.58 -- --

Total 100% -- --

Sample size 192 -- -- I I I I I I 

Below-Average Classes 

College & graduate major in field 11.5 2.15 15.5 2.93 

College or graduate major plus a minor in field 11.0 2.76 13.6 3.44 

College or graduate major but no minor in field 37.1 4.09 43.7 5.43 

College or graduate minor in field 26.2 5.51 18.0 4.28 

No major or minor in field 14.2 3.50 9.1 2.65 

Total 100% 100% 

Sample size 568 277 I I I I I I 

Average Classes 

College & graduate major graduate major in 15.1 1.71 25.4 2.43 

College or graduate major plus a minor in field 9.1 1.17 14.6 2.73 

College or graduate major but no minor in field 46.2 3.41 35.5 3.08 

College or graduate minor in field 15.8 2.39 15.9 2.02 

No major or minor in field 13.9 3.18 8.6 1.68 

Total 100% 100% 

Sample size 1,974 1,189 I I I I I I 

128 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table A2.7. Numbers for Figures 2.8 and 2.9: Percentage distributions of 12th grade mathematics and 

science students, by achievement level of the class and teacher educational background: 1992. 

(Continued) 

Class level and teacher education Mathematics Science 

Percent S.E. Percent S.E. 

Above Average Classes 

College & graduate major in field 27.3 1.99 29.3 3.44 

College or graduate major plus a minor in field 14.1 1.48 11.6 1.78 

College or graduate major but no minor in field 41.8 2.35 37.7 2.97 

College or graduate minor in field 14.1 1.64 12.7 1.83 

No major or minor in field 2.7 0.49 8.7 1.44 

I Total I 100% I I 100% I I 

I Sample size I 1,959 I I 1,618 I I 

I AP Classes I 

College & graduate major in field 38.2 4.39 50.8 5.09 

College or graduate major plus a minor in field 21.4 3.22 12.2 2.54 

College or graduate major but no minor in field 30.1 3.61 29.4 4.80 

College or graduate minor in field 9.1 4.58 6.7 2.00 

No major or minor in field 1.2 0.56 0.9 0.56 

I 

Total 

I 

100% 

I I 

100% 

I I Sample size 618 429 

NOTE: Owing to rounding, percentages may not sum to 100. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), First and Second Follow-Up surveys and 1992 High School Transcripts tile. 

129 
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Experiences in Science and Mathematics 

Table A3.l. Numbers for Figure 3.1: Percentage of 1991-1992 12th Graders Taking Mathematics and 

Science Courses, by Student Background Characteristics. 

I 

I 

I 

Variable Mathematics Science 

% SE N % SE N 

I All Students .95 I 661 I 13,8621 48 I 1.02 I 13,862 I 

IGender 

Male 68 1.29 6,952 49 1.42 6,952 

Female 63 1.14 6,910 47 1.24 6,910 

IRace/Ethnicity 

Asian 76 2.94 1,024 60 3.43 1,024 

Hispanic 64 2.54 1,572 42 2.71 1,572 

Black 69 2.44 1,229 44 2.70 1,229 

White 65 1.13 9,875 48 1.22 9,875 

American Indian 65 7.45 132 52 9.62 132 

ISocio-economic Quartile 

Lowest 57 1.77 2,537 37 1.62 2,537 

Low-Middle 60 1.84 3,209 39 1.58 3,209 

High-Middle 67 1.40 3,471 49 1.56 3,471 

Highest 75 1.68 4,532 61 2.05 4,532 

1990 Math and Science Achievement Score Quartile 

Lowest 50 2.29 2,139 35 1.96 2,352 

Low-middle 60 1.82 2,933 39 1.74 2,911 

High-middle 67 1.41 3,467 46 1.83 3,411 

Highest 79 1.30 4,226 65 1.74 4,027 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), First and Second Follow-Up surveys and 1992 High School Transcripts file. 

130 
High School Seniors' Instructional 

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Table A3.2. Numbers for Figure 3.2: Percentage of 1991-1992 twelfth grade mathematics students 

enrolled in classes with different achievement levels, by student background characteristics. 

I 

I 

Variable Remedial Low Average 

Above 

Average AP 

Sample 

Size 

All Students % 4.0 12.4 40.6 34.2 8.7 

5,714 

SE .47 1.08 1.77 1.38 .75 

I Gender 

Male % 3.8 13.8 43.3 31.5 7.7 

2,908 

SE .54 1.74 2.66 1.88 .85 

Female % 4.3 10.8 37.4 37.5 10.0 

2,806 

SE .75 1.04 1.82 1.66 1.23 

IRace/Ethnicity 

Asian % 4.6 8.1 25.6 43.1 18.7 

450 

SE 1.54 2.89 3.22 3.91 2.51 

Hispanic % 9.3 15.6 38.6 31.2 5.3 

657 

SE 2.76 2.51 3.74 4.59 2.25 

Black % 5.5 19.3 44.7 27.2 3.3 

567 

SE 1.30 3.58 3.29 3.03 .82 

White % 2.9 11.1 41.0 35.3- 9.6 

3,981 

SE .42 1.24 2.25 1.68 .96 

131 
High School Seniors' Instructional 

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Table A3.2. Numbers for Figure 3.2: Percentage of 1991-1992 12th grade mathematics students enrolled 

in classes with different achievement levels, by student background characteristics. 

(Continued) 

Above Sample 

Variable Remedial Low Average Average AP Size 

I Socio-economic Quartile I 

Lowest % 7.5 17.9 44.5 27.6 2.6 

967 

SE 1.08 1.99 3.05 2.60 .53 

Low-middle % 4.9 14.6 43.5 32.5 4.5 

SE 1.24 1.99 3.65 2.72 1.21 

1,250 

High-middle % 3.0 10.6 41.6 35.9 8.8 

1,465 

SE .55 1.51 2.28 2.12 1.54 

Highest % 2.0 9.2 35.5 38.0 15.3 

SE .65 2.47 4.04 2.87 1.73 

1,990 

I1990 Achievement Score Quartile I 

Lowest % 12.1 30.2 47.0 10.0 0.6 

737 SE 1.49 2.75 2.76 1.38 .32 

Low-middle % 4.6 15.9 56.9 22.3 0.3 

SE .89 1.92 3.64 2.42 .15 1,109 

High-middle % 1.5 8.3 42.2 44.8 3.1 

SE .40 1.24 2.45 2.49 .96 

1,494 

Highest % 0.3 1.7 25.8 48.6 23.5 

SE .17 .37 3.82 2.83 2.03 1,961 

NOTE: Blank cells indicate that there are less than 30 cases in the cell. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

132 
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Table A3.3. Numbers for Figure 3.3: Percentage of 1991-1992 12th grade science students enrolled in 

classes with different achievement levels, by student background characteristics. 

Variable Low Average 

Above 

Average AP 

Sample 

Size 

All Students % 8.1 35.2 47.1 9.7 

3,855 

SE .76 1.64 1.86 .98 

I Gender 

Male % 9.8 36.0 44.6 9.5 

1,915 SE 1.16 1.94 2.16 1.03 

Female % 6.5 34.4 49.3 9.8 

1,940 

SE .94 2.41 2.65 1.46 

IRace/Ethnicity I 

Asian % 8.1 22.6 44.9 24.4 

359 

SE 3.64 3.20 4.59 3.94 

Hispanic % 10.9 35.4 45.9 7.8 

358 

SE 3.44 4.28 4.64 1.97 

Black % 9.2 42.2 43.0 5.6 

276 

SE 1.95 6.03 6.76 2.22 

White % 7.6 35.0 47.8 9.6 

2,818 

SE .86 1.90 2.17 1.16 

I 

133 
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Table A3.3. Numbers for Figure 3.3: Percentage of 1991-1992 12th grade science students enrolled in 

classes with different achievement levels, by student background characteristics. (Continued) 

Variable Low Average 

Above 

Average AP 

Sample 

Size 

I Socio-economic Quartile I 

Lowest % 15.2 47.8 33.8 3.1 

514 

SE 1.95 3.62 3.62 .98 

Low-middle % 11.0 38.9 46.3 3.8 

759 SE 1.78 2.82 2.72 .70 

High-middle % 9.0 36.2 45.9 8.8 

966 

SE 1.83 2.82 3.09 2.35 

Highest % 3.2 27.5 53.5 15.7 

1,603 SE .62 2.47 3.23 1.62 

I 1990 Achievement Score Quartile I 

Lowest % 18.5 52.1 28.0 1.4 

457 SE 2.55 4.38 4.55 .53 

Low-middle % 10.3 51.4 35.6 2.8 

696 SE 2.16 3.48 3.57 .64 

High-middle % 

SE 

7.8 

1.53 

33.0 53.3 5.9 

972 

3.10 3.60 1.12 

Highest % 2.1 20.4 59.6 17.9 

1,451 SE .43 2.12 2.57 1.95 

NOTE: Blank cells indicate that there are less than 30 cases in the cell. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

134 
Table A3.4. Standard errors for means of math instructional variables reported by the teachers of the sampled 12th-grade math 

students, by student background (see Table 3.1 for means). 

Variable 

Gender Socioeconomic Quartile Race-Ethnicity 

Males Females Low Mid-low Mid-high High Asian Hispanic Black White 

Instructing whole class 1.059 .885 1.487 1.291 1.319 2.283 1.981 2.245 1.404 .892 

Instructing small groups .979 .481 2.117 .745 1.084 .747 .919 2.339 .920 .755 

Instructing individuals 1.007 .667 .948 .596 .787 1.546 1.290 2.837 1.099 .733 

Maintaining order .698 .507 .758 .409 .690 .671 .576 1.613 1.996 .480 

Administering tests .489 .331 .826 .454 .487 .590 .742 .667 .757 .407 

Administrative tasks .196 .177 .366 .273 .294 .221 .507 .731 .535 .123 

Conducting lab periods .564 .150 .880 .882 1.008 1.125 .567 .372 .237 .427 

Lecture .048 .028 . .055 .052 .052 .059 .101 .070 .077 .037 

Use computers .049 .039 .071 .043 .071 .044 .071 .149 .063 .038 

Use audio-visual materials .072 .048 .062 .064 .053 .055 .132 .119 .114 .058 

Use teacher-led. discussion .076 .044 .061 .068 .070 .100 .108 .145 .096 .058 

Recitation .038 .031 .060 .048 .068 .070 .072 .067 .050 .033 

Use student-led discussion .046 .068 .052 .046 .064 .060 .072 .065 .076 .050 

Cooperative groups .052 .044 .062 .045 .060 .034 .094 .094 .070 .045 

Seatwork .085 .055 .080 .052 .087 .084 .100 .153 .085 .069 

Student oral reports .033 .052 .042 .029 .032 .030 .031 .049 .046 .037 

Homework minutes/day .756 .687 1.347 .985 .838 1.101 1.269 1.376 1.232 .665 

Emphasis: Problem-solving .021 .022 .046 .029 .028 .027 .050 .051 .045 .019 

Emphasis: Applications .034 .024 .051 .047 .041 .059 .046 .045 .041 .028 

Emphasis: Mechanics .024 .020 .044 .042 .040 .039 .043 .050 .040 .020 

SOURCE: U.S. Depar.tment of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up survey. 
Table A3.S. Standard errors for means of science instructional variables reported by the teachers of the sampled 12th-grade math ...... 

I.>) students, by student background (see Table 3.2 for means). °' 

Variable 

Gender Socioeconomic Status Quartile Race-Ethnicity 

Male Female Low Mid-low Mid-high High Asian Hispanic Black White 

Instructing whole class 1.063 1.746 1.487 1.291 1.319 2.283 1.964 1.972 1.886 1.345 

Instructing small groups .718 .941 2.117 .745 1.084 .747 1.084 3.776 1.206 .726 

Instructing individuals .600 1.169 .948 .596 .787 1.546 1.477 1.469 1.098 .480 

Maintaining order .434 .559 .758 .409 .690 .671 .400 .642 1.403 .316 

Administering tests .352 .519 .826 .454 .487 .590 .743 1.001 1.297 .335 

Administrative tasks .199 .227 .336 .273 .294 .221 .231 .421 .389 .217 

Conducting lab periods .710 .946 .880 .882 1.008 1.125 1.479 1.086 1.364 .782 

Lecture .042 .047 .055 .052 .052 .059 .093 .073 .080 .040 

Use computers .038 .048 .071 .043 .071 .044 .065 .101 .157 .032 

Use audio-visual materials .046 .046 .062 .064 .053 .055 .108 .082 .110 .043 

Use teacher-led discussion .050 .081 .061 .068 .070 .100 .094 .102 .125 .061 

Recitation .040 .063 .060 .048 .068 .070 .084 .082 .161 .045 

Use student-led discussion .045 .044 .052 .046 .064 .060 .062 .071 .142 .037 

Cooperative groups .037 .037 .062 .045 .060 .034 .091 .096 .061 .035 

Seatwork .048 .075 .080 .052 .087 .084 .074 .099 .179 .056 

Student oral reports .022 .026 .042 .029 .032 .030 .038 .066 .066 .021 

Homework minutes/day .772 .874 1.347 .985 .838 1.101 1.843 2.638 1.853 .704 

Laboratory minutes/week 2.037 1.998 3.210 2.325 2.654 2.224 4.177 3.714 4.403 1.736 

Emphasis: Inquiry .024 .026 .046 .029 .028 .027 .038 .078 .055 .022 

Emphasis: Science & Society .031 .050 .051 .047 .041 .059 .076 .057 .107 .037 

Emphasis: Memorizing Facts .032 .032 .044 .042 .040 .039 .060 .050 .057 .030 

Composite frequency of 

computer use 

.028 .031 .052 .034 .038 .036 .053 .055 .080 .026 

Composite frequency of 

student presentations 

.021 .025 .034 .029 .029 .031 .040 .048 .058 .021 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Appendix B: 

Methodological and Technical Notes 

137 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Appendix B: Methodological and Technical Notes 

B.1 Description of the Sample 

The data analyzed in this report are drawn primarily from the NELS:88 second (1992) follow-up 

smveys of students and their teachers. NELS:88 began in 1988 with a national sample of about 24,000 

eighth-graders selected from 1,052 public and ·private schools. The study collected questionnaire and 

cognitive achievement data from the students in 1988, 1990, and 1992, and followed the students beyond 

high school with mail questionnaires and phone interviews in 1994. While the students were in middle 

and high school, data were also collected from their teachers, principals, and parents. The high school 

transcripts of the students were collected after the 1991-1992 school year. Participants who dropped out 

of high school were followed up in 1990 and 1992. In 1992, 12 percent of the 1988 eighth-grade cohort 

were classified as dropouts in the NELS:88 survey (McMillan, Kaufman, & Whitener, 1994, Table 18). 

