Science Proficiency and Course Taking

in High School

The Relationship of Science Course-taking Patterns to

Increases in Science Proficiency Between 8th and 12th

Grades

	

 
 



 
 

 	  	

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Science Proficiency and Course Taking

in High School

The Relationship of Science Course-taking Patterns to

Increases in Science Proficiency Between 8th and 12th

Grades

Timothy Madigan

Bureau of the Census

	

 
 



 
 

 	  	

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Foreword

Relatively little attention has been given to the relationship between course taking and achievement in

science. This report examines factors related to gains in science proficiency between 8th and 12th

grade. This analysis uses achievement testing and transcript data in the National Education

Longitudinal Study of 1988 (NELS:88) to investigate how changes in science proficiency are related to

science course-taking histories of high school students. Like an earlier report by Rock, Owings, and

Lee (National Center for Education Statistics 1994) on changes in the mathematics proficiency of

students between 8th and 10th grades, the analysis takes into account initial proficiency of students—a

crucial characteristic related to both gains in proficiency and course-taking patterns. This focus

enables the reader to understand how course-taking patterns are related to gains in proficiency among

students who in eighth grade were at the bottom, middle, and top of the science proficiency

distribution. The report also explores the extent to which gains in science proficiency are related to

student race-ethnicity, gender, and socioeconomic background, after accounting for differences among

these groups in science course taking.

Mary Frase

Acting Associate Commissioner


Table of Contents

Foreword....................................................................................................................................................... iii

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

Highlights ................................................................................................................................................... viii

Introduction....................................................................................................................................................1

Science Proficiency Levels .............................................................................................................................2

The Science Proficiency Level of Students and Changes Over Time.........................................................2

Science Course-taking Patterns and Gains in Science Proficiency Level...................................................4

Science Course Taking and Gains in Proficiency Level by 8th Grade Proficiency

Level................................................................................................................................................................6

Increases in Proficiency Level, Type and Number of Science Courses, and

Demographic Factors: A Multiple Logistic Regression Approach ...........................................................7

Exploring How Gender, Race-ethnic, and Socioeconomic Differences in Chances

of Increasing in Science Proficiency Level Are Influenced by Variation in

Science Course Taking...................................................................................................................................9

Summary.......................................................................................................................................................11

Appendix A ..................................................................................................................................................16

Logistic Regression..........................................................................................................................24

Appendix B: Technical Notes for NELS:88 ...............................................................................................25

Respondents Who Were Missing Key Information......................................................................26

Sampling Errors...............................................................................................................................28

Variables Used in Analysis.............................................................................................................29

References .....................................................................................................................................................31
List of Tables

Table 1. Percent of 1988 8th-grade students whose science proficiency level decreased,

remained the same, or increased between 1988 and 1992, by selected school and student

characteristics .................................................................................................................................................4

Table 2. Percent of 1988 8th-grade students who took various semesters of science and types

of science courses in high school by selected school and student characteristics ....................................5

Table 3. Percent of 1988 8th-grade students whose science proficiency increased by one or

more levels between 1988 and 1992 by 8th-grade science proficiency level, semesters of

science, curriculum, and science courses taken in high school..................................................................6

Table 4. Estimated logistic regression coefficients for the regression of increase in science

proficiency level between 1988 and 1992 on student, school, and course-taking characteristics

by science proficiency level in 8th grade......................................................................................................8

Table 5. Logistic regression coefficients for contrasts of interest in models predicting changes

of increasing in science proficiency level with and without controls for course taking ........................10

Appendix A

Table A1. Standard errors for table 1.........................................................................................................16

Table A2. Standard errors for table 2.........................................................................................................17

Table A3. Standard errors for table 3.........................................................................................................18

Table A4. Data for Figure 1: Percent of NELS students at different levels of science proficiency:

1988 and 1992 ...............................................................................................................................................19

Table A5. Standard errors for table A4......................................................................................................19

Table A6. Percent of NELS students at various levels of science proficiency in 1992...........................20

Table A7. Percent of 1988 8th-grade students whose science proficiency level decreased,

remained the same or increased between 1988 and 1992 .........................................................................21

Table A8. Estimated logistic regression coefficients for the regression of increase in science

proficiency level between 1988 and 1992 on student, school, and course-taking characteristics..........22

Table A9. Estimated odds ratios for the logistic regression coefficients in table 4................................23

Appendix B

Table B1. Percentage of respondents who were missing key information, by demographic

and schooling characteristics.......................................................................................................................27


List of Figures

Figure 1. Science proficiency levels of NELS students at two points in time ..........................................3

Figure 2. Change in science proficiency levels of 1988 8th-graders between 1988 and 1992, by

proficiency level in 1988 ................................................................................................................................3

Figure 3. Percent of 1988 8th-grade students who increased in science proficiency level

between 1988 and 1992 by semesters of science taken in high school.......................................................6

Figure 4. Percent of 1988 8th-grade students who increased in science proficiency level

between 1988 and 1992 by type of science courses taken...........................................................................6


Acknowledgments

The author would like to thank all those who helped in the production of this report. Nabeel Alsalam,

Mary Frase, and Jeffery Owings from the National Center for Education Statistics (NCES) provided

abundant feedback from start to finish. Paul Siegel and Suzanne Bianchi from the Census Bureau

provided many useful suggestions. Mary Pontorno and Christopher Gaebler from the Census Bureau

and Bruce Daniel from Pinkerton Computer Consultants, Inc. provided data and programming

assistance.

A host of additional reviewers helped by providing invaluable comments or advice. They include

Larry Suter from the National Science Foundation; Sentra Raizen of the Center for Science

Improvement; Thomas Hoffer of the National Opinion Research Center; Don Rock and Judy Pollack of

Educational Testing Service; Robert Burton, Sue Ahmed, Andrew Kolstad, and Jeanne Griffith from

NCES; and Deborah Carter from the American Council for Education.

Rebecca Pratt and Carol Rohr from Pinkerton Computer Consultants, Inc. and Margaret Harding from

the Census Bureau provided help with desktop publishing and graphics production.