The base year students dispersed into a much larger number of high schools, such that it was 

infeasible to collect information from the teachers and principals in all of the schools represented by the 

original student sample. Subsampling of the original students was thus used in the 1990 and 1992 followup surveys. The data collected by the NELS:88 second follow-up teacher survey were restricted to the 

math and science teachers of those NELS:88 students who were enrolled in one of 1,374 schools which 

were selected for the teacher and principal surveys. These data allow researchers to investigate the effects 

of school experiences on student outcomes, and the sample is thus referred to as the "contextual sample" 

of schools and students. These schools were a systematically-drawn subset of the 2,258 schools NELS:88 

sample members were attending in the spring of 1991, when student tracing for the second follow-up took 

place. While drawn systematically, the subsample of original students was not fully representative of the 

1991-1992 population of high school seniors. This was because some seniors were repeating that grade, 

had skipped ahead a grade at some point, or had stopped out of high school for a time but had returned. 

To gain full representation of the sophomore and senior cohorts, NELS:88 augmented its original eighthgrade sample with 862 students in the first follow-up and 264 new respondents in the second follow-up. 

The contextual subsample included 15,695 students, 96 percent of whom were enrolled as seniors 

in 1992. Since our concern in this study is focused on the seniors, we excluded all students who were 

not classified as seniors in the 1991-92 school year. This left a full sample of 15,105 students. Of the 

15,105, 10,603 were enrolled in a science or math course during the 1991-1992 school year and thus had 

teachers eligible for the survey. The goal of the NELS:88 second follow-up teacher survey was to obtain 

data from either a science or a mathematics teacher of each student enrolled in those courses. Since about 

40 percent of the seniors were taking both courses simultaneously, this goal required certain selection 

procedures. The rule used was to select the same subject area as the 1988 base year subject which was 

selected for the student. 

From the pool of 10,603 seniors, 6,337 were selected to have their mathematics teachers surveyed 

and 4,266 were selected to have their science teachers surveyed. The science and mathematics teachers 

were surveyed in the spring of 1992. Questionnaires were mailed to a total of 5,657 teachers; 5,100, or 

90 percent, completed a form. The completed forms covered the targeted classes of 9,634 of the 10,603 

(91 percent) seniors enrolled in science or mathematics. 

It is important to keep in mind at all points of this study that (a) many 12th graders do not take 

science and math, and (b) the 12th graders who do take these subjects are on average higher achievers and 

thus not a representative sample of the larger grade or age cohorts. Nonetheless, it is not the case that 

139 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

only the most advanced students take science and mathematics during their senior years. As was evident, 

students from a wide range of ability levels and social backgrounds take these courses. 

The result of this complex design is that the sample of students, properly weighted, is 

representative of 1991-1992 school year seniors. Further, the subsamples with teacher-supplied 

information on science and mathematics courses are representative of seniors who took those courses. The 

weight used in all of the tabulations included in this report is the NELS:88 contextual-sample weight, 

named F2CXTWT. 

As a result of the decision to include only one set of teacher data per eligible student, the 

proportions of students who have science or mathematics teacher data are substantially lower than the 

proportions who actually took science or mathematics as seniors. To obtain an estimate of the latter, one 

must tum to the transcript data. Transcripts were collected for 13,862 of the 15,105 seniors (92 percent). 

These students are used in the analyses of senior-year enrollments. All tabulations of data from the 

transcript study included in this report also used the contextual-sample weight, F2CXTWT. 

Missing data. This report uses data from several different components of the NELS:88 data base, 

and data from one or more the components are missing for many students. Students who are missing 

values for one or more of the variables used in the tables are excluded from the table, but are not excluded 

from other tabulations where they have complete data. The main sources of missing data are from 

instrument nonresponse on the transcript data, the 1990 and 1992 principal questionnaires (used in ch. 4), 

and the 1990 and 1992 achievement tests. We did not find any large differences on the variables used 

in the analyses across subsamples. Our rationale for not excluding cases on a listwise basis was that, for 

descriptive purposes, it is better to use all the information available in obtaining estimates. Listwise 

deletion is appropriate when a series of models is estimated, and one thus wants to make sure that sample 

differences are not producing misrepresentations of patterns (or lack thereof) across models. 

B.2 Sampling Errors 

Sampling errors refer to the chance discrepancies between the population and a sample drawn from 

it. The size of the errors are inversely related to the sample size, but determining the proper degrees of 

freedom is complicated when surveys use complex sample designs. The NELS:88 sampling procedures 

were designed to produce a sample that would be broadly representative of students across the country 

from public and private schools, and from many different types of social backgrounds. This required a 

complex classification of all schools and further subclassifications of students within selected schools. 

Students from the different cells defined by the classification scheme were sampled with different 

probabilities of inclusion. In order to obtain accurate estimates of population values, analysts must thus 

use sampling weights which adjust the contributions of each case according to the number of other 

individuals in the sampled population whom he or she represents. All numbers presented in this report 

are calculated using the NELS:88 public-use design weight named F2CXTWT. This weights the sampled 

individuals according to the number of 1992 twelfth graders that each sampled member represents. The 

subset of cases for whom this weight was defined consisted of the 15,695 students who attended the 

schools selected for inclusion in the teacher and school administrator components and who participated 

in the 1992 survey. Early graduates were also included in this sample. 

The clustering and stratification used in the NELS:88 sampling design also results in larger 

uncertainty of population values than would an equal-sized simple random sample. All estimates, standard 

140 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

errors, and significance tests reported were thus calculated taking into account the sample design. The 

SUDAAN statistical analysis program was used to estimate the standard errors taking into account the 

complex survey design. The program uses a Taylor Series estimator for the variance calculations. 

B.3 Description of Measures 

STUDENT BACKGROUND VARIABLES. Student background variables such as gender, race/ethnicity, 

family socioeconomic status, and others listed below were used to define subgroups for comparison 

throughout this report. Except as specified below, these were taken directly from the student data file; 

the variable name from that file is indicated in parentheses following the descriptive variable name. 

SES: The measure of student socioeconomic status (SES) is a composite constructed from parent reports 

of their educational attainments (highest degrees earned), occupation (ranked in tenns of prestige), 

and income; and student reports of household possessions. These four components were each 

standardized to have a mean of zero and a standard deviation of one, and then averaged for each 

student. The resulting continuous variable is named F2SES 1, and is used in the correlational 

analyses presented here. For categorical breakdowns, we used the SES quartile variable named 

F2SES 1 Q. The quartiles were defined from the weighted distribution of F2SES1; as a result, the 

unweighted sample sizes in each quartile differ significantly. 

Gender: Student sex was coded mainly from base year self-reports which were checked and corrected 

with infonnation from the first and second follow-ups and name infonnation (F2SEX). 

Race/ethnicity: Student race-ethnicity (F2RACE1). This is a composite variable coded mainly from 

base-year self-reports, but corrected as additional information from the first and second follow-ups 

became available. The composite was constructed from two questions, one asking for the 

student's race, and the other at;king for Hispanic ethnic identity. Hispanic identity was given 

precedence over racial identification. 

COURSE TYPES. Two variables are used in this report to characterize the types of courses in which 

the seniors were enrolled: the subject-area of the courses, derived from the NELS:88 1992 Transcript 

Study; and the achievement level or track of the class about which the teacher responded in the 1992 

teacher questionnaire. Appendix C contains a discussion of the difficulties of linking the transcript data 

to the teacher reports. 

Achievement level of class: This is a composite variable constructed from the teacher's responses to two 

questions in the 2nd follow-up questionnaire: 

(1) "Which of the following best describes the "track" this class is considered to be? (a) 

remedial, (b) general, (c) vocational/technical/business, (d) college-prep/ honors, or (e) 

AP." (F2T2_3); 

(2) "Which of the following best describes the achievement level of the students in this class 

compared with the average 12th grade student in this school? This class consists 

primarily of students with: (a) higher achievement levels, (b) average achievement levels, 

(c) lower achievement levels, or (d) widely differing achievement levels." (F2T2_ 4). 

141 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

We constructed a composite with the following five levels: remedial, below average, average, 

above average, and AP. Remedial and AP assignments were made first, based on information from 

F2T2_3. Uncoded cases were then assigned to the remaining categories based on the values of F2T2_ 4. 

Students in classes which the teacher characterized as "widely differing achievement levels" were coded 

as "average." 

TOPICAL COVERAGE: Topical coverage within math and science courses was measured with items 

asking teachers whether various topics were covered in the course in which one or more NELS:88 students 

were enrolled. Different batteries of topics were used for teachers of mathematics, biology, chemistry, 

and physics. Teachers were asked "Have you taught or reviewed the following topics in this math 

(Biology/ Chemistry/ Physics) class this year?" Response options included (1) "No, but it was taught 

previously," (2) "Yes, but I reviewed it only," (3) "Yes, I taught it as new content," (4) "No, but I will 

teach or review it later this school year," and (5) "No, topic is beyond the scope of this course." For 

present purposes, the first four options were collapsed into a single category, to create a dichotomy 

between "past or present coverage" versus "no coverage." 

The topics asked of math teachers included: 

• integers (F2T2_15A); 

e patterns and functions (F2T2_15B); 

• linear equations (F2T2_15C); 

• polynomials (F2T2_15D); 

• properties of geometric figures (F2T2_15E); 

• coordinate geometry (F2T2_15F); 

• proofs (F2T2_15G); 

• trigonometry (F2T2_15H); 

• statistics (F2T2_15I); 

• probability (F2T2_15J); 

• calculus (F2T2_15K). 

Biology topics covered were: 

• cell structure and function (F2T2_20A); 

• genetics (F2T2_20B); 

• diversity of life (F2T2_20C); 

• metabolism/regulation of organism (F2T2_20D); 

• behavior of the organism (F2T2_20E); 

• reproduction/development of the organism (F2T2_20F); 

• human biology (F2T2_20G); 

• evolution (F2T2_20H); 

• ecology (F2T2_20I). 

Topics asked of chemistry teachers included: 

• atomic and molecular structure (F2T2_21A); 

• properties and changes in matter (F2T2_21B); 

• periodic system (F2T2_21C); 

142 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

• energy relationships (F2T2_21D); 

• reactions (F2T2_21E); 

• inorganic chemistry (F2T2_21F); 

• organic chemistry (F2T2_21G); 

• environmental chemistry (F2T2_21H); 

• chemistry of life processes (F2T2_21I); 

• nuclear chemistry (F2T2_21J). 

Topics asked of physics teachers included: 

• sources of energy (F2T2_22A); 

• forces, time, and motion (F2T2_22B); 

• molecular/nuclear physics (F2T2_22C); 

• energy/matter transformations (F2T2_22D); 

• sound and vibrations (F2T2_221j:); 

• light (F2T2_22F); 

• electricity and magnetism (F2T2_22G); 

• solids/fluids/gases (f2T2_22H). 

INSTRUCTIONAL VARIABLES. Instructional variables include the goals, methods, and time 

allocations of teachers. The measures used here are all taken from the NELS:88 1992 Teacher 

Questionnaire. All items refer to the specific math and science courses in which the sampled NELS:88 

students were enrolled. Factor analysis was used to determine whether the large number of instructional 

variables could be reduced to a smaller set of readily-inteipretible underlying common factors. All 

composite variables described below were constructed from items which factored together; the items were 

combined into the composites by averaging the nonmissing values across the indicated items. 

Time Availability: Two variables measuring the overall availability of instruction time are taken directly 

from teacher responses. A question about the amount of class time asked, "Approximately how 

many minutes per week does this class meet regularly (not including lab periods)?" (F2T2_10). 

A second question about time for laboratories asked, "Approximately how many minutes per week 

does this class have lab sessions?" (F2T2_11). Both questions asked the teacher to write in the 

number of minutes. 

Instructional Emphases: These items asked teachers, "In this math (science) class, how much emphasis 

do you give to each of the following objectives?" Response options included (1) None, (2) Minor, 

(3) Moderate, and (4) Major. For mathematics, the objectives were: 

• Understanding the nature of proofs (F2T2_14A); 

• Memorizing facts, rules, and steps (F2T2_14B); 

• Learning to represent problem structures in multiple ways (e.g., graphically, algebraically, 

numerically, etc.) (F2T2_14C); 

• Integrating different branches of mathematics (e.g., geometry, algebra) into a unified 

framework (F2T2_14D); 

• Conceiving and analyzing effectiveness of multiple approaches to problem solving 

(F2T2_14E); 

143 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

• Performing calculations with speed and accuracy (F2T2_14F); 

• Showing importance of math in daily life (F2T2_14G); 

• Solving equations (F2T2_14H); 

• Raising questions and formulating conjectures (F2T2_14I); 

• Increasing students' interest in math (F2T2_14J). 

For science, the objectives were: 

• Increasing students' interest in science (F2T2_18A). 

• Leaming and memorizing scientific facts, principles, and rules (F2T2_18B). 

• Leaming scientific methods (F2T2_18C). 

• Preparing students for further study in science (F2T2_18D). 

• Developing problem solving/inquiry skills (F2T2_18E). 

• Developing skills in lab techniques (F2T2_18F). 

• Leaming about application of science to environmental issues (F2T2_18G). 

• Showing the importance of science in daily life (F2T2_18H). 

Time Allocations: Teachers in both subjects were asked to "Indicate about what percent of class time 

is spent in a typical week doing each of the following with this class?" Six response options were 

provided: (1) None, (2) <10%, (3) 10-24%, (4) 25-49%, (5) 50-74%, and (6) 75-100%. For some 

tabulations, these were recoded to the midpoints of the categories, and the variables were treated 

as continuous percent measures. Activities included the following: 

• Providing instruction to the class as a whole (F2T2_12A); 

• Providing instruction to small groups of students (F2T2_12B); 

• Providing instruction to individual students (F2T2_12C); 

• Maintaining order/ disciplining students (F2T2_12D); 

• Administering tests or quizzes (F2T2_12E); 

• Performing routine administrative tasks (e.g., taking attendance, making announcements, 

etc.) (F2T2_12F); 

• Conducting lab periods (F2T2_12G). 

Teaching Methods: Teachers in both subjects were asked, "How often do you use the following teaching 

methods or media?" Five response options were offered: (1) Never/ Rarely, (2) 1-2 Times a 

Month, (3) 1-2 Times a Neek, (4) Almost Every Day, and (5) Every Day. 

• Lecture (F2T213AA); 

• Use computers (F2T213AB); 

• Use audio-visual material (F2T213AC); 

• Have teacher-led whole-group discussion (F2T213AD); 

• Have students respond orally to questions on the subject matter (F2T213AE); 

• Have student-led whole-group discussions (F2T213AF); 

• Have students work together in cooperative groups (F2T213AG); 

• Have students complete individual written assignments or worksheets in class 

(F2T213AH); 

• Have students give oral reports (F2T213AI). 

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Science Class Activities: Science teachers were asked, "How often do you do each of the following 

activities in this science class?" Response options were (1) Never/ Rarely, (2) 1-2 Times a Month, 

(3) 1-2 Times a Week, (4) Almost Every Day, and (5) Every Day. The activities listed were: 

• Have students do an experiment or obsexvation individually or in small groups 

(F2T2_19A). 

• Demonstrate an experiment or lead students in systematic obseivations (F2T2_19B). 

• Require students to turn in written reports on experiments or obseivations (F2T2_19C). 

• Discuss current issues and events in science (F2T2_19D). 

• Have students use computers for data collection and analysis (F2T2_19E). 

• Use computers for demonstrations/simulations (F2T2_19F). 

• Have students give oral reports (F2T2_19G). 

• Have students independently design and conduct their own science projects (F2T2_19H). 

• Discuss career opportunities in scientific and technological fields (F2T2_19I). 

• Discuss controversial inventions and technologies (F2T2_19J). 

Amount of Homework Assigned: Teachers in both subjects were asked, "Approximately how much 

homework do you typically assign each day to this class?" Responses were recorded in minutes 

per day (F2T2_8). 

Composite variables created to characterize mathematics instruction: 

• Emphasis on higher-order thinking skills (0;=.75), calculated by taking the mean of 

• Learning to represent problem structures in multiple ways (e.g., graphically, 

algebraically, numerically, etc.) (F2T2_14C); 

• Integrating different branches of mathematics (e.g., geometry, algebra) into a 

unified framework (F2T2_14D); 

• Conceiving and analyzing effectiveness ofmultiple approaches to problem solving 

(F2T2_14E); 

• Raising questions and formulating conjectures (F2T2_14I). 

• Emphasis on the relevance of math ( 0;=.58), calculated by taking the mean of 

• Showing importance of math in daily life (F2T2_14G); 

• Increasing students' interest in math (F2T2_14J). 

Emphasis on mechanical skills (0;=.42), calculated by taking the mean of 

• Memorizing facts, rules, and steps (F2T2_14B); 

• Performing calculations with speed and accuracy (F2T2_14F); 

• Solving equations (F2T2_14H). 

Composite variables created to characterize science instruction: 

• Emphasis on inquiry skills ( 0;=.63), calculated by taking the mean of 

• Learning scientific methods (F2T2_18C). 

• Preparing students for further study in science (F2T2_18D). 

• Developing problem solving/inquiry skills (F2T2_18E). 

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• Developing skills in lab techniques (F2T2_18F). 

• Emphasis on relevance of science (a=.65), calculated by taking the mean of 

• Learning about application of science to environmental issues (F2T2_18G). 

• Showing the importance of science in daily life (F2T2_18H). 

• Use of labs in science (a=.70), calculated by taking the mean of 

• Conducting lab periods (F2T2_12G); 

• Developing skills in lab techniques (F2T2_18F). 

• Have students do an experiment or observation individually or in small groups 

(F2T2_19A). 

• Require students to turn in written reports on experiments or observations 

(F2T2_19C). 

• Frequency of computer usage (a=.88), calculated by taking the mean of 

• Use computers (F2T213AB); 

• Have students use computers for data collection and analysis (F2T2_19E). 

• Use computers for demonstrations/simulations (F2T2_19F). 

• Frequency of student presentations in class (a=.76), calculated by taking the mean of 

• Have student-led whole-group discussions (F2T213AF); 

• Have students give oral reports (F2T213AI, asked of both math & science 

teachers); 

• Have students give oral reports (F2T2_19G, asked of science teachers only). 

INDIVIDUAL TEACHER BACKGROUND. 

Education: Teachers were asked, "What were your major and minor fields of study for your bachelor's 

degree?" (F2T4_9Al - F2T4_911, F2T4_9A2 - F2T4_912), and "What were your primary and 

secondary fields of study for your highest graduate degree?" (F2T4 lOA1- F2T41011, F2T410A2 

- F2T410l2). Response options for both questions were identical and included "(b) 

Mathematics," "(c) Natural/physical sciences," and "(d) Life/biological sciences." We combined 

the responses to create two five level typologies, one for math teachers and one for science 

teachers: 

1 = Undergraduate major and primary graduate study in field (i.e., math or science). 

2 = Undergraduate major m: graduate primary study in field, and undergraduate minor 

or graduate secondary study in field. 

3 = Undergraduate major m: graduate primary study in field, but no minor or 

secondary study. 

4 = Undergraduate minor and/or graduate secondary study in field. 

5 = No major or minor in field at either the undergraduate or graduate level. 

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SCHOOL LOCATION AND DEMOGRAPHIC CHARACTERISTICS. 

Region: Region of the country in which the student's second follow-up school was located 

(G12REGON). The four levels of the variable are Northeast, Midwest, South. and West. These 

correspond to the standard U.S. Census regions. 

Urbanicity: Type of school district, diocese, or county in which the student's second follow-up school 

was located (G12URBN3). Schools are classified as (1) urban: located in a central city of one 

of the U.S. Census Metropolitan Statistical Areas (MSA); (2) suburban: located in the area 

surrounding a central city, and within the MSA; and (3) rural: located outside of any MSA. 

School Enrollment Size: Number of students enrolled in 12th grade during the 1991-1992 school year 

(G12ENROL). In order to n01malize the distribution of this variable for the regression analyses, 

the natural logarithm of G12ENROL is used. 

School SES Composition: Principals were asked, "What percentage of the total student body in your 

school receives the following special services?" One of the services listed was "Free or reducedprice school lunch program" (F2C25A). Students are eligible for free school lunches if their 

household is at or below the official U.S. poverty level, and are eligible for reduced lunch if their 

household income is 100-120% of the official poverty level. For present purposes, this variable 

was collapsed in four categories: 1 =0-5%, 2 =6-20%, 3 =21-50%, and 4 =more than 50%. 

School Sector: All schools in the NELS:88 study were classified as either public, Catholic, National 

Association of Independent Schools (NAIS), or other private (G12CTRL2). 

SCHOOL- AND DEPARTMENT-ORGANIZATIONAL CHARACTERISTICS. 

Teacher Coordination. Teachers were asked in the 2nd follow-up questionnaire, "To what extent do you 

agree that each of the following statements describes either a characteristic or enforced policy of 

your department or subject area?" Responses to the following statements were averaged to 

construct a composite measure of teacher coordination. These items show a very similar pattern 

of intercorrelations for science and math teachers. The student-level items have internal 

consistency coefficients of a=.63 in math and a=.73 in science. 

• I am encouraged to be familiar with the contents and specific goals of the courses taught 

by other teachers in my department (F2T3_5C); 

• I am encouraged to coordinate the content of my courses with teachers in my department 

(F2T3_5D); 

• Faculty consultation or approval is needed for changes in course objectives or content 

(F2T3_5E); 

• I am encouraged to coordinate the content of my courses with teachers outside my 

department (F2T3_5F). 

Teachers' Discussions about Instructional Matters: Teachers in both subjects were asked, "How 

frequently do you discuss each of the following issues with other teachers or a department 

advisor?" Response options were (1) Never, (2) Sometimes, and (3) Often. These items share 

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a common factor and were averaged to form a composite measure of collegial discussions. The 

student-level items have an internal consistency of a=.82 in math and a=.82 in science. 

• Adapting material to particular students (F2T3_10B); 

• New instructional techniques in my subject (F2T3_10C); 

• Subject area curriculum (F2T3_10D); 

• Curriculum for a particular course (F2T3_10E); 

• Test content and testing procedures (F2T3_10F); 

• Grading issues (F2T3_10G). 

Control Teacher Has over Content and Methods: Teachers in both subjects were asked, "How much 

control do you feel you have IN YOUR CLASSROOM over each of the following areas of your planning 

and teaching?" Response options ranged from No control=l to Complete control=6. The items factored 

into two sets, control over content (a=.73 in math and a=.69 in science) and control over methods (a=.66 

in math and a=.64 in science). The content items include: 

• Selecting textbooks and other instructional materials (F2T3_1A); 

• Selecting content, topics, and skills to be taught (F2T3_1B). 

The control over methods items include: 

• Selecting teaching techniques (F2T3_1C); 

• Disciplining students (F2T3_1D); 

• Determining amount of homework (F2T3_1E). 

Principal's Leadership. Teachers in both subjects were asked, "To what extent do you agree that each 

of following statements describes a characteristic or enforced policy of your school or school 

administrator?" Response options are l=Strongly disagree, 2=Disagree, 3=Agree, and 4=Strongly agree. 

The following nine items were averaged to construct composite measures, with student-level internal 

consistencies of a=.86 in math and a=.86 in science: 

• The academic standards at this school are too low (F2T3_7A, reverse coded); 

• There is broad agreement among the entire school faculty about the central mission of the 

school (F2T3_7B); 

• The school administrator knows what kind of school he/she wants and has communicated 

it to the staff (F2T3_7C); 

• The school administrator deals effectively with pressures from outside the school (parents, 

school board, budgetary) that might otherwise affect my teaching (F2T3_7D); 

• The school administrator knows the problems faced by staff (F2T3_7E); 

• Necessary materials (e.g., textbooks, supplies, copy machine) are readily available as 

needed by the staff (F2T3 _ 7F); 

• Staff members are recognized for a job well done (F2T3_7G); 

• Grading practices are consistent and fair (F2T3_7H); 

• Rules against cheating are actively enforced (F2T3_7I). 

School Graduation Requirements: Principals were asked in 1992 if students are required to pass a 

minimum competency tests in math and science. In 1990, the principals were asked to indicate the 

number of math and science courses students had to complete in order to graduate. 

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• math is included on a minimum competency test for 12th grade (F2C45A); 

• science is included on a minimum competency test for 12th grade (F2C45B); 

• amount of math course-work required for graduation (F1C70B); 

• amount of science course-work required for graduation (F1C70C). 

Accountability for Student Achievement: Principals were asked in 1992, "How much influence do you 

feel each of the following factors has on how your superiors evaluate your performance?" One factor was 

"The performance of your school's students on standardized tests." Response options were l=No 

influence, 2=Minor influence, and 3=Great deal of influence (F2C62A). 

In 1990, the principals were asked whether the state or local district offers a financial award or 

recognition to schools for raising student achievement levels (F1C89). 

INDIVIDUAL STUDENT ACHIEVEMENT. Scores on the NELS:88 1992 math and science 

achievement tests are used as the dependent variables in the analysis presented in Chapter V. All of the 

equations include the 1990 test scores as independent variables. 

Composite Achievement Scores: First and second follow-up achievement scores based on IRT-estimated 

number right: 

• mathematics (F12XMIRR and F22XMIRR); 

• science (F12XSIRR and F22XSIRR). 

Probability of Proficiency Scores & Proficiency Levels: The probability of proficiency scores index 

the likelihood that the student has mastered different levels of achievement. The proficiency level 

variables are dichotomous indicators of whether the student's probability of proficiency exceeds 

. 75 for the skill level in question. The first and second follow-up proficiency probability and 

levels for math and science are defined in the NELS:88 second follow-up codebook as follows: 

• Math Level 1: Simple arithmetical operations on whole numbers; essentially single step 

operations which rely on rote memory (F22XMPP1 & F22XMPL1); 

• Math Level 2: Simple operations with decimals, fractions, powers and roots (F22XMPP2 

& F22XMPL2); 

• Math Level 3: Simple problem solving, requmng the understanding of low level 

mathematical concepts (F22XMPP3 & F22XMPL3); 

• Math Level 4: Understanding of intermediate level mathematical concepts and/or having 

the ability to formulate multi-step solutions to word problems (F22XMPP4 & 

F22XMPL4); 

• Math Level 5: Proficiency in solving complex multi-step word problems and/or the ability 

to demonstrate knowledge of mathematics material found in advanced mathematics 

courses (F22XMPP5 & F22XMPL5); 

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• Highest Level of Math Proficiency, defined by combining the dichotomous proficiency 

level indicators to create a single index (F22XMPRO); 

• Science Level 1: Understanding of everyday science concepts; "common knowledge" that 

can be acquired in everyday life (F22XSPP1 & F22XSPL1); 

• Science Level 2: Understanding of fundamental science concepts upon which more 

complex science knowledge can be built (F22XSPP2 & F22XSPL2); 

• Science Level 3: Understanding of relatively complex scientific concepts; typically 

requiring an additional problem-solving step (F22XSPP3 & F22XSPL3); 

• Highest Level of Science Proficiency, defined by combining the dichotomous proficiency 

level indicators to create a single index (F22XSPRO); 

Test Quartiles: Used as a measure of student's academic background. These variables were constructed 

by grouping students into quartiles of the distribution of the first follow-up mathematics and 

science IRT-estimated number-right scores (math: F12XMQ, science: F12XSQ). 