Highlights

A number of previous cross-sectional studies

have found a strong relationship between a

student’s course-taking history in science during

high school and his or her current achievement in

science. However, it has been difficult to interpret

this evidence as the effect of course taking. It is

equally plausible that students who take more

science courses or more difficult science courses

would also have been high achievers if tested

before high school. With extensive longitudinal

data on both achievement and course taking now

at hand, a more definitive analysis is possible.

This analysis uses data on science achievement

and transcript reports of science course taking of

students from the National Education

Longitudinal Study of 1988 (NELS:88) to estimate

the relationship between their science course

taking and the change in their science proficiency

level between 8th and 12th grades.

 How many students increase in science

proficiency level between 8th and 12th grades?

Fifty-four percent of students showed an increase

in their science proficiency level, while 35 percent

stayed at the same level and 11 percent declined.

The chances of increasing in science proficiency

level varied with the demographic and academic

characteristics of students.

 Is taking more science courses related to gains in

science proficiency level between 8th and 12th

grades?

Generally speaking, taking eight or more

semesters of science was positively associated

with increasing in science proficiency level. This

result held in most situations even after

accounting for the association between

socioeconomic status (SES), achievement level in

eighth grade, gender, and race-ethnicity on the

one hand and both course taking and increasing

in science proficiency on the other. The number

of science courses taken was not, however, the

only information about course taking available in

NELS:88. Information on the level of science

course taken was also available and proved

useful.

 Is taking advanced level science courses such as

physics and chemistry related to gains in science

proficiency between 8th and 12th grades?

For students who started at the top science

proficiency level in eighth grade, taking more

advanced science courses was related to increases

in science proficiency level. Furthermore, after

controlling for level of science course taken,

evidence of a positive relationship between the

number of science courses and chances of

increasing in science proficiency level was not

found. Taking challenging science courses seems

to be crucial for high initial achievers.

For students who started at low to middle levels

of science proficiency in eighth grade, both taking

advanced level science courses and a higher

number of science courses were related to

increasing in science proficiency level.

 Are demographic characteristics of students related

to chances of increasing in science proficiency level

during high school?

The answer is yes. Asian and white students

were more likely than black and Hispanic

students to increase in science proficiency level.

Students of parents with high levels of education,

occupational rankings, and incomes (i.e., high

SES) were more likely to increase in science

proficiency level than students of parents with

lower levels.

 After accounting for differences between

demographic groups in the number and level of

science courses taken, do differences in their

chances of increasing in science proficiency level

disappear?

Gender, race, and familial SES continued to

exhibit a relationship to chances of increasing in

science proficiency level even after adjusting for

differences in science course taking. In future

research on this topic, researchers might consider

alternative intervening variables or ways of

extracting more information out of the coursetaking variables.
Introduction

Some people are concerned that our nation’s

students are being out-paced in scientific literacy

by students from other advanced, industrial

nations.1

 Many education professionals and

policymakers have outlined solutions to this

problem. Increasing the number of science

courses required for high school graduation,

some have argued, will help students in the U.S.

progress toward becoming first in the world in

science achievement.2

 Others have called for an

integrated approach to science which

continuously exposes all students to science

material throughout high school.3

These recommendations for more exposure to

science are based in part on research that has

documented a positive relationship between

course taking and achievement.4

 Jones et al.5

found a positive relationship between total

number of science (and mathematics) credits a

high school student took and his or her science

proficiency level in 12th grade. Mullis and

Jenkins 6 also found a positive relationship

between course taking and proficiency, but

questioned the nature of the relationship because

brighter students may simply take more courses.

In the area of mathematics, Rock, Owings and

Lee7

 have shown course taking to be positively

related to increases in a student's proficiency level

between 8th and 10th grades. Among students

who started at the same proficiency level in

eighth grade, those who took higher level

mathematics courses were more likely to increase

to higher proficiency levels two years later than

students who did not take higher level courses.

Their results suggest that course taking affects

mathematics proficiency. More importantly, they

show that taking more advanced mathematics

courses seems to help both low and high

achievers.

Differential course-taking patterns may be

responsible for part of the gap between the

mathematics and science achievement of high

school males versus females and of whites and

Asians compared to blacks and Hispanics.8

 Blacks

and Hispanics take fewer mathematics and

science courses than whites and Asians and the

science courses they take are clustered at lower

levels.9

 High school males are less likely to stop

taking science and mathematics courses than

females.10 Indeed, in mathematics, Rock, Owings

and Lee found that the types of mathematics

courses males and females took explained some

of the difference in gains in mathematics

proficiency levels between 8th and 10th grades.

Furthermore, research comparing public and

private schools and on effective schools in general

has found that good schools are often organized

around a challenging academic or college

preparatory curriculum.11

This report uses longitudinal data to examine

whether students at the same level of science

proficiency during eighth grade have higher

science proficiency levels four years later if they

took more semesters of science in the interim as

compared to students who took fewer semesters

of science. It will ascertain the relationship

between taking challenging science courses in

high school and experiencing gains in science

proficiency. In addition, the relationships among

school and student characteristics, high school

curriculum and changes in proficiency level are

also examined.

The analysis begins by describing the distribution

of students across levels of science proficiency, the

amount of change in proficiency between 8th and

12th grades, and the course-taking patterns of

students. The relationship between increases in

proficiency level and science course taking while

controlling initial proficiency level is then

examined. Results from this section should be

useful to people who ponder whether lowachieving students would benefit from tougher

course-taking standards. Finally, the relative

influences of family background, student

demographic characteristics, and school and

course-taking factors on chances of increasing in

science proficiency level are modeled with

multiple, logistic regression.

Data from the National Education Longitudinal

Study of 1988 (NELS:88) were analyzed in this

report. These data provide the best available

resource to examine growth in science proficiency

during high school. Other non-longitudinal

national surveys have provided only crosssectional snapshots of the relationship between

course taking and achievement. This does not

facilitate the testing of causal relationships.

Previous longitudinal surveys sponsored by the


National Center for Education Statistics (NCES)

spanned only part of a high school student's

career and therefore, provided an incomplete

picture of achievement during high school.12

In NELS:88 the same students were interviewed

in eighth grade and 2 and 4 years later when most

were in 10th and 12th grades, and detailed

course-taking histories of the students were

obtained through a transcript study component.

These features, combined with measures of

student science proficiency at multiple points of

time, help make NELS:88 a valuable resource for

researchers interested in exploring factors related

to gains in achievement or differences in

achievement among students.

In 1992, transcripts were collected for a sample

(14,283) of the original eighth-grade students.

The NELS:88 sample used in this report is

comprised of 7,584 students representing the

longitudinal panel who had 8th and 12th grade

science scores and complete transcript records.13

Science Proficiency Levels

To measure change in student achievement over

time requires a measure that covers a broad range

of achievement, both within a grade level and

across grades as students advance through

school. A psychometric methodology called item

response theory (IRT) is ideal for measuring such

change. It characterizes a wide range of items on

achievement tests in terms of how difficult they

are and, in particular, of how likely students with

various levels of proficiency are to answer them

correctly. IRT allows for the introduction of new

and more difficult test items over time that relate

to the performance scale created from items

administered earlier during a student’s career.

Thus, when a cohort of students who were tested

in 8th grade reach 12th grade, more difficult test

items can be included on the 12th grade test

which cover a higher range of performance and

yet report test performance on the scale that was

constructed for them when they were eighthgraders.

An alternative to calculating an IRT scale score is

to assign each student at each grade to a

proficiency level. Based upon common difficulty

levels of groups of items used on the science

achievement test in NELS:88, certain criteria were

established to represent thresholds of

understanding basic science concepts and

applications.14 In the base year, students were

assigned to level “Below 1” if their test results

indicated that they did not understand simple

scientific facts or information. This was

determined if they did not correctly answer at

least three out of four test questions relating to

basic scientific knowledge. They were assigned to

level “1” if their test performance indicated that

they understood basic science, i.e., they answered

at least three of the level 1 questions correctly.

This level of understanding could be obtained

through everyday experiences. They were

assigned to level “2” if they, in addition to being

at level 1, understood science concepts that were

fundamental to, or laid the foundation for, the

building up of more complex scientific

knowledge. They needed to correctly answer at

least three items from a group of four

representing fundamental science concepts. In a

similar manner, in the followup surveys students

could have been assigned to the above levels or to

level “3,” which represents an understanding of

complex science concepts and additional

problem-solving abilities.15 These gross levels of

proficiency are useful for describing achievement

of U.S. students or modeling school and family

processes involved with learning.16

The Science Proficiency Level of

Students and Changes Over Time

Almost half of the 1988 eighth-grade students

scored at science level 1 (figure 1 and table A4).

Some 22 percent were below level 1 and 31

percent above level 1. Four years later, when they

reached 12th grade, 15 percent of the students

were below level 1. The majority of students

were at level 2 or higher. Based on previous

cross-sectional research, it is not surprising to find

that over one-fifth of eighth- grade students have

little understanding of basic science and that by

the end of high school, fifteen percent still do

not.17

Because NELS:88 is longitudinal and assesses

student achievement at multiple points in time, it

provides researchers with data ideal for

examining how much growth in achievement

occurs during high school. Between 1988 and

1992 some 54 percent of students improved their


science proficiency by one or more levels (figure 2

and table A7).

A little more than one-third (35 percent) remained

at the same level while 11 percent lost ground.

(These results are based on changes from one

proficiency level to another and do not take into

account changes in proficiency within a level.)

Nearly the same proportion of students decreased

or simply maintained their science proficiency

level as the proportion who increased.

The large percentage of students who did not

gain at least one level may reflect a variety of

factors. Students may have simply forgotten

what they learned by 1988 or during the interim

covered in this study, especially if they had not

taken any science recently. They may have

gained but not enough to cross the threshold to

the next level. At any rate, these results are

consistent with findings from other research

about students: (1) they spend a large amount of

time tending to—or being distracted by—

maintenance and procedural matters (i.e.,

announcements, the taking of attendance, the

collection of sick notes and assignments, the

distribution of hallway passes, the changing of

rooms and teachers, the correction of out-of-line

students) rather than engaging in instructional

activities,18 (2) they receive inflated grades

although their performance on objective tests may

not warrant it,19 and (3) they pursue little

advanced science coursework.20

The likelihood of students increasing their science

proficiency level is a function of their initial

science proficiency. Students who started at the

highest level were least likely to increase. There

are a variety of possible explanations for this

pattern.21 It may reflect regression to the mean.22

Indeed, students who started at level 2 were more

likely than those at level 1 to decrease. The lower

chances of increasing among high proficiency

eighth-graders might also reflect varying

difficulties in moving from one level to the next.

Lower levels represent competency in basic,

everyday science and higher levels represent

more complex problem solving skills in addition

to all lower level skills. Thus, it may be possible

that moving up may be easier for students who

start at the lower end of the proficiency

distribution. Finally, more students may have

been clumped not far below the threshold for

level 1 science proficiency than below that for

higher levels. If that were the case, moving up in

proficiency level would have been more likely for

those at the bottom. Whatever the explanation,

the results found here are in agreement with

some other longitudinal findings on gains in

achievement: students initially low in

achievement are more likely to gain than students

with higher initial achievement.23

By cross-classifying changes in science proficiency

level with various student and school

characteristics, one can see which groups of

students were most likely to change (table 1).24

Figure 1.—Science proficiency levels of NELS students at

two points in time

















	






		  	
  

  	


 


  1  	 
 


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

Education Statistics, National Education Longitudinal Study of

1988.

Figure 2.—Change in science proficiency levels

of 1988 8th-graders between 1988 and

1992, by proficiency level in 1988

















	







    

 	
 
  


 


	 


SOURCE: U.S. Department of Education, National Center

for Education Statistics, National Longitudinal Study of 1988.