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Appendix C: 

Identifying Courses in the NELS:88 

2nd Follow-up Teacher Data 

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Appendix C: Identifying Courses in the NELS:88 2nd Follow-up Teacher Data 

The NELS:88 second follow-up data have three different course-type variables, each with different 

strengths and weaknesses. One measure is the subject matter of the courses as identified in the student 

transcripts; we examined the numbers of students in each of these course types in Chapter I. Ability levels 

of the mathematics curriculum usually follow the subject designations of classes quite closely and range 

from pre-algebra to algebra 1, geometry, algebra 2, trigonometry, pre-calculus, and calculus. The students 

for whom teacher data were collected were distributed across these levels as follows: 

basic (basic, general, applied, 

& pre-algebra) . . . . . . . . . . . . . . . 594 10.3 

algebra 1 . . . . . . . . . . . . . . . . . . . . . . . . 204 3.5 

geometry . . . . . . . . . . . . . . . . . . . . . . . . 385 6.7 

algebra 2 . . . . . . . . . . . . . . . . . . . . . . . . 641 11.1 

advanced (trigonometry, 

pre-calculus, 

probability & statistics . . . . . ... . 1,762 30.6 

calculus ........................ . 789 13.7 

transcript, but can't identify . . . . . . . . . . . 1,095 19.0 

missing transcript data . . . . . . . . . . . . . . . 281 4.9 

5,751 100.0% 

Levels in science are somewhat less clearly linked to subject areas, but generally correspond to 

biology, chemistry, physics, and advanced laboratory courses. 

basic - survey 270 7.0 

biology 1 or bio. specialty 646 16.6 

chemistry 1 or chem. specialty 518 13.3 

physics 1 or physics specialty 1,007 25.9 

specialized survey 46 1.2 

advanced biology 229 5.9 

advanced chemistry or physics 243 6.3 

transcript, but can't identify 713 18.4 

missing transcript data 211 5.4 

3,883 100.0% 

While in many respects optimal, the subject designations from the transcript file were not directly 

linked to the second follow-up teacher data, and some disjunctures between the files make the linkage 

difficult for many students. As the figures above show, 19 percent of the math students and 18.4 percent 

of the science students lack sufficient infonnation to detennine which one of the courses on the student's 

transcript the teacher was referencing. Another 4.9 percent of the math students and 5.4 percent of the 

science students had no transcript data available. Despite their richness and theoretical utility, the missing 

data for 24 percent of the cases renders the transcript data unusable as a means of characterizing the 

courses which the teachers described unless further archival work and coding is completed. 

The other available measures refer mainly to the achievement or ability level of the classes. One 

measure is the teacher's report of the "track" designation of the class. Prior research has mainly 

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conceptualized high school curriculum differentiation in terms of three tracks: vocational, collegepreparatory, and general. That scheme has been mainly used to classify students, rather than classes. In 

fact, recent studies have called that schema into question, because the traditional categories do not 

correspond to distinct courses within particular subjects. In mathematics, virtually all of the courses taken 

by 12th graders are encompassed by algebra, geometry, trigonometry, precalculus, and calculus. But 

which of these are vocational, college-preparatory, and general? The NELS:88 second follow-up survey 

answered this question by asking the math and science teachers to categorize each of their courses as one 

of five different tracks (F2T2_3). Students are distributed among the tracks as follows: 

Math Science 

Remedial 5 2 

General 21 25 

Vocational, Technical, Business 6 3 

College Prep or Honors 59 61 

AP 9 9 

100% 100% 

The strength of this scheme is that it maps the courses onto a familiar set of categories. However, the 

meanings of the "general," "vocational," and "college prep" tracks are less than obvious when one focuses 

on science and mathematics, and it is conceivable that teachers interpreted these rubrics in quite different 

ways. The meanings of "remedial" and "AP," in contrast, are much less ambiguous and thus more useful. 

Yet another measure of the type of the class comes from teacher responses to a question asking 

about the achievement level of the students in the class compared with the average 12th grade student in 

the school as a whole (F2T2_4). The distribution of students across the four response options was as 

follows: 

Math Science 

Higher achievement levels 47 56 

Average achievement levels 31 26 

Lower achievement levels 14 8 

Widely differing achievement levels 8 9 

100% 100% 

The advantage of this variable is that it directly taps the achievement or ability grouping dimension of 

curriculum differentiation. One possible problem for some purposes is that the levels of the classes are 

defined in reference to the school, as opposed to a less contextualized, more absolute standard. The 

relative level of achievement in a given class may be high in relation to a low-achieving senior class, but 

only average or below compared to seniors across the country. Another problem is that the question is 

"double-barreled": the response options mix two dimensions, the central tendency and the dispersion. The 

fourth response option, "widely differing," could in principle pick up classes at high, average, or low mean 

achievement levels; but courses which teachers describe as "high," "average," or "low" could also have 

widely differing levels of achievement. One obvious shortcoming is that the response options do not 

discriminate among the roughly 50 percent of students in classes with above-average achievement levels. 

Most senior mathematics and science classes are quite selective, taken by students seeking admission in 

more demanding college programs. Despite being "above average," the average achievement levels of 

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Experiences in Science and Mathematics 

these classes are often very different. In mathematics, for example, the algebra 2, trigonometry, analytic 

geometry, and calculus classes taken by seniors are all likely to have above-average achievement levels 

in many high schools. 

Since the transcript-derived course data have an unacceptably high number of missing data, we 

confined our efforts to measuring only the other dimension, the achievement or ability level of the classes. 

Each of the latter two measures has its strengths and weaknesses, and we thus developed a composite 

typology drawing mainly on the achievement-level variable, but distinguishing classes described as 

"remedial" and "AP" on the track variable. Since the number of remedial science students was so small, 

these students were combined with the "below average" category in science. For the science and 

mathematics classes described as having "widely differing" levels of achievement and which were not also 

classified as remedial or AP, we assumed the level was "average." The distribution of the resulting 

composite variable is shown in Table A2. l and Figure 2.1 in the text. 

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Appendix D: 

Regression Tables 

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Table D3.1. Estimated effects of student background variables and the achievement level of the student 

class on teacher-reported mathematics instructional variables from OLS regressions: 1992. 

Dependent 

Variable Variable 

Model 1 Model 2 

Coeff. S.E. Coeff. S.E. 

% class 

time for 

whole-group 

instruction 

Intercept 43.805 7.602 57.33 10.985 

Female (vs. male) 0.025 1.301 -0.654 1.177 

Asian (vs. white) 0.6 2.058 -0.259 1.943 

Hispanic (vs. white) -1.054 2.472 0.01 2.131 

Black (vs. white) 3.191 1.668 4.47 1.71 

American Indian (vs. white) 4.345 4.63 4.827 4.207 

SES 1.783 1.058 0.724 1.034 

Achievement Level: AP (vs. avg) 7.068 2.406 

Achievement Level: Above Avg (vs. avg) 2.879 1.507 

Achievement Level: Low (vs. avg) -7.715 2.634 

Achievement Level: Remedial (vs. avg) -16.818 3.467 

R-Squared 0.006 0.06 

N 5,222 5,200 

Class time 

spent on 

whole-group 

instruction 

Intercept 4.219 0.338 4.956 0.509 

Female (vs. male) -0.008 0.057 -0.037 0.05 

Asian (vs. white) 0.034 0.086 0.001 0.081 

Hispanic (vs. white) -0.076 0.13 -0.023 0.105 

Black (vs. white) 0.149 0.069 0.205 0.071 

American Indian (vs. white) 0.184 0.196 0.207 0.173 

SES 0.076 0.045 0.028 0.044 

Achievement Level: AP (vs. avg) 0.3 0.098 

Achievement Level: Above Avg (vs. avg) 0.122 0.062 

Achievement Level: Low (vs. avg) -0.335 0.115 

Achievement Level: Remedial (vs. avg) -0.878 0.217 

R-Squared 0.007 0.07 

N 5,222 5,200 

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Table D3.1. Estimated effects of student background variables and the achievement level of the student 

class on teacher-reported mathematics instructional variables from OLS regressions: 1992. 

(Cont'd) 

Dependent 

Variable Variable 

Model 1 Model 2 

Coeff. S.E. Coeff. S.E. 

% class 

time for 

discipline 

Intercept 5.637 4.25 10.163 7.125 

Female (vs. male) -0.752 0.799 -0.271 0.747 

Asian (vs. white) -1.676 0.702 -0.901 0.596 

Hispanic (vs. white) 1.051 1.597 0.872 1.62 

Black (vs.white) 4.203 2.183 3.68 2.035 

American Indian (vs. white) -2.283 0.915 -2.546 0.921 

SES -1.238 0.465 -0.697 0.48 

Achievement Level: AP (vs. avg) -5.177 0.793 

Achievement Level: Above Avg (vs. avg) -3.315 0.93 

Achievement Level: Low (vs. avg) 2.969 1.797 

Achievement Level: Remedial (vs. avg) 1.642 1.714 

R-Squared 0.021 0.053 

N 5,164 5,142 

Class time 

spent 

maintaining order 

Intercept 1.818 0.295 2.393 0.447 

Female (vs. male) -0.083 0.051 -0.034 0.047 

Asian (vs. white) -0.165 0.069 -0.079 0.059 

Hispanic (vs. white) 0.073 0.093 0.056 0.098 

Black (vs. white) 0.307 0.128 0.25 0.116 

American Indian (vs. white) -0.126 0.123 -0.156 0.112 

SES -0.098 0.033 -0.04 0.031 

Achievement Level: AP (vs. avg) -0.591 0.067 

Achievement Level: Above Avg (vs. avg) -0.34 0.058 

Achievement Level: Low (vs. avg) 0.288 0.101 

Achievement Level: Remedial (vs. avg) 0.139 0.128 

R-Squared 0.028 0.104 

N 5,164 5,142 

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Table D3.1. Estimated effects of student background variables and the achievement level of the student 

class on teacher-reported mathematics instructional variables from OLS regressions: 1992. 

(Cont'd) 

Dependent 

Variable Variable 

Model 1 Model 2 

Coeff. S.E. Coeff. .S.E. 

Homework 

minutes/ 

day 

Intercept 21.402 5.378 2.456 7.177 

Female (vs. male) 2.671 0.963 1.567 0.946 

Asian (vs. white) 4.196 1.416 1.77 1.169 

Hispanic (vs. white) 5.62 1.651 6.219 1.65 

Black (vs. white) -0.199 1.427 1.387 1.286 

American Indian (vs. white) -2.021 3.32 -1.122 2.881 

SES 3.696 0.751 2.095 0.803 

Achievement Level: AP (vs. avg) 18.824 1.737 

Achievement Level: Above Avg (vs. avg) 8.051 1.175 

Achievement Level: Low (vs. avg) -3.576 1.685 

Achievement Level: Remedial (vs. avg) -7.074 1.52 

R-Squared 0.038 0.174 

N 5,603 5,581 

Emphasis 

on higherorder 

thinking 

skills 

Intercept 2.842 0.168 3.065 0.259 

Female (vs. male) 0.059 0.028 0.032 0.029 

Asian (vs. white) 0.06 0.051 0.02 0.044 

Hispanic (vs. white) 0.038 0.05 0.065 0.059 

Black (vs. white) 0.078 0.05 0.127 0.045 

American Indian ( vs. white) 0.104 0.099 0.116 0.086 

SES 0.124 0.023 0.085 0.023 

Achievement Level: AP (vs. avg) 0.293 0.045 

Achievement Level: Above Avg (vs. avg) 0.134 0.035 

Achievement Level: Low (vs. avg) -0.291 0.049 

Achievement Level: Remedial (vs. avg) -0.39 0.102 

R-Squared 0.027 0.11 

N 5,617 5,599 

Key: Model 1: student background variables only. 

Model 2: student background variables plus achievement level of the class. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

161 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D3.2. Estimated effects of student background variables and the achievement level of the student 

class on teacher-reported science instructional variables from OLS regressions: 1992. 

Dependent 

Variable 

Variable 

Model 1 Model 2 

Coeff. S.E. Coeff. S.E. 

% class 

time for 

whole-class 

instruction 

Intercept 77.507 15.855 73.508 17.961 

Female (vs. male) 2.288 1.699 1.955 1.656 

Asian (vs. white) -1.646 2.228 -2.606 2.076 

Hispanic ( vs. white) -2.401 2.197 -2.616 2.112 

Black (vs. white) 1.012 2.246 0.736 2.17 

American Indian (vs. white) -25.222 13.841 -25.507 14.042 

SES 0.978 0.986 -0.056 0.993 

Achievement Level: AP (vs. avg) 5.959 2.414 

Achievement Level: Above Avg 

(vs. avg) 

2.631 2.239 

Achievement Level: Low (vs. avg) -3.464 2.387 

R-Squared 0.022 0.031 

N 3,460 3,444 

Class time 

spent on 

whole-class 

instruction 

Intercept 6.187 1.001 

- 5.999 1.083 

Female (vs. male) 0.085 0.075 0.072 0.073 

Asian (vs. white) -0.062 0.096 -0.104 0.09 

Hispanic (vs. white) -0.1 0.095 -0.108 0.092 

Black (vs. white) 0.057 0.096 0.045 0.093 

American Indian (vs. white) -1.648 0.917 -1.659 0.923 

SES 0.034 0.044 -0.009 0.044 

Achievement Level: AP (vs. avg) 0.258 0.106 

Achievement Level: Above Avg 

(vs. avg) 

0.109 0.099 

Achievement Level: Low (vs. avg) -0.133 0.105 

R-Squared 0.041 0.049 

N 3,460 3,444 

162 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D3.2. Estimated effects of student background varfables and the achievement level of the student 

class on teacher-reported science instructional variables from OLS regressions: 1992. 

(Cont'd) 

Dependent 

Variable 

Variable 

Model 1 Model 2 

Coeff. S.E. Coeff. S.E. 