Male students were more likely than females to

increase their science proficiency level between

8th and 12th grades, 56 and 51 percent

respectively. Higher proportions of Asian

students than black, Hispanic, or American

Indians increased in proficiency levels between

8th and 12th grades. White students were more

likely than black and Hispanic students to

increase. Students from higher SES backgrounds

were generally more likely than students from

lower SES backgrounds to increase in science

proficiency over the high school years. NonCatholic, private high school students were more

likely than public to increase in level of

proficiency and less likely to decrease.

Science Course-taking Patterns and

Gains in Science Proficiency Level

Differences in the chances of increasing in science

proficiency level may be related to differences in

the number and types of science courses taken by

students. Indeed, a cross-classification of science

course taking by student characteristics reveals

considerable variation (table 2).25,26

Groups of students who took many science

courses or more advanced courses tended to be

the same ones who in table 1 were more likely to

show an increase in science proficiency level.

White students were more likely than blacks to

increase in proficiency level and 29 percent of

whites took 8 or more semesters of science27

compared to 18 percent of blacks. Students from

high SES backgrounds were more likely to

increase in science proficiency level and 42

percent took 8 or more semesters of science.

Students from lower SES backgrounds were less

likely (26 percent or less) to take 8 or more

semesters of science. Males were more likely to

increase than females and they were more likely

to have taken physics, but did not differ in the

number of courses taken.

These patterns suggest the possibility that course

taking may account for at least some of the

observable differences between groups in the

likelihood of increasing in science proficiency

level. One exception to this pattern involves the

variable representing 1988 science proficiency

level. In this case, students who had high science

proficiency levels in 1988 took more courses and

more rigorous ones but were less likely to

advance. This exception to the general pattern

illustrates the complexity of the relationship

between changes in science proficiency on the one

hand and course taking and initial science

proficiency on the other hand. This relationship

will be investigated in more detail in a multiple

logistic regression analysis below.

Both the amount and nature of science course

taking is related to likelihood of gains in science

proficiency level. Of students who took 8 or more

semesters of science during high school, 68

percent increased one or more levels in science

proficiency (figure 3 and table A7).

In contrast, among students who took less than 4

semesters of science, 40 percent increased their

level of proficiency. Except for the comparison

between students who took 4–5.99 versus less

than 4 semesters of science, as the number of

semesters of science increased, the more likely

students were to increase their proficiency.

Table 1.—Percent of 1988 8th-grade students whose

science proficiency level decreased,

remained the same, or increased between

1988 and 1992, by selected school and

student characteristics

School and student Change in science proficiency level

characteristics Decrease Same Increase

 Total 11 35 54

Gender

 Male 11 33 56

 Female 11 38 51

Race-ethnicity

 Asian 8 30 62

 Hispanic 11 41 49

 Black 18 42 39

 White 10 34 56

 American Indian 15 45 40

SES quartile

 Low 17 42 42

 Low-medium 14 39 47

 Medium-high 10 35 55

 High 6 29 65

Type of school

 Public 12 36 53

 Catholic 9 33 58

 Other private 4 27 69

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

Education Statistics, National Longitudinal Study of 1988.


The type of science course taken by students was

related to increases in science proficiency level.

Students who took physics were significantly

more likely to increase in science proficiency than

both groups who took less rigorous courses.

Those who took chemistry only were more likely

to increase than those who took neither

chemistry nor physics. Of students whose

transcripts indicated that they took physics, 70

percent increased in science proficiency level

(figure 4) compared to 54 percent of students who

took chemistry but not physics and 42 percent of

students who took neither physics or chemistry.

Table 2.—Percent of 1988 8th-grade students who took various semesters of science and types of

 science courses in high school by selected school and student characteristics

Number of semesters of science: Science courses taken

No

School and chemistry- Chemistrystudent characteristics 0.0-3.99 4.0-5.99 6.0-7.99 8.0 or more physics no physics Physics

 Total 6 33 34 27 38 34 28

Gender

Male 6 34 32 28 39 30 31

Female 6 33 36 26 37 39 24

Race-ethnicity

Asian 3 32 29 36 26 33 42

Hispanic 8 46 29 17 52 31 18

Black 6 43 33 18 47 35 18

White 6 31 35 29 36 35 29

American Indian 6 49 31 14 60 19 21

SES quartile

Low 11 48 29 12 63 26 11

Low-medium 7 41 32 20 48 32 20

Medium-high 5 33 36 26 36 37 27

High 3 19 36 42 17 39 44

Type of school

Public 6 35 33 26 40 34 26

Catholic 1 25 39 34 17 37 47

Other private 4 20 43 33 16 37 47

Curriculum

Academic 2 18 39 42 16 42 43

General 9 46 31 15 56 29 15

Vocational 13 57 26 5 73 21 6

Science courses

No chemistry-physics 14 66 18 2 — — —

Chemistry-no physics 1 21 56 22 — — —

Physics 1 5 28 67 — — —

1988 proficiency level

Below 1 11 46 31 11 60 29 11

Level 1 5 35 35 24 39 36 25

Level 2 2 21 34 42 20 36 44

— Not available.

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

of 1988.


Science Course Taking and Gains in

Proficiency Level by 8th Grade

Proficiency Level

We have just seen that students who take more

science courses are more likely to increase their

science proficiency level. We saw earlier that

students with high levels of initial proficiency

were less likely to increase their science

proficiency than students with low initial levels of

proficiency (figure 2), and that students with

higher initial proficiency levels were more likely

than students with low initial proficiency to take

more science courses (table 2). In order to unravel

how course taking is related to gains in

proficiency, the next step in the analysis

incorporates students' initial science proficiency

level into the examination of the relation between

increases in levels of science proficiency and

taking science courses.

A strong, positive relationship existed between

taking a high number of science courses during

high school and increases in level of science

proficiency regardless of science proficiency level

in 1988 (table 3). Students who took eight or

more semesters of science were more likely to

increase their science proficiency level than

students with the same initial proficiency level

who took fewer semesters of science.