% class 

time for 

discipline 

Intercept -12.427 8.913 -10.515 9.369 

Female (vs. male) 0.019 0.563 0.252 0.581 

Asian (vs. white) -0.33 0.506 0.175 0.544 

Hispanic (vs. white) 0.871 0.745 1.042 0.799 

Black (vs. white) 2.105 1.356 2.216 1.297 

American Indian (vs.white) 14.77 8.166 14.866 8.309 

SES -1.186 0.321 -0.572 0.331 

Achievement Level: AP (vs. avg) -3.82 0.573 

Achievement Level: Above Avg 

(vs. avg) 

-1.604 0.651 

Achievement Level: Low (vs. avg) 2.971 1.245 

R-Squared 0.049 0.071 

N 3,434 3,418 

Class time 

spent 

maintaining order 

Intercept 0.514 0.637 1.011 0.695 

Female (vs. male) -0.007 0.046 0.019 0.046 

Asian (vs. white) 0.003 0.055 0.077 0.057 

Hispanic (vs. white) 0.051 0.071 0.079 0.078 

Black (vs. white) 0.119 0.106 0.134 0.096 

American Indian (vs. white) 1.076 0.576 1.09 0.596 

SES -0.149 0.028 -0.071 0.029 

Achievement Level: AP (vs. avg) -0.546 0.058 

Achievement Level: Above Avg 

(vs. avg) 

-0.236 0.058 

Achievement Level: Low (vs. avg) 0.236 0.096 

R-Squared 0.056 0.111 

N 3,434 3,418 

163 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D3.2. Estimated effects of student background variables and the achievement level of the student 

class on teacher-reported science instructional variables from OLS regressions: 1992. 

(Cont'd) 

Dependent 

Variable 

Variable 

Model 1 Model 2 

Coeff. S.E. Coeff. S.E. 

Homework 

minutes/ 

day 

Intercept -2.261 8.81 -29.681 9.141 

Female (vs. male) 0.814 0.98 0.115 0.935 

Asian (vs. white) 7.44 1.877 4.186 1.839 

Hispanic (vs. white) 6.177 2.599 4.856 2.28 

Black (vs. white) 3.771 1.936 3.423 1.876 

American Indian (vs. white) 12.711 7.066 12.574 6.491 

SES 3.868 0.661 1.062 0.631 

Achievement Level: AP (vs. avg) 24.033 2.801 

Achievement Level: Above Avg 

(vs. avg) 

8.09 1.192 

Achievement Level: Low (vs. avg) -3.534 1.375 

R-Squared 0.038 0.181 

N 3,744 3,726 

Lab 

minutes/ 

week 

Intercept 38.991 12.895 16.387 19.849 

Female (vs. male) 1.402 2.649 1.137 2.536 

Asian (vs. white) 6.847 4.428 3.088 4.521 

Hispanic (vs. white) 5.315 4.123 0.306 3.563 

Black (vs. white) 5.755 4.751 4.853 4.641 

American Indian (vs. white) -3.991 5.598 -4.651 4.794 

SES 3.298 1.642 -0.31 1.749 

Achievement Level: AP (vs. avg) 26.469 9.02 

Achievement Level: Above Avg 

(vs. avg) 

10.959 3.38 

Achievement Level: Low (vs. avg) -9.68 5.065 

R-Squared 0.004 0.04 

N 3,459 3,442 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D3.2. Estimated effects of student background variables and the achievement level of the student 

class on teacher-reported science instructional variables from OLS regressions: 1992. 

(Cont'd) 

Dependent 

Variable 

Variable 

Model 1 Model 2 

Coeff. S.E. Coeff. S.E. 

Emphasis 

on lab use 

Intercept 3.001 0.308 2.846 0.395 

Female (vs. male) 0.017 0.043 0.001 0.04 

Asian (vs. white) -0.022 0.057 -0.037 0.057 

Hispanic (vs. white) 0.079 0.067 0.051 0.059 

Black (vs. white) -0.02 0.066 -0.023 0.063 

American Indian (vs. white) -0.252 0.242 -0.261 0.27 

SES 0.037 0.025 -0.001 0.027 

Achievement Level: AP (vs. avg) 0.158 0.095 

Achievement Level: Above Avg 

(vs. avg) 

0.201 0.051 

Achievement Level: Low (vs. avg) -0.209 0.074 

R-Squared 0.005 0.04 

N 3,834 3,817 

Emphasis 

on inquiry 

skills 

Intercept 3.196 0.158 2.923 0.199 

Female (vs. male) 0.001 0.029 -0.026 0.028 

Asian (vs. white) -0.0ll 0.04 -0.043 0.039 

Hispanic (vs. white) 0.005 0.078 -0.022 0.075 

Black (vs. white) 0.049 0.055 0.04 0.05 

American Indian (vs. white) 0.067 0.08 0.049 0.072 

SES 0.071 0.021 0.017 0.02 

Achievement Level: AP (vs. avg) 0.294 0.052 

Achievement Level: Above Avg 

(vs. avg) 

0.25 0.04 

Achievement Level: Low (vs. avg) -0.256 0.058 

R-Squared O.Ql 0.109 

N 3,596 3,579 

165 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D3.2. Estimated effects of student background variables and the achievement level of the student 

class on teacher-reported science instructional variables from OLS regressions: 1992. 

(Cont'd) 

Dependent 

Variable 

Variable 

Model 1 Model2 

Coeff. S.E. Coeff. S.E. 

Use of 

computers 

Intercept 1.358 0.219 1.105 0.251 

Female (vs. male) -0.026 0.038 -0.029 0.038 

Asian (vs. white) 0.034 0.058 0.025 0.06 

Hispanic (vs. white) -0.017 0.062 -0.018 0.061 

Black (vs. white) 0.175 0.082 0.178 0.08 

American Indian (vs. white) -0.155 0.133 -0.156 0.14 

SES 0.068 0.024 0.051 0.025 

Achievement Level: AP (vs. avg) 0.116 0.064 

Achievement Level: Above Avg 

(vs. avg) 

0.103 0.047 

Achievement Level: Low (vs. avg) -0.01 0.064 

R-Squared 0.014 0.021 

N 3,828 3,811 

Use of 

Student 

Presentations 

Intercept 0.981 ·0.155 0.912 0.186 

Female (vs. male) 0.019 0.028 0.02 0.028 

Asian (vs. white) -0.031 0.043 -0.045 0.044 

Hispanic (vs. white) 0.061 0.05 0.061 0.051 

Black (vs. white) 0.16 0.06 0.16 0.06 

American Indian (vs. white) 0.181 0.086 0.188 0.089 

SES 0.027 0.019 0.021 0.019 

Achievement Level: AP (vs. avg) 0.091 0.06 

Achievement Level: Above Avg 

(vs. avg) 

-0.017 0.038 

Achievement Level: Low (vs. avg) 0.001 0.054 

R-Squared 0.01 0.013 

N 3,833 3,816 

Key: Model 1: student background variables only. 

Model 2: student background variables plus achievement level of the class. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

166 
Table D4.1. Logistic regression estimates of the effects of student background and school variables on the odds of students taking 

mathematics and science in 1991-1992 school year: 1992. 

Mathematics Model 1 Mathematics Model 2 Science Model 1 Science Model 2 

Variable 

Coeff. S.E Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Intercept I 0.812 I 0.134 I -0.342 I 0.519 I -0.002 I 0.108 I -1.15 I 0.563 

I Student Background Variables 

SES Composite 0.418 0.051 0.419 0.054 0.485 0.054 0.511 0.052 

Black (vs. white) 0.366 0.136 0.381 0.151 0.075 0.119 -0.013 0.135 

Hispanic (vs. white) 0.317 0.131 0.222 0.136 -0.024 0.125 -0.074 0.149 

Asian (vs. white) 0.601 0.157 0.491 0.171 0.328 0.156 0.301 0.162 

American Indian (vs. white) 0.177 0.274 0.014 0.254 0.305 0.414 -0.064 0.32 

-

Female (vs. male) -0.218 0.069 -0.224 0.066 -0.047 0.067 -0.103 0.064 

I Urbani city 

Urban (vs. suburban) 0.086 0.112 0.104 0.126 0.21 0.109 0.01 0.128 

Rural (vs. suburban) 0.005 0.097 0.03 0.096 -0.023 0.084 -0.07 0.095 

I Region of U.S 

Midwest (vs. Northeast) -0.158 0.115 -0.044 0.124 -0.297 0.115 -0.234 0.124 

South (vs. Northeast) -0.061 0.128 -0.039 0.135 -0.572 0.117 -0.525 0.128 

West (vs. Northeast) -0.407 0.13 -0.304 0.147 -0.189 0.124 -0.092 0.145 

I School control type 

Catholic (vs. public) 0.458 0.191 0.233 0.211 0.412 0.2 0.396 0.238 

NAIS (vs. public) 1.256 0.429 0.917 0.455 1.511 0.372 1.041 0.334 

Other Private (vs. public) 0.075 0.362 -0.56 0.363 0.056 0.442 -0.39 0.433 

I 

I 

I 

I 

I 
00 

,_. 

O'I 

Table D4.l. Logistic regression estimates of the effects of student background and school variables on the odds of students taking 

mathematics and science in 1991-1992 school year: 1992. (Cont'd) 

Variable 

Mathematics Model 1 Mathematics Model 2 Science Model 1 Science Model 2 

Coeff. S.E Coeff. S.E. Coeff. S.E. Coeff. S.E. 

Percent students eligible for subsidized lunch 

6-20% (vs. 0-5%) -0.062 0.123 -0.166 0.117 0.065 0.108 0.1 0.11 

21-50% (vs. 0-5%) -0.151 0.126 -0.33 0.125 0.224 0.11 0.214 0.124 

51 %+ (vs. 0-5%) 0.05 0.17 -0.145 0.177 0.29 0.16 0.161 0.189 

I School organizational variables 

12th grade enrollment size 

(natural log) 

0.05 0.065 0.06 0.073 

Importance of test scores in 

evaluation of principal 

0.036 0.064 0.011 0.066 

School rewarded for high 

achievement vs. not 

-0.052 0.111 -0.003 0.113 

School has minimum 

competency requirement for 

math/science vs. not 

-0.113 0.1 -0.287 0.096 

Years math/science required 

for graduation 

0.214 0.074 0.22 0.069 

R-Squared 0.04 0.045 0.057 0.061 

N 13,743 9,886 13,743 9,917 

I 

Key: Model 1: all variables listed except school organizational variables. 

Model 2: school organizational variables included. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88). 
Table D4.2. Estimated effects of student background and school variables on mathematics instruction variables, from OLS 

regressions: 1992. 

Independent 

Variables 

Higher-order 

thinking 

Emphasis: 

practical 

applications 

Emphasis: 

mechanical 

operations 

Minutes/day of 

homework 

assigned 

% class time 

devoted to wholeclass 

% class time 

devoted to 

discipline 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

Intercept 1.718 0.526 2.863 0.615 2.511 0.471 10.847 16.096 -3.758 19.021 15.521 8.723 

I Student Socioeconomic Background I 

SES Composite 0.145 0.022 -0.039 0.021 0.031 0.018 3.89 0.596 2.497 0.818 -1.173 0.375 

I Student Sex (vs. Male) I 

Female I 0.021 I 0.026 I -0.002 I 0.021 I -0.014 I 0.023 I 2.244 I 0.791 I 0.534 1.1 I -0.431 I 0.577 I I I 

I Student Race/Ethnicity (vs. White) I 

Asian 0.078 0.068 -0.065 0.065 0.024 0.051 3.226 1.7 -1.222 2.131 -3.368 1.449 

Hispanic 0.013 0.051 0.13 0.059 -0.003 0.043 0.096 1.422 -4.261 3.437 -0.921 1.929 

Black 0.045 0.048 0.076 0.053 0.088 0.044 0.87 1.507 0.484 2.168 -1.112 1.346 

American Indian -0.033 0.123 -0.258 0.18 0.157 0.128 -8.52 3.342 -1.151 5.221 -3.167 1.99 

I Urbanicity (vs. Suburban) I 

Urban 0.077 0.047 0.03 0.051 -0.019 0.037 1.442 1.502 -2.951 1.902 2.652 1.528 

Rural -0.045 0.048 -0.013 0.049 -0.044 0.044 -1.728 1.398 -1.722 2.096 -0.113 1.009 
0 

...... Table D4.2. Estimated effects of student background and school variables on mathematics instruction variables, from OLS -..J 

regressions: 1992. (Cont'd) 

Independent 

Variables 

Higher-order 

thinking 

Emphasis: 

practical 

applications 

Emphasis: 

mechanical 

operations 

Minutes/day of 

homework 

assigned 

% class time 

devoted to wholeclass 

% class time 

devoted to 

discipline 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

IRegion of U.S. (vs. Northeast) I 

Midwest 0.021 0.055 -0.056 0.061 -0.004 0.045 4.826 1.392 -6.87 2.369 -0.579 0.874 

South 0.074 0.054 0.115 0.055 0.151 0.042 2.737 1.434 -5.395 2.329 0.54 0.874 

West -0.08 0.061 -0.003 0.068 -0.021 0.046 4.481 1.472 -11.775 2.535 1.788 1.562 

I School Control Type (vs. Public) I 

Catholic -0.026 0.081 -0.226 0.102 -0.071 0.077 -0.066 2.673 14.668 3.064 -1.918 1.708 

NAIS -0.116 0.088 -0.103 0.148 -0.267 0.124 4.196 3.307 16.906 3.75 -2.307 1.558 

Other Private -0.016 0.108 -0.204 0.177 -0.102 0.216 4.361 6.373 15.771 4.311 1.706 4.028 

% Students Receiving Federal Lunch (vs. 0-5%) 

6-20% -0.02 0.048 0.013 0.053 0.043 0.041 -1.175 1.424 3.837 1.874 0.374 0.622 

21-50% 0.002 0.055 0.095 0.052 0.127 0.044 -1.635 1.56 6.105 2.185 0.395 0.743 

51%+ 0.135 0.08 -0.074 0.096 0.123 0.072 -0.544 2.736 10.166 3.723 5.649 4.372 

Number 12th Graders Enrolled in the School 

Ln( enrollment) -0.018 0.025 -0.092 0.033 -0.033 0.025 -1.125 0.848 3.276 1.065 0.038 0.39 
Table D4.2. Estimated effects of student background and school variables on mathematics instruction variables, from OLS 

regressions: 1992. (Cont'd) 

I 

Independent Higher-order Emphasis: Emphasis: Minutes/day of % class time % class time 

Variables thinking practical mechanical homework devoted to whole- devoted to 

applications operations assigned class discipline 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. · S.E. Coeff. S.E. Coeff. S.E. 

Accountability of Principals for Achievement Outcomes 

Importance of 0.035 0.025 0.016 0.028 0.001 0.023 0.929 0.875 -0.83 1.157 -1.368 0.904 

student perfonnance 

and standardized 

tests on evaluation 

of principi,u 

Effective schools -0.095 0.044 -0.021 0.049 -0.005 0.036 1.372 1.239 0.262 1.919 1.138 0.67 

recognized (0-1) 

I Graduation Requirements 

Must pass math 0.037 0.038 0 0.042 0.002 0.033 -0.377 1.099 4.534 1.57 1.106 0.811 

min. competency 

(0-1) 

Years of math 

required 

0.023 0.028 0.005 0.034 -0.001 0.025 -0.741 0.772 -2.772 1.06 -0.453 0.425 

--.J 

-
..... 

-.J 

N 

Table D4.2. Estimated effects of student background and school variables on mathematics instruction variables, from OLS 

regressions: 1992. (Cont'd) 

Independent 

Variables 

Higher-order 

thinking 

Emphasis: 

practical 

applications 

Emphasis: 

mechanical 

operations 

Minutes/day of 

homework 

assigned 

% class time 

devoted to wholeclass 

% class time 

devoted to 

discipline 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

School Organizational Characteristics 

Teacher's rating of 

principal's 

leadership 

-0.069 0.037 0.019 0.042 0.017 0.037 0.794 1.135 -0.441 1.506 0.532 0.846 

Teacher influence: 

methods 

0.033 0.026 0.064 0.037 0.021 0.025 0.163 0.738 2.157 1.274 -1.13 0.444 

Teacher influence: 

curriculum 

0.041 0.016 0.03 0.015 -0.003 0.015 0.494 0.49 0.684 0.751 -0.216 0.369 

Teachers coordinate 

content 

0.159 0.038 0.099 0.038 0.033 0.032 0.811 1.025 0.111 1.565 -0.652 0.546 

Teachers discuss 

content w/tchrs 

0.285 0.046 0.239 0.051 0.087 0.045 2.455 1.644 0.052 2.116 0.197 0.889 

R-Squared 0.144 0.1 0.049 0.083 0.076 0.06 

N 3,823 3,823 3,825 3,807 3,807 3,760 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up 

survey. 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D4.3. Estimated effects of student background and school variables on science instruction variables, 

from OLS regressions: 1992. 

Emphasis: Emphasis: Minutes/day of 

Independent inquiry practical Emphasis: facts homework Minutes/week 

Variables learning applications and principles assigned lab work 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

Intercept 1.581 0.643 1.931 0.994 0.672 1.004 22.357 21.921 36.346 46.904 

I Student Socioeconomic Background 

SES Composite 0,078 0.02 -0.042 0.031 -0.014 0.031 3.119 0.667 3.565 .655 

IStudent Sex (vs. Male) 

Female 0.048 0.027 0.036 0.041 0.041 0.043 1.39 1.095 3.42 2.319 

I Student Race/Ethnicity (vs. White) 

Asian 0.025 0.05 -0.148 0.076 -0.087 0.08 9.258 2.249 15.433 4.945 

Hispanic -0.044 0.064 -0.002 0.077 0.069 0.084 0.814 2.512 4.128 5.543 

Black -0.056 0.057 -0.077 0.123 -0.038 0.071 0.5 1.946 4.479 5.115 

American Indian -0.03 0.113 0.158 0.197 0.386 0.209 -6.684 4 -15.138 9.179 

I Urbanicity (vs. Suburban) 

Urban 0.072 0.051 0.209 0.083 -0.006 0.084 1.34 2.271 -2.694 4.423 

Rural 0.062 0.055 0.012 0.076 0.074 0.075 -0.274 1.586 -4.092 5.43 

I Region of U.S. (vs. Northeast) 

Midwest -0.006 0.071 -0.054 0.094 0.267 0.083 -1.962 1.817 -4.062 5.564 

South 0.106 0.D75 0.098 0.097 0.228 0.087 0.878 1.733 -4.91 5.069 

West -0.049 0.067 -0.027 0.111 0.032 0.104 0.011 2.539 -10.209 6.02 

I School Control Type (vs. Public) 

Catholic 0.095 0.087 -0.13 0.132 0.167 0.168 -1.526 3.138 1.119 7.112 

NAIS 0.239 0.107 -0.361 0.187 0.133 0.216 9.079 6.97 19.793 10.876 

Other Private 0.1 0.123 -0.097 0.419 0.053 0.258 -1.738 5.69 -8.568 8.375 

I % Federal Lunch (vs. 0-5%) 

6-20% 0.166 0.055 0.133 0.087 0.078 0.095 -1.169 1.798 6.35 4.223 

21-50% 0.171 0.065 0.179 0.091 -0.006 0.1 -0.534 1.983 6.412 6.227 

51%+ 0.174 0.092 0.079 0.158 -0.021 0.132 1.955 3.385 -6.805 7.556 

I 

I 

I 

I 

I 

I 

I 

173 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D4.3. Estimated effects of student background and school variables on science instruction variables, 

from OLS regressions: 1992. (Cont'd) 

Independent 

Variables 

Emphasis: 

inquiry 

learning 

Emphasis: 

practical 

applications 

Emphasis: facts 

and principles 

Minutes/day of 

homework 

assigned 

Minutes/week 

lab work 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Number 12th Grade Students Enrolled I 

Ln(emollment) 0.007 0.032 -0.05 0.048 0.028 0.046 -1.051 1.081 3.097 2.5 

I School Accountability I 

Eval. by test scores 0.084 0.038 -0.038 0.046 0.051 0.042 0.947 0.912 4.602 2.597 

School recognition -0.015 0.061 0.041 0.096 0.043 0.11 -2.248 1.636 1.949 3.741 

I Graduation Requirements I 

Science min. 

competency -0.02 0.056 0.091 0.085 0.069 0.074 2.059 2.095 -1.443 4.293 

Years science -0.094 0.034 0.01 0.041 0.055 0.045 -2.272 0.916 -5.98 2.529 

ISchool Organizational Characteristics I 

Teachers' rating of 

principal's leadership -0.078 0.037 -0.095 0.054 -0.035 0.059 -2.322 1.344 -2.843 3.747 

Teacher influence: 

methods 0.058 0.029 0.109 0.046 0.008 0.048 0.832 0.978 -0.443 2.462 

Teacher influence: 

curriculum 0.025 0.Q17 -0.001 0.028 0.013 0.023 0.523 0.594 2.779 1.49 

Teachers coordinate 

content 0.035 0.034 0.147 0.057 0.094 0.059 1.897 1.752 3.072 3.154 

Teachers discuss 

content 0.173 0.056 0.273 0.083 -0.115 0.083 0.373 1.987 1.809 4.309 

R-Squared 0.102 0.094 0.044 0.063 0.047 

N 2,493 2,492 2,491 2,463 2,464 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88). 

174 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table 04.3. Effects of school variables on science instruction, from OLS regressions. (Cont'd) 

% class time % class time Frequency of 

Independent Emphasis on devoted to whole- devoted to Frequency of student oral 

Variables lab work class discipline computer use reports 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

Intercept 1.07 0.823 40.579 28.439 3.181 9.089 0.731 0.716 0.967 0.552 

I Student Socioeconomic Background I 

SES Composite 0.062 0.028 0.406 0.949 -1.108 0.257 0.074 0.022 0.017 0.018 

I Student Sex (vs. Male) I 

Female 0.094 0.039 2.191 1.196 0.288 0.425 0.006 0.037 0.045 0.025 

I Student Race/Ethnicity (vs. White) I 

Asian 0.073 0.072 -1.971 2.15 -0.702 0.716 0.139 0.066 0.006 0.048 

Hispanic 0.047 0.076 -3.262 2.245 1.402 1.05 -0.051 0.065 -0.007 0.061 

Black 0.004 0.084 -0.723 2.37 1.547 1.323 0.161 0.09 0.057 0.062 

American Indian -0.04 0.173 -0.807 7.038 0.925 1.493 -0.08 0.084 0.12 0.133 

I Urbanicity (vs. Suburban) I 

Urban -0.015 0.066 2.849 2.437 -1.143 0.726 -0.042 0.062 0.051 0.053 

Rural 0.033 0.084 -3.054 2.763 -0.476 0.782 -0.079 0.065 -0.018 0.049 

I Region of U.S. (vs. Northeast) I 

Midwest -0.015 0.101 2.483 3.155 0.052 0.787 0.006 0.081 -0.037 0.057 

South -0.052 0.098 4.105 3.416 0.328 0.923 -0.061 0.065 0.133 0.056 

West -0.094 0.095 -2.581 3.344 0.027 0.918 -0.165 0.082 0.083 0.061 

I School Control Type (vs. Public) I 

Catholic 0.062 0.109 3.106 4.569 1.086 1.201 -0.125 0.12 -0.16 0.097 

NAIS 0.39 0.157 5.015 4.549 -0.695 1.167 0.188 0.168 -0.119 0.138 

Other Private -0.15 0.16 4.003 10.468 1.776 3.655 -0.247 0.121 0.016 0.243 

I % Federal Lunch (vs. 0-5%) I 

6-20% 0.197 0.074 -3.674 2.203 -0.394 0.646 0.071 0.063 0 0.05 

21-50% 0.221 0.094 -2.415 2.929 0.213 0.798 0.085 0.063 -0.064 0.055 

51%+ 0.048 0.158 3.778 3.641 -0.979 1.023 0.064 0.105 -0.07 0.095 

175 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D4.3. Effects of school variables on science instruction, from OLS regressions. (Cont'd) 

% class time % class time Frequency of 

Independent Emphasis on devoted to whole- devoted to Frequency of student oral 

Variables Jab work class discipline computer use reports 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

INumber 12th Grade Students Enrolled 

Ln(enrollrnent) 0.083 0.043 -0.204 1.444 0.164 0.444 0.04 0.041 -0.051 0.034 

I School Accountability 

Eval. by test scores 0.117 0.048 -1.863 1.689 0.306 0.385 0.021 0.038 -0.05 0.025 

School recognition 0.004 0.053 1.644 2.103 0.93 0.845 -0.068 0.06 -0.101 0.046 

IGraduation Requirements I 

Science min. 

competency -0.133 0.073 3.348 2.545 2.743 1.131 -0.033 0.068 0.068 0.047 

Years science -0.09 0.043 0.194 1.347 0.66 0.426 -0.011 0.037 -0.011 0.028 

I School Organizational Characteristics 

Teachers' rating of 

principal's -0.083 0.052 -2.382 1.861 -0.224 0.644 -0.035 0.054 0.011 0.044 

leadership 

Teacher influence: 

methods 0.022 0.041 3.375 1.564 -0.938 0.456 0.005 0.031 0.016 0.029 

Teacher influence: 

curriculum 0.045 0.023 -0.096 0.887 -0.736 0.276 0.063 0.023 0.004 0.017 

Teachers coordinate 

content O.Dl8 0.049 0.182 1.558 0.581 0.548 0.D25 0.055 0.061 0.036 

Teachers discuss 

content 0.222 0.065 -4.617 2.302 -0.545 0.814 0.17 0.065 0.221 0.054 

R-Squared 0.094 0.052 0.055 0.072 0.074 

N 2,518 2,475 2,446 2,516 2,520 

I 

I 

I 

I 

SOURCE: U.S. Department or Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88). 

176 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D5.1. Effects of student background, school variables, class achievement level, teacher education, 

and instructional variables on sophomore-to-senior achievement growth in mathematics, 

from OLS regressions: 1992. 

Independent Variables 

Model 1 Model 2 Model 3 

Coeff. S.E. Coeff. S.E. Coeff. S.E. 

Intercept 15.363 4.35 16.158 4.711 17.137 4.553 

Sophomore !RT-Estimated Number Right: Math 

ITest Score I 0.866 I 0.014 I 0.862 I 0.Ql5 I 0.848 I 0.014 I 

I Urbanicity (vs. Suburban) I 

Urban 0.151 0.437 -0.176 0.447 -0.063 0.422 

Rural -0.004 0.36 -0.09 0.361 -0.028 0.354 

I Region of the Country (vs. Northeast) I 

Midwest -0.506 0.412 -0.622 0.417 -0.599 0.426 

South -0.589 0.382 -0.574 0.398 -0.456 0.415 

West -1.284 0.466 -1.219 0.485 -1.102 0.5 

I School Control Type (vs. Public) I 

Catholic 0.496 0.7 0.779 0.714 0.524 0.702 

NAIS 0.493 0.658 1.413 0.759 1.133 0.712 

Other Private 0.669 0.853 0.975 0.882 0.625 0.865 

% Students Receiving Subsidized Lunches (vs. 0-5%) 

6-20% -0.053 0.392 -0.18 0.411 -0.191 0.394 

21-50% -0.651 0.342 -0.657 0.355 -0.577 0.36 

51%+ -0.712 0.532 -0.628 0.537 -0.705 0.537 

I Number 12th Grade Students I 

Ln(enrollment) 0.101 0.255 0.201 0.254 0.069 0.252 

I Student Sex (vs. Male) I 

I Female I -1.041 I 0.257 I -1.037 I 0.267 I -1.017 I 0.271 I 

177 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D5.1. Effects of student background, school variables, class achievement level, teacher education, 

and instructional variables on sophomore-to-senior achievement growth in mathematics, 

from OLS regressions: 1992. (Cont'd) 

Independent Variables 

Model 1 Model2 Model3 

Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Student Sex (vs. Male) I 

IFemale I -1.041 0.257 I -1.037 0.267 I -1.017 I 0.271 I I I IStudent Race/Ethnicity (vs. White) I 

Asian 0.323 0.441 0.183 0.491 0.006 0.539 

Hispanic 0.046 0.585 0.069 0.588 -0.051 0.616 

Black -0.833 0.445 -0.753 0.466 -0.92 0.481 

American Indian 0.88 0.847 1.25 0.937 0.937 0.921 

I Student Socioeconomic Background I 

SES Composite 0.574 0.203 0.549 0.213 0.508 0.216 

I Class Achievement Level (vs. Average) I 

AP 2.718 0.607 2.739 0.63 2.438 0.733 

Above Average 1.161 0.344 1.148 0.364 0.934 0.377 

Low -1.656 0.428 -1.569 0.441 -1.157 0.469 

Remedial -3.129 0.708 -3.018 0.75 -2.509 0.776 

I Teacher Education (vs. Major/none) I 

Major/major 0.156 0.357 0.121 0.356 

Major/minor -0.514 0.39 -0.611 0.405 

Minor only -0.461 0.375 -0.435 0.376 

None/none -1.528 0.457 -1.155 0.439 

178 
I 

Table D5.1. Effects of student background, school variables, class achievement level, teacher education, 

and instructional variables on sophomore-to-senior achievement growth in mathematics, 

from OLS regressions: 1992. (Cont'd) 

High School Seniors' Instructional 

Experiences in Science and Mathematics 

Independent Variables 

Model 1 Model 2 Model 3 

Coeff. S.E. Coeff. S.E. Coeff. S.E. 