For students who took less than eight semesters

of science a positive relationship between number

of semesters of science and increases in science

proficiency level was less evident. Among

students who scored below science proficiency

level 1 in eighth grade, there were no significant

differences in chances of increasing in science

proficiency if they took anywhere from 0 to 7.99

semesters of science. However, students who

were at level 1 in eighth grade and took 6–7.99

semesters of science were more likely to increase

in science proficiency level than students at level 1

who took less science. Those who took 4–5.99

semesters were not more likely to increase than

those who took 0–3.99 semesters. Among

students who scored at level 2 in eighth grade,

 	

    
 


 
 
 
  
 
 
 
 


  
     


 !
 
   
 !
 
  

















	

     
 


 	 


   


 	 



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

Education Statistics, National Longitudinal Study of 1988.

Figure 4.—Percent of 1988 8th-grade students who

increased in science proficiency level

between 1988 and 1992 by type of

science courses taken

















	

 





 




 



	 


 


 	 



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

Education Statistics, National Education Longitudinal Study

of 1988.

Table 3.—Percent of 1988 8th-grade students

whose science proficiency increased

by one or more levels between 1988

and 1992 by 8th-grade science

proficiency level, semesters of science,

curriculum, and science courses taken

in high school

Proficiency level in 1988

Course-taking and Level Level

curriculum Below 1 1 2

 Total 63 55 46

Semesters of science

0.0–3.99 50 35 27

4.0–5.99 60 40 27

6.0–7.99 64 59 42

8.0 or more 85 75 59

Curriculum

Academic 68 67 53

General 60 45 36

Vocational 63 39 16

Science courses

No chemistry-physics 58 37 18

Chemistry-no physics 65 59 41

Physics 86 75 63

SOURCE: U.S. Department of Education, National

Center for Educational Statistics, National Education

Longitudinal Study of 1988.
	

those who took 6–7.99 semesters of science were

more likely to increase in science proficiency than

students who took 4–5.99 semesters. These two

groups of students were not more likely to

increase than students who took 0–3.99 semesters

of science.28

At every level of initial proficiency a strong,

significant relationship was found between taking

physics and whether students increased in

science proficiency level. Students who took

physics were more likely to increase than those

who took chemistry but not physics or neither. In

addition, students who started at levels 1 and 2

and took only chemistry were more likely to

increase than students who did not take

chemistry.

The type of high school curriculum reported by

the student was also related to increases in their

science proficiency level.29 Students who started

out at proficiency levels 1 and 2 in eighth grade

and who identified themselves as being in an

academic curriculum were more likely than those

reporting they were in a general or vocational

curriculum to increase their science proficiency

level . For students who started below level 1,

however, there was no significant relationship

between self-reported curriculum and gains in

science proficiency level.

Increases in Proficiency Level, Type

and Number of Science Courses, and

Demographic Factors: A Multiple

Logistic Regression Approach

The number and type of science courses taken

were found to be related to increases in science

proficiency level. These two predicators of

increases are related to each other and to other

predictors of increases such as self-reported

curriculum, socioeconomic status, gender, and

race. The ability to sort out which of these

predictors has an independent effect on increases

while controlling for the effects of the others

would prove valuable to our understanding of

the complexity of factors related to increases in

science proficiency. Logistic regression is an

advanced, multivariate statistical technique which

allows one to sort out such complexity. It is

designed for estimating the relationship of a

qualitative or quantitative explanatory variable to

a dichotomous outcome variable (in this case,

whether a student increased his or her level of

science proficiency), taking into account the

relationship of other explanatory variables to the

outcome variables. A technical description of

logistic regression can be found in the appendix.

Table 4 contains the results of three logistic

regression models, one for students at each level

of eighth-grade science proficiency.30 The

explanatory variables used in each model are

listed on the left hand side of the table. For

example, variables representing gender, raceethnicity, SES, type of school, semesters of

science, self-identified curriculum, and type of

science courses taken are believed to be related to

the chances of a student increasing in science

proficiency level. Below each variable are its

categories and the contrast group is in

parentheses. The contrast group is the group that

all other groups under a particular variable

should be compared with (the comparison group,

in other words). The coefficients for each

category of every variable are in the center of the

table. A positive coefficient indicates that the

relationship is in a positive direction (or the group

of interest has a greater chances than the contrast

group of increasing) and vice versa. An asterisk

represents a statistically significant relationship

between being in a particular category and the

likelihood of increasing in science proficiency

level, compared to the contrast category in

parentheses.

The level of rigor of science courses taken in high

school was related to increases in science

proficiency level (table 4). Across all three levels

of eighth-grade science proficiency, students who

did not take physics or chemistry were

significantly less likely to increase in science

proficiency level than students who took physics.

Among students who started at levels one and

two, those who took neither physics or chemistry

were less likely to increase than those who took

chemistry.

The type of curriculum that students reported

being in was related to increases in science

proficiency level for students who started at

science proficiency levels one and two in eighth

grade. Students who reported being in a general



or vocational curriculum were less likely to

increase in proficiency than students who

reported being in an academic curriculum.

For students in the upper part of the science

proficiency distribution, the rigor of courses taken

and curriculum appear more related to increases

in science proficiency level than the quantity of

courses taken. Among students at science

proficiency level 2 in eighth grade, the number of

semesters of science taken was not related to

increases in science proficiency level, whereas

both the type of science courses and self-reported

curriculum were.

These results call into question the general

emphasis on taking more courses for increasing

achievement. For high achieving students, this

emphasis seems especially inappropriate. The

number of courses taken by students who start at

the high end of the proficiency distribution is an

imperfect indication of the type of courses taken

or curriculum enrolled in. If researchers attempt

to predict achievement gains with a variable

measuring number of courses and do not account

for type of courses taken and curriculum, they

will probably obtain spurious relationships.

Among students who started at the lower or

middle science proficiency levels there is evidence

of a positive relationship between the number of

science courses taken and chances of increasing in

science proficiency level. Those who took less

than eight semesters of science were less likely to

increase in proficiency level than those who took

eight or more semesters.31

Differences in the number and rigor of courses

taken by students from various demographic

backgrounds did not completely eliminate

differences in their chances of increasing in

science proficiency, especially at levels 1 and 2.

Table 4.—Estimated logistic regression coefficients for the regression of increase in science proficiency level

between 1988 and 1992 on student, school, and course-taking characteristics by science proficiency

level in 8th grade

Science proficiency level in 1988

 Below 1 Level 1 Level 2

Intercept 2.22 (0.37) 1.75 (0.15) 0.60 (0.15)

Gender (vs. female)

Male 0.22 (0.17) 0.22 * (0.09) 0.44 * (0.11)

Race-ethnicity (vs. white)

Asian -0.13 (0.33) -0.07 (0.23) 0.25 (0.21)

Hispanic -0.20 (0.16) -0.28 (0.18) -0.16 (0.28)

Black -0.71 * (0.19) -0.87 * (0.17) -0.82 * (0.25)

American Indian -0.30 (0.56) -0.89 * (0.43) 0.23 (1.07)

SES (vs. high)

Low -0.31 (0.31) -0.83 * (0.17) -0.73 * (0.20)

Low-medium 0.08 (0.31) -0.77 * (0.13) -0.47 * (0.18)

Medium-high -0.15 (0.34) -0.44 * (0.13) -0.22 (0.14)

Type of school (vs. public)

Catholic 0.17 (0.37) -0.40 * (0.20) -0.14 (0.21)

Other private -0.02 (0.37) 0.01 (0.24) 0.54 * (0.20)

Semesters of science (vs. 8.0 or more)

0–3.99 -1.13 * (0.34) -0.71 * (0.24) 0.34 (0.44)

4.0–5.99 -0.63 * (0.29) -0.59 * (0.16) -0.20 (0.25)

6.0–7.99 -0.63 * (0.31) -0.33 * (0.13) -0.21 (0.14)

Curriculum (vs. academic)

General -0.04 (0.21) -0.48 * (0.10) -0.37 * (0.14)

Vocational 0.23 (0.24) -0.44 * (0.18) -0.83 * (0.29)

Science courses (vs. physics)

No chemistry-physics -1.04 * (0.27) -0.77 * (0.15) -1.60 * (0.24)

Chemistry-no physics -0.82 * (0.30) -0.33 * (0.12) -0.67 * (0.13)

* p<0.05 or t>1.96 for the test hypothesis of no difference in science proficiency growth between this group and the omitted group.

NOTE: Standard errors of the estimates are in parentheses.

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


When these factors were taken into

consideration through multiple logistic

regression, significant differences in chances of

increasing in science proficiency level remained

between males and females who started out at

levels 1 and 2 in eighth grade: males were more

likely to increase. Significant differences

persisted between blacks and whites at all

levels of initial proficiency with blacks less

likely to increase.

Students from low and low-medium SES

backgrounds who started at levels 1 and 2 in

high school remained significantly less likely to

increase their science proficiency level than

students from high SES backgrounds. Students

from medium-high SES backgrounds who

started at level 1 were also less likely to

increase than students from advantaged

backgrounds. Students from other (i.e., nonCatholic) private schools who were at

proficiency level 2 in eighth grade continued to

be more likely to increase in proficiency level

than public school students. Students from

Catholic schools who started at level 1 were

less likely than public school students to

increase.32

Exploring How Gender, Race-ethnic,

and Socioeconomic Differences in

Chances of Increasing in Science

Proficiency Level Are Influenced by

Variation in Science Course Taking

The evidence that course taking is strongly

associated with the likelihood of increasing in

science proficiency level between 8th and 12th

grades is compelling. Equally important is the

evidence showing that the chances of increasing

are lower for females than for males, for blacks

than for whites, and for students from low than

those from high SES backgrounds. The next

natural question is to ask to what extent do

differences in course-taking behavior between

these groups account for differences in chances of

increasing in science proficiency level. If a

student characteristic that is negatively associated

with chances of increasing is also negatively

related to taking higher levels or numbers of

science courses, then one would expect that

characteristic to have a smaller negative

relationship to chances of increasing once

differences in course taking are taken into

account.

Characteristics of black students tend to fit the

criteria which would lead one to expect a

reduction in the (negative) relationship between

being black and chances of increasing in science

proficiency level. The simple descriptive statistics

in tables 1 and 2 indicate that black high school

students were less likely than whites to take 8 or

more science courses or to take physics (18 versus

29 percent). They were also less likely to increase

in science proficiency level (39 versus 56 percent).

In a simple logistic regression model comparing

black and white students’ chances of increasing in

science proficiency level, accounting for

differences in science course taking significantly

reduces the estimated coefficient representing

blacks (table 5, from -.68 to -.56). 33 In other

words, being a black student has less of a

negative relationship to chances of increasing

once adjustments are made for differences

between blacks and whites in science course

taking.

Males may outperform females on tests of science

achievement in part because, as some researchers

argue, males were more exposed to science.

Above it is shown that males were more likely

than females to increase in science proficiency

level (table 1). But there is no evidence

suggesting that they took a larger number of

science courses (table 2). Males were more likely

to have taken physics, however. Given these

results and considering the logic outlined above,

one would not expect course taking to explain a

substantial part of the gender gap in chances of

increasing.

Results from logistic regression analyses confirm

this expectation. In a simple logistic regression

model comparing male and female students’

chances of increasing in science proficiency level,

adding course-taking variables had little effect on

the estimated coefficient for gender (table 5, from

.21 to .20). The 5 percent decrease in magnitude is

not a significant change. Adjusting for differences

in course taking does not reduce the relationship

of gender to chances of increasing in science

proficiency level because the differences in science


course taking between males and females were

small.