IInstructional Variables 

% class time spent in whole 

group discussion 

0.125 0.17 

% class time spent maintaining 

order 

-0.405 0.157 

Minutes/day of homework 

assigned 

0.013 0.01 

Emphasis on higher-order 

thinking skills 

0.732 0.248 

Emphasis on practical 

applications ' 

-0.594 0.272 

Emphasis on mechanical 

operations 

0.041 0.259 

R-Squared 0.856 0.858 0.862 

N 4,671 4,354 4,110 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

179 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D5.2. Effects of student background, school variables, class achievement level, teacher education, 

and instructional variables on sophomore-to-senior achievement growth in science, from 

OLS regressions: 1992. 

I 

Independent Variables Model 1 Model2 Model 3· 

Coeff. S.E. Coeff. S.E. Coeff. S.E 

Intercept 12.255 2.873 12.174 2.816 11.877 2.872 

Sophomore !RT-Estimated Number Right: Science 

I Test Score 0.726 I 0.018 I 0.725 I 0.019 I 0.729 I 0.017 I I IUrbanicity (vs. Suburban) 

Urban 0.202 0.29 0.162 0.304 0.355 0.252 

Rural 0.154 0.277 0.237 0.276 0.486 0.241 

I Region of U.S. (vs. Northeast) I 

Midwest 0.033 0.265 0.003 0.275 -0.049 0.267 

South -0.346 0.258 -0.32 0.279 -0.436 0.266 

West 0.096 0.306 0.191 0.329 0.325 0.307 

I School Control Type (vs. Public) ,· I 

Catholic 0.515 0.669 0.421 0.688 0.063 0.409 

NAIS -1.032 1.212 -1.134 1.309 -1.403 1.323 

Other Private -0.439 0.598 -0.232 0.622 -0.605 0.635 

% Students Receiving Subsidized Lunch (vs. 0-5%) 

6-20% -0.026 0.335 0.039 0.345 -0.257 0.256 

21-50% -0.429 0.312 -0.472 0.318 -0.682 0.276 

51%+ -0.519 0.384 -0.536 0.407 -0.908 0.379 

I Number 12th Grade Students I 

Ln(enrollment) 0.212 0.125 0.202 0.132 0.254 0.118 

I Student Sex (vs. Male) I 

I Female -0.559 0.2 I -0.576 I 0.21 -0.42 I 0.194 I I I I 

I Student Race/Ethnicity (vs. White) I 

Asian -0.122 0.363 -0.315 0.293 -0.466 0.312 

Hispanic -0.548 0.284 -0.526 0.306 -0.455 0.31 

Black -0.915 0.304 -0.912 0.322 -0.779 0.316 

American Indian -2.152 0.832 -2.625 0.826 -1.823 0.779 

180 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D5.2. Effects of student background, school variables, class achievement level, teacher education, 

and instructional variables on sophomore-to-senior achievement growth in science, from 

OLS regressions: 1992. (Cont'd) 

I 

Independent Variables Model 1 Model 2 Model 3 

Coeff. S.E. Coeff. S.E. Coeff. S.E 

I Student Socioeconomic Background I 

I SES Composite 0.304 0.129 0.241 0.134 0.22 I 0.136 I I I I I I 

Student Achievement Level (vs. Average) 

AP 1.092 0.347 0.993 0.378 0.77 0.423 

Above Average 0.917 0.211 0.9 0.22 0.913 0.221 

Low -0.813 0.377 -0.749 0.393 -0.524 0.419 

I Teacher Education (vs. Major/none) 

Major/major 0.484 0.304 0.371 0.268 

Major/minor 0.122 0.296 0.239 0.3 

Minor only 0.032 0.267 0.006 0.259 

None/none -0.092 0.272 -0.064 0.313 

I Instructional Variables I 

% class time spent in whole 

group instruction 

0.054 0.095 

% class time spent 

maintaining order 

-0.009 0.152 

Minutes/day of homework 

assigned 

0.002 0.007 

Emphasis on lab work -0.02 0.175 

Emphasis on inquiry skills 0.246 0.221 

Emphasis on practical 

applications 

-0.351 0.146 

Emphasis on scientific facts 0.063 0.135 

Use of computers 0.142 0.171 

Use of student presentations 0.041 0.17 

R2 0.668 0.666 0.683 

N 3,090 2,832 2,619 I I I I 

SOURCE: U.S. Department or Education, National Center for Education Statistics, National Education Longitudinal Study or 1988 

(NELS:88), Second Follow-Up survey. 

I 

181 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table DS.3. Estimated effects of student background, school, class achievement level, teacher, and 

instruction variables on grade 12 composite mathematics achievement, by grade 10 

composite mathematics achievement quartile, from OLS regressions: 1992. 

I 

I 

Subsample: Grade 10 

achievement quartile 

1 (lowest) 

Grade 10 achievement 

quartiles 2 & 3 

(middle) 

Grade 10 

achievement quartile 

4 (highest) 

Coeff. S.E. Coeff. S.E. Coeff. S.E. 

IIntercept I 5.22 8.724 I 21.423 I 6.163 I 27.554 I 6.628 I 

Sophomore !RT-Estimated Number Right: Mathematics 

ITest Score 0.953 0.082 0.779 0.03 0.622 I 0.036 I I I I I I IUrbanicity (vs. Suburban) I 

Urban -0.797 0.644 0.086 0.547 0.303 0.515 

Rural 0.083 0.529 -0.156 0.502 0.18 0.393 

IRegion of U.S. (vs. Northeast) 

Midwest -0.828 0.917 -1.147 0.564 0.135 0.358 

South 0.47 0.688 -0.828 0.567 -0.356 0.436 

West 0.025 0.882 -0.893 0.656 -1.367 0.474 

I School Control (vs. Public) I 

Catholic 2.888 3.054 0.316 0.87 0.522 0.827 

NAIS -2.324 1.475 -1.792 1.601 1.753 0.855 

Other private -5.07 2.057- 1.134 1.245 0.011 0.988 

% Students Receiving Subsidized Lunch (vs. 0-S%) 

6-20% 1.392 0.77 -0.18 0.532 -0.808 0.418 

21-50% 0.62 0.819 -0.601 0.477 -0.823 0.499 

51%+ -0.602 0.829 -0.416 0.636 0.25 0.694 

INumber 12th Grade Students 

ILn(enrollment) I 0.348 I 0.353 0.039 0.321 0.019 I 0.29 I I I 

I Student Sex (vs. Male) 

IFemale I -0.979 0.486 I -1.372 0.405 I -0.482 I 0.284 I I I Student Race/Ethnicity (vs. White) 

Asian 3.342 1.456 -0.915 0.68 0.158 0.59 

Hispanic 0.357 0.606 -0.747 0.782 0.42 0.653 

Black -1.056 0.645 -0.419 0.62 -1.546 1.064 

American Indian 0.716 1.434 1.003 1.116 0.23 1.115 

182 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table DS.3. Estimated effects of student background, school, class achievement level, teacher, and 

instruction variables on grade 12 composite mathematics achievement, by grade 10 

composite mathematics achievement quartile, from OLS regressions: 1992. (Cont'd) 

Subsample: Grade 10 

achievement quartile 

1 (lowest) 

Grade 10 achievement 

quartiles 2 & 3 

(middle) 

Grade 10 

achievement quartile 

4 (highest) 

Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Student Socioeconomic Background I 

I SES Composite 0.567 0.364 0.357 0.263 0.529 I 0.244 I I I I I I 

Student Achievement Level (vs. Average) 

AP 3.387 1.288 5.713 2.416 3.568 0.641 

Above Average 2.128 0.803 1.007 0.491 1.221 0.438 

Low -0.761 0.552 -0.93 0.626 -0.129 1.01 

Remedial -1.392 0.832 -2.346 1.25 -3.648 1.148 

I Teacher Education (vs. Major/none) I 

Major/major 0.559 0.924 0.242 0.508 -0.022 0.406 

Major/minor 0.559 0.983 -0.696 0.57 -0.591 0.418 

Minor only -0.534 0.646 -0.322 0.45 -0.475 0.572 

None/none -0.277 0.653 -1.511 0.586 -0.82 0.604 

I Instructional Variables I 

% class time spent in 

whole group instruction 

0.098 0.245 0.254 0.255 0.008 0.162 

% class time spent 

maintaining order 

-0.442 0.206 -0.504 0.2 -0.084 0.197 

Minutes/day of homework 

assigned 

0.028 0.017 0.018 0.014 0 0.01 

Emphasis on higher order 

thinking skills 

0.409 0.429 0.737 0.325 0.703 0.389 

Emphasis on practical 

applications 

-1.006 0.514 -0.548 0.347 -0.33 0.27 

Emphasis on mechanical 

operations 

-0.069 0.469 -0.089 0.361 0.034 0.302 

R-Squared 0.388 0.577 0.47 

N 536 2,009 1,565 I I I I I 

SOURCE: U.S. Department of Educatloo, National Center for Education Statistics, Natlooal Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

183 
High School Seniors' Instructional 

Experiences in Science and Mathematics 

Table D5.4. Estimated effects of student background, school, class achievement level, teacher, and 

instruction variables on composite grade 12 science achievement, by grade 10 composite 

science achievement quartile, from OLS regressions: 1992. 

Grade 10 Grade 10 Grade 10 

achievement quartile achievement quartiles achievement 

Subsample: 1 (lowest) 2 & 3 (middle) quartile 4 (highest) 

Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Intercept I 16.362 I 6.791 I 6.582 I 3.414 I 15.675 I 4.655 

Sophomore IRT-Estimated Number Right: Science 

ITest Score I 0.336 I 0.117 I 0.842 I 0.049 I 0.521 I 0.047 

IUrbanicity (vs. Suburban) 

Urban 0.21 0.62 0.475 0.311 0.619 0.452 

Rural 1.029 0.564 0.361 0.285 0.284 0.349 

IRegion of U.S. (vs. Northeast) 

Midwest -1.605 0.617 0.027 0.31 -0.299 0.349 

South -1.323 0.69 -0.296 0.31 -0.541 0.357 

West 0.292 0.752 0.773 0.413 -0.397 0.464 

ISchool Sector (vs. Public) 

Catholic 0.758 1.03 0.205 0.566 -0.573 0.52 

NAIS 1.378 1.563 -0.631 0.812 -1.881 1.588 

Other Private -1.519 1.688 -0.119 0.826 0.085 1.178 

% Students Receiving Subsidized Lunch (vs. 0-5%) 

6-20% 0.321 0.836 -0.216 0.343 -0.153 0.285 

21-50% -0.492 0.726 -0.366 0.332 -0.743 0.362 

51%+ -0.693 0.872 -0.441 0.482 -1.232 0.666 

INumber 12th Grade Students 

I Ln(enrollment) I -0.058 I 0.325 I 0.301 I 0.15 I 0.032 I 0.176 

I Student Sex (vs. Male) 

I Female I 0.471 I 0.513 I -0.587 I 0.255 I -0.391 I 0.248 

I Student Race/Ethnicity (vs. White) 

Asian -1.668 1.484 -1.324 0.411 0.758 0.385 

Hispanic -1.955 0.794 -0.446 0.437 0.408 0.543 

Black -1.696 0.589 -0.43 0.353 -0.062 0.878 

American Indian -3.938 1.365 0.884 0.732 -0.449 0.99 

I 

I 

I 

I 

I 

184 
Table D5.4. Estimated effects of student background, school, class achievement level, teacher, and 

instruction variables on composite grade 12 science achievement, by grade 10 composite 

science achievement quartile, from OLS regressions: 1992. (Cont'd) 

High School Seniors' Instructional 

Experiences in Science and Mathematics 

I 

Subsample: 

Grade 10 

achievement quartile 

1 (lowest) 

Grade 10 

achievement quartiles 

2 & 3 (middle) 

Grade 10 

achievement 

quartile 4 (highest) 

Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Student Socioeconomic Background 

I SES Composite 0.034 I 0.368 0.196 I 0.195 I 0.304 0.19 I I I I 

Student Achievement Level (vs. Average) 

AP 0.431 1.267 1.075 0.513 0.867 0.537 

Above Average 0.998 0.646 0.983 0.302 0.622 0.315 

Low 0.696 0.84 -0.66 0.4 -1.986 0.761 

I Teacher Education (vs. Major/none) I 

Major/major 0.196 0.701 0.772 0.311 0.19 0.375 

Major/minor 2.243 0.775 -0.084 0.421 0.413 0.352 

Minor only 0.147 0.713 -0.367 0.325 0.664 0.385 

None/none 0.285 0.755 0.047 0.44 0.272 0.546 

I Instructional Variables I 

% class time spent in whole 

group instruction 

0.124 0.226 -0.095 0.131 0.134 0.115 

% class time spent 

maintaining order 

-0.345 0.3 0.004 0.173 0.217 0.217 

Minutes/day of homework 

assigned 

0.037 0.012 0.004 0.008 -0.005 0.01 

Emphasis on lab -0.003 0.362 -0.157 0.231 -0.029 0.258 

Emphasis on inquiry learning 0.608 0.558 -0.117 0.335 0.485 0.306 

Emphasis on practical 

applications 

-0.391 0.444 -0.51 0.192 -0.078 0.185 

Emphasis on scientific facts 0.566 0.342 -0.025 0.18 0.02 0.181 

Use of computers -0.373 0.298 0.107 0.224 0.425 0.244 

Use of student presentations 0.035 0.447 0.355 0.239 -0.312 0.236 

R-Squared 0.34 0.438 0.231 

N 309 1,224 1,086 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 

(NELS:88), Second Follow-Up survey. 