Examining how course taking affects the

relationship of gender and race-ethnicity to

chances of increasing in science proficiency level

would be as easy and straightforward as in the

above analyses if course taking was the only

explanation for increasing. But chances of

increasing are also related to initial science

proficiency level and to socioeconomic status

(figure 2 and table 1). One can more thoroughly

understand how course taking relates to gender

and race-ethnicity differences in chances of

increasing in science proficiency by also

considering the role of such additional correlates.

Towards this end, a logistic regression model was

estimated to predict chances of increasing for

males and females while adjusting for differences

in initial science proficiency level, socioeconomic

status, race-ethnicity, and type of school (e.g.,

“full controls”). When course-taking variables

were then added to this model, the relationship

between gender and chances of increasing in

science proficiency level changed in the direction

opposite of what was expected—it increased (.23

versus .28). The coefficient representing the

contrast between males and females became 22

percent larger, indicating that males were even

more likely to increase than females when course

taking was controlled.

Table 5.—Logistic regression coefficients for contrasts of interest in models predicting changes of

 increasing in science proficiency level with and without controls for course taking

Control variables Percentage difference3

Other Course-taking

Contrast of Course-taking predictors plus other Column Column

interest None only1 only2 predictors 1 versus 2 3 versus 4

1 2 3 4

Black vs. -0.68 -0.56 -0.69 -0.77 18% 12%

white (0.12) (0.11) (0.12) (0.12)

Male vs. 0.21 0.20 0.23 0.28 5% 22%

female (0.06) (0.07) (0.07) (0.08)

Low vs. -0.97 -0.56 -1.12 -0.67 42% 40%

high SES (0.10) (0.11) (0.13) (0.13)

Low-medium -0.74 -0.45 -0.83 -0.5 39% 40%

vs. high SES (0.10) (0.10) (0.11) (0.11)

Medium-high -0.44 -0.27 -0.51 -0.32 39% 37%

vs. high SES (0.09) (0.09) (0.10) (0.11)

1

 Course taking is represented by three variables: number of science course, type of science courses, and self-identified

curriculum.

2

 The other predictor variables in the model are initial science proficiency level, type of school, and the remaining

demographic variables (i.e., for Race-ethnicity, the latter would include Gender and SES).

3

 In log-odds coefficients. Specifically, the absolute value of the coefficient in the reduced model minus the coefficient

in the fuller model divided by the coefficient in the reduced model.

NOTE: Coefficients represent the log-odds ratio. Exponentiating the coefficient produces the odds ratio. For example,

exponentiating -.69 leads to .50 which implies that the odds of an increase in science proficiency level are one-half as

great among blacks compared to whites. Standard errors are in parentheses.

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

of 1988.
There is an explanation behind this increase. In

this sample, once adjustments were made for

differences in initial proficiency, SES, and type of

school, females were slightly more likely than

males to take more science courses and to report

that they were in an academic curriculum.34

When this course-taking advantage is statistically

removed through regression analysis, the end

result is a larger difference between males and

females in chances of increasing in science

proficiency level.

In contrast to the simple bivariate model where

adding course-taking variables reduced the

negative relationship between black students

versus white and chances of increasing in science

proficiency level, adding course-taking variables

to the model containing additional correlates did

not change the black versus white comparison (-

.69 versus -.77). Specifically, the logistic

coefficient representing chances of increasing for

blacks compared to whites appears to be larger

once course-taking differences are controlled.

However, this change is not large enough to be

considered substantively important (12 percent is

less than the 15 percent criteria described in

footnote 33).

Further analyses of the data on black and white

course-taking patterns helped to explain why this

outcome occurred. 35 There is no abundant

evidence that blacks who were at the same SES

and proficiency level as whites were more likely

than whites in this sample to have taken more of

the courses related to increasing in science

proficiency level (although the coefficients tended

to be in the positive direction, they were either

smaller or only slightly larger than their standard

errors). Thus, when course-taking variables were

added to the model predicting chances of

increasing in science proficiency level, the

coefficient representing the contrast between

blacks versus whites did not become significantly

larger.

A large body of literature describes how students

from low socioeconomic backgrounds are placed

into less demanding groups, courses, and

curriculums, a practice which tends to exacerbate

differences in achievement among students.36 One

would expect, therefore, that after adjusting for

course-taking differences, the fact that students

were from low socioeconomic backgrounds

would have less of an impact on their chances of

increasing in science proficiency level.

Students from low SES backgrounds in NELS:88

were clearly less likely than those from high SES

backgrounds to take 8 or more semesters of

science or to take physics—even among students

who started at the same science proficiency level

in eighth grade. This consistent negative

correlation is important according to the logic

outlined above for it implies that SES will be less

related to chances of increasing in science

proficiency once course-taking differences are

controlled. In fact when course-taking variables

were added to the bivariate and full models

predicting chances of increasing, large reductions

occurred in the coefficients representing students

from the lower versus highest socioeconomic

backgrounds (table 5, from -.97 to -.56 and -1.12

to -.67 respectively).37

In summary, no overwhelmingly strong nor

consistent evidence was found to support the

hypothesis that differences between males and

females or whites and blacks in chances of

increasing in science proficiency level are

accounted for by differences in the number or

level of science course taking. This interpretation

is tentative, and additional analysis and data are

required to further clarify the evidence. In

contrast, a substantial part of the positive

relationship between a student’s SES background

and chances of increasing appears to be due to

differences in course taking.

Summary

Previous cross-sectional studies have shown

course taking to be related to achievement, with

higher performing students tending to take a

higher number of and more difficult courses.

This relationship, however, may be interpreted in

at least two ways. More course taking may lead

to higher achievement or students who take more

courses may have been higher achievers to begin

with.38 Longitudinal data allows for investigating

changes in proficiency while taking initial

performance levels into account. This analysis

examined the relationship between gains in

science proficiency level and science course taking

for a group of 8th-graders in 1988 over a 4-year


period, taking into account a variety of

characteristics of students, including initial

science proficiency level.

The major finding from this analysis is that

students who take higher level science courses are

more likely to gain in science proficiency level

than those who do not. This relationship was

especially evident for students who started at the

top level of proficiency in the eighth grade.