185 
00 

Table D5.5. Estimated effects of student background, school variables, class achievement level, teacher education, and instructional variables on 

,... the probability of proficiencya at different levels of grade 12 mathematics, from OLS regression: 1992. 

0\ 

Dependent Variable: Probability of Probability of Probability of Probability of Probability of 

Profic.: Level 1 Profic.: Level 2 Profic.: Level 3 Profic.: Level 4 Profic.: Level 5 

Subsample: Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 

profic.<Level 1 profic.=Level 1 profic.=Level 2 profic.=Level 3 profic.=Level 4 

(lowest) 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

Intercept 41.153 44.306 0.728 45.279 170.409 61.953 64.008 41.115 -33.942 18.903 

Grade 10 Probability of Proficiency at Each Level 

Grade 10 test 0.406 0.053 0.75 0.055 0.615 0.056 0.834 0.041 2.451 0.208 

I Student Sex (vs. Male) 

Female -2.42 2.544 -1.48 2.796 -7.185 3.726 -1.888 2.094 -4.487 1.18 

I Student Race/Ethnicity (vs. White) 

Asian 1.612 3.957 3.427 9.613 1.871 8.022 -16.76 4.875 -0.652 2.629 

Hispanic 2.74 2.981 -1.669 4.201 -11.029 6.282 -2.125 5.673 -0.291 2.407 

Black -6.075 3.466 -4.264 4.536 2.537 5.559 -5.644 7.875 -7.397 2.672 

American Indian -4.25 4.689 2.852 8.031 5.841 23.112 -0.444 12.289 -7.577 2.342 

I Student Socioeconomic Background 

SES Composite -2.094 1.796 10.859 2.536 6.482 2.581 1.845 1.865 0.816 0.772 

I Urbanicity (vs. Suburban) 

Urban -9.228 3.53 -4.903 4.942 2.264 5.393 4.14 3.844 1.667 1.823 

Rural -0.646 3.166 -2.577 3.951 9.441 5.051 -2.086 3 4.853 1.699 

I 

I 

I 

I 
Table DS.S. Estimated effects of student background, school variables, class achievement level, teacher education, and instructional variables on 

the probability of proficiencya at different levels of grade 12 mathematics, from OLS regression: 1992. (Cont'd) 

Dependent Variable: Probability of Probability of Probability of Probability of Probability of 

Profic.: Level 1 Profic.: Level 2 Profic.: Level 3 Profic.: Level 4 Profic.: Level S 

Subsample: Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 

profic.<Level 1 •' profic.=Level 1 profic.=Level 2 profic.=Level 3 profic.=Level 4 

(lowest) 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Region of U.S. (vs. Northeast) I 

Midwest -5.999 3.889 -1.242 4.358 -10.796 5.671 2.819 3.078 4.727 2.005 

South -1.851 3.593 9.529 4.891 -9.074 5.366 3.317 3.028 1.337 2.472 

West -4.233 4.172 -0.77 5.397 1.844 6.395 -3.091 4.243 -0.804 2.359 

I School Control Type (vs. Public) I 

Catholic 13.02 6.615 11.856 8.453 15.139 9.907 -7.386 5.653 0.768 2.553 

NAIS 4.875 9.896 41.766 10.982 -7.162 12.333 4.22 7.781 13.588 7.181 

Other Private 0 0 -14.257 11.743 -34.561 20.464 8.276 7.639 6.592 3.96 

% Students Receiving Subsidized Lunch (vs. 0-S%) 

6-20% 5.838 3.835 0.519 4.429 -8.022 5.384 -10.105 3.237 -3.81 1.645 

21-50% 7.702 4.029 -0.215 4.264 -10.12 5.113 -9.257 3.369 -2.738 1.888 

51%+ 5.14 4.085 -4.665 4.995 -1.569 7.343 -4.459 4.95 -6.93 2.486 

.... 

00 

--.J 
..... 

00 Table D5.5. Estimated effects of student background, school variables, class achievement level, teacher education, and instructional variables on 00 the probability of proficiencya at different levels of grade 12 mathematics, from OLS regression: 1992. (Cont'd) 

Dependent Variable: Probability of Probability of Probability of Probability of Probability of 

Profic.: Level 1 Profic.: Level 2 Profic.: Level 3 Profic.: Level 4 Profic.: Level 5 

Subsample: Grade 10 Grade 10 Grade 10 Grade 10 Grade 10 

profic.<Level 1 profic.=Level 1 profic.=Level 2 profic.=Level 3 profic.=Level 4 

(lowest) 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Number 12th Grade Students 

Ln(enrollment) 6.084 2.335 1.394 2.11 -2.125 2.95 0.87 2.022 2.649 0.943 

I Achievement Level (vs. Average) 

AP 0 0 28.323 6.739 -7.786 11.949 12.555 4.33 20.701 2.125 

Above Average 8.298 2.688 3.112 3.54 0.652 5.228 5.975 2.61 5.704 1.114 

Low -6.404 3.12 -7.036 3.723 -15.869 5.709 -6.115 4.635 2.775 3.05 

Remedial -17.839 5.291 -15.053 6.034 -20.669 7.732 -2.729 10.393 4.797 3.963 

I Teacher Education (vs. Major/none) 

Major/major -0.013 4.322 4.62 3.886 -6.509 4.792 1.802 3.524 1.124 1.606 

Major/minor 4.419 3.302 -0.184 5.121 -3.51 6.6 -4.703 3.142 -4.385 1.721 

Minor only 2.277 3.599 0.033 3.873 -2.335 4.103 -3.289 2.725 -1.121 1.837 

None/none 0.667 3.276 -1.342 4.792 5.821 6.457 -11.722 3.763 -6.098 4.383 

I 

I 

I 
...... 

\0 

Table D5.5. Estimated effects of student background, school variables, class achievement level, teacher education, and instructional variables on 

the probability of proficiencya at different levels of grade 12 mathematics, from OLS regression: 1992. (Cont'd) 

Dependent Variable: Probability of 

Profic.: Level 1 

Probability of 

Profic.: Level 2 

Probability of 

Profic.: Level 3 

Probability of 

Profic.: Level 4 

Probability of 

Profic.: Level 5 

Subsample: Grade 10 

profic.<Level 1 

(lowest) 

Grade 10 

profic.=Level 1 

Grade 10 

profic.=Level 2 

Grade 10 

profic.=Level 3 

Grade 10 

profic.=Level 4 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Instructional Variables I 

% class time spent in whole 

group instruction 

-0.019 1.287 1.372 1.703 -4.748 2.273 0.515 1.522 2.01 0.934 

% class time spent 

maintaining order 

1.276 1.5 -2.789 1.374 -2.338 2.253 0.6 1.357 -2.814 0.726 

Minutes/day of homework 

assigned 

-0.161 0.08 0.12 0.086 0.406 0.141 0 0.082 -0.045 0.035 

Emphasis on higher order 

thinking skills 

4.723 2.415 0.225 2.858 7.423 3.252 9.201 2.236 -0.602 1.325 

Emphasis on practical 

applications 

-4.359 2.207 -5.695 2.853 -4.517 3.286 -4.774 1.975 0.252 1.124 

Emphasis on mechanical 

operations 

-3.806 2.675 -0.948 2.962 3.166 3.419 -1.501 2.529 -1.519 1.3 

R-Squared 0.567 0.500 0.424 0.534 0.497 

N 367 656 506 1,066 1,152 

a The levels of proficiency are described in the text of Chapter 5. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, National Education Longitudinal Study of 1988 (NELS:88), Second Follow-Up survey • 

00 
,_. Table D5.6. Estimated effects of student background, school variables, class achievement level, teacher education, and instructional variables on 1.0 

0 the probability of proficiencya at different levels of grade 12 science, from OLS regression: 1992. 

Dependent Variable: Probability of Probability of Probability of Probability of . 

Proficiency: Level 1 Proficiency: Level 2 Proficiency: Level 3 Proficiency: Level 3 

Subsample: Grade 10 profic.<Level 1 Grade 10 profic.=Level 1 Grade 10 profic.=Level 2 Grade 10 profic.=Level 3 _ 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

Intercept 137.571 59.175 -23.475 40.928 61.275 43.853 82.03 56.701 

Grade 10 Probability of Proficiency at Each Level 

Grade 10 test ' 0.251 0.057 0.637 0.04 0.631 0.054 0.376 0.059 

I Urbanicity (vs. Suburban) I 

Urban 6.04 6 6.376 3.914 7.178 3.862 3.672 4.224 

Rural 9.434 6.586 2.814 3.322 5.837 3.552 -1.655 4.732 

I Region of U.S. (vs. Northeast) I 

Midwest -9.761 7.836 1.717 3.723 3.662 3.727 -5.347 4.353 

South -5.28 8.139 0.535 3.787 1.117 3.64 -6.058 5.02 

West 13.071 8.47 4.454 4.306 8.921 5.455 -1.694 5.145 

I School Control Type (vs. Public) I 

Catholic 6.793 11.988 3.761 5.825 6.007 7.773 -4.855 7.666 

NAIS 10.387 13.01 3.041 9.5 -3.784 8.192 -1.134 13.948 

Other Private -29.538 13.58 15.574 13.506 -16.181 11.881 -8.563 14.384 
Table D5.6. Estimated effects of student background, school variables, class achievement level, teacher education, and instructional variables on 

the probability of proficiencya at different levels of grade 12 science, from OLS regression: 1992. (Cont'd) 

Dependent Variable: Probability of 

Proficiency: Level 1 

Probability of 

Proficiency: Level 2 

Probability of 

Proficiency: Level 3 

Probability of 

Proficiency: Level 3 

Subsample: Grade 10 profic.<Level 1 Grade 10 profic.=Level 1 Grade 10 profic.=Level 2 Grade 10 profic.=Level 3 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

% Students Receiving Subsidized Lunch (vs. 0-5%) 

6-20% -0.471 7.006 4.851 3.973 -1.916 3.927 0.919 3.5 

21-50% -1.894 6.371 -0.206 4.118 -10.265 4.201 -3.493 4.745 

51%+ -19.11 10.235 -1.962 4.883 -10.358 7.031 -17.232 9.532 

I Number 12th Grade Students I 

Ln( enrollment) -2.738 3.879 2.067 1.894 2.094 2.071 0.905 2.293 

I Student Sex (vs. Male) I 

Female 9.045 5.171 -8.317 2.371 -8.974 2.934 -6.101 3.311 

I Student Race/Ethnicity (vs. White) I 

American Indian -41.745 18.166 10.363 6.84 8.46 13.152 -26.709 15.266 

Asian -33.131 11.431 -3.92 4.944 -10.821 4.364 3.552 6.121 

Hispanic -16.707 8.886 -1.796 4.744 -13.171 5.803 4.3 8.072 

Black -9.557 7.019 -10.695 4.481 -8.079 5.505 -21.573 10.396 

I Student Socioeconomic Background 

SES Composite 1.767 3.096 0.41 1.948 3.478 2.455 6.321 2.711 

I 
..... 

\0 Table D5.6. Estimated effects of student background, school variables, class achievement level, teacher education, and instructional variables on

N the probability of proficiencya at different levels of grade 12 science, from OLS regression: 1992. (Cont'd) 

Dependent Variable: Probability of Probability of Probability of Probability of 

Proficiency: Level 1 Proficiency: Level 2 Proficiency: Level 3 Proficiency: Level 3 

Subsample: Grade 10 profic.<Level 1 Grade 10 profic.=Level 1 Grade 10 profic.=Level 2 Grade 10 profic.=Level 3 

Coeff. S.E. Coeff. S.E. Coeff. S.E. Coeff. S.E. 

I Achievement Level (vs. Average) I 

AP -3.059 11.218 9.473 6.637 16.756 5.475 13.132 5.876 

Above Average 3.045 6.052 10.969 3.062 7.613 3.685 10.302 4.764 

Low -1.386 6.912 -7.539 3.61 -9.205 6.935 -19.509 9.995 

I Teacher Education (vs. Major/none) I 

Major/major 5.609 6.542 2.906 3.336 2.569 3.482 5.496 3.596 

Major/minor 13.435 7.267 -1.001 4.17 6.7 5.311 -0.021 4.39 

Minor only -4.38 6.546 -5.213 3.382 -1.259 4.756 8.94 5.063 

None/none -9.088 10.625 -2.338 4.007 -0.253 5.126 -4.288 8.092 
Table D5.6. Estimated effects of student background, school variables, class achievement level, teacher education, and instructional variables on 

the probability of proficiencya at different levels of grade 12 science, from OLS regression: 1992. (Cont'd) 

Dependent Variable: Probability of 

Proficiency: Level 1 

Probability of 

Proficiency: Level 2 

Probability of 

Proficiency: Level 3 

Probability of 

Proficiency: Level 3 

Subsample: Grade 10 profic.<Level 1 Grade 10 profic.=Level 1 Grade 10 profic.=Level 2 Grade 10 profic.=Level 3 

IInstructional Variables 

% class time spent in 

whole group instruction 

Coeff. 

5.186 

S.E. 

2.379 

Coeff. 

1.03 

S.E. 

1.273 

Coeff. 

-1.806 

S.E. 

1.558 

Coeff. 

0.136 

S.E. 

2.153 

I 

% class time spent 

maintaining order 

-0.35 3.122 -0.253 1.744 -0.027 1.941 3.68 2.311 

Minutes/day of 

homework assigned 

0.176 0.11 -0.007 0.08 0.005 0.066 -0.168 0.144 

Emphasis on lab -0.461 4.566 -0.659 2.288 -1.879 2.615 -1.586 3.364 

Emphasis on inquiry 

skills 

7.349 5.979 2.65 3.045 6.346 3.686 4.878 4.256 

Emphasis on science in 

society 

1.768 4.111 -2.578 1.932 -9.085 2.128 1.868 2.278 

Emphasis on scientific 

facts 

1.349 3.256 -0.574 1.664 -3.67 2.255 0.732 2.211 

Use of computers -4.033 4.117 -1.65 2.377 1.695 2.709 5.161 3.043 

Use of student 

presentations 

-6.077 5.415 4.29 2.396 -1.698 3.007 3.899 3.169 

R-Squared 0.46 0.477 0.331 0.362 

N 283 684 821 572 

w 

\0- a The levels of proficiency are described in the text of Chapter 5. 
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