Among students who started at the lowest level

of proficiency in the eighth grade, this

relationship was relatively weaker. However,

their chances of gaining in proficiency were also

related to the number of science courses that they

had taken. Science course taking, therefore, is

important for students at all levels of initial

science proficiency.

The rigor of course taking was highly related to

the likelihood of increasing in science proficiency

level over a 4-year period for 1988 eighth-graders,

even after taking into account a number of other

factors, including number of science courses

taken. Among students at similar levels of

science proficiency in 1988, those who took

physics in high school were more likely to

demonstrate a gain in science proficiency level

than those who did not. Except for students with

low levels of eighth-grade science proficiency,

those who took chemistry were more likely to

increase than those who took neither chemistry

nor physics. Similarly, except for students who

started at the lowest level, those who said that

they were in an academic curriculum were more

likely to increase than those who said they were

in another type of curriculum.

The number of science courses taken in high

school was also related to gains in science

proficiency level, but not consistently across all

groups of students. When the rigor of courses

and other factors were taken into account, the

number of courses taken was not related to gains

in proficiency level for those students who had

demonstrated relatively high levels of proficiency

as eighth-graders. Among students who had low

to moderate levels of proficiency in eighth grade,

however, those who took many semesters of

science (eight or more) were more likely to gain in

proficiency level than those who took less than

eight. The most consistent pattern seems to be

that what science courses students take in high

school is more related to increases in science

proficiency level than the number of science

courses.

Turning to the relationship between demographic

characteristics of students and chances of

increasing in science proficiency level, some

findings seem noteworthy. While some analysts

have argued that differences in course-taking

patterns are the reasons for differential

achievement among students from various

demographic backgrounds, the evidence

presented here casts some doubt on this

argument. Even after taking differences in course

taking and self-identified curriculum into account,

students from high SES backgrounds who started

high school at middle or high levels of science

proficiency were more likely to increase in level

than students from low SES backgrounds. In

addition, males who started at middle or high

levels of proficiency were more likely than

females to increase, and white students were

more likely to increase than black students. These

findings from demographic comparisons point to

the need for more comprehensive research on

gender, race, and SES differences in science

achievement growth.

Although transcripts from NELS do not reveal

what was taught in specific courses, they do

indicate the course level, e.g., whether it was

remedial, general, honors, or advanced

placement. In future analysis of factors related to

proficiency growth, researchers might want to

pursue such descriptive details about the courses

taken by students. They might also explore

whether the motivations that students have

toward pursuing a career in science affects their

gains in science proficiency. Do motivations

explain part or all of the gender, race-ethnic, and

SES differences in chances of gaining in science

proficiency? Or are characteristics of science

teachers such as credentials, experience, or

attitudes toward equitably teaching all students

responsible for the differences? What role do

parents play in the learning of science during

high school? Many interesting questions await to

be answered. This analysis only has tapped into

a tiny part of the enormous information in

NELS:88 about student achievement over time.


Notes

1. International Mathematics and Science Assessments, U.S.

Department of Education, National Center for Education

Statistics (NCES) 1992.

2. National Commission on Excellence in Education, A

Nation at Risk, 1983; see also Walberg 1984.

3. Aldridge 1992; National Science Teachers Association (NSTA)

1990.

4. See Welch, Anderson, and Harris 1982; Rock, Owings, and

Lee, U.S. Department of Education 1994; relating to the ACT see

Garibaldi 1992.

5. 1992 in The 1990 Science Report Card; see also table 2 below.

6. 1988, p.90 in The Science Report Card by Mullis and Jenkins.

7. See note 4 above. Also see Hoffer et. al, U.S. Department of

Education 1995.

8. See The 1990 Science Report Card for evidence of the gap

and some evidence of differential course taking; see also Levin,

Sabar and Libman 1991.

9. Hill, Pettus and Hedin 1990.

10. Crawley and Coe 1990.

11. Mackenzie 1983; Purkey and Smith 1983; Walberg and

Shanahan 1983; Coleman and Hoffer 1987; Lee and Bryk 1989,

Chubb and Moe 1990; Mullis et. al. 1994.

12. In fact, results from preliminary analyses of NELS:88

achievement data suggest that less growth in achievement

occurred over the last two years of high school than the first

two (Ralph et. al 1996; see also Alexander, Entwisle and

Dauber 1994 for evidence of decreasing gains in

achievement as students proceed through school). The High

School and Beyond longitudinal survey of 1980, which

produced data that is used widely by education

researchers, covered only the last two years of high school—

the least productive in terms of overall gains in achievement

across students. It was, however, an improvement over the

National Educational Longitudinal Survey of 1972, which

covered only the final year of high school.

Some 24,599 eighth-grade students from across the nation

were interviewed in the base year (1988). Followup studies

attempted to re-interview these same students 2 and 4 years

later when most, but not all, were in 10th and 12th grades,

respectively. Descriptions of the sampling design, item

nonresponse, and the variables included in the report are

reported in Appendix B.

13. Both base year and second followup science proficiency

scores were available for 9,832 of the 24,599 base year students.

Of these students, 9,322 did not drop out of high school

permanently between the surveys (i.e., they could be dropouts

who returned to school or alternative completers). Of these

students, 7,584 had complete transcript information available.

Thus, the scope of the report is limited to a longitudinal sample of

1988 eighth-graders who had science test scores available at

two points in time, had complete transcript records, and were

enrolled in school during the spring of 1992. (Students who did

not reach 12th grade by 1992 were excluded from this analysis

because they had incomplete transcript data.) The data were

weighted by a relative weight which was created by dividing

the expansion panel weight (F2PNLWT) by the average

expansion panel weight. The weighing scheme did not

compensate for test or transcript non-response. Additional

information about the sample is presented in Appendixes A and

B.

14. For details see the Psychometric Report by Rock et. al., U.S.

Department of Education 1991 and the Second Followup:

Student Component Data File User’s Manual, U.S. Department of

Education 1992.

15. Levels have the same interpretation in both years. Note,

however, that level 3 was not part of the base-year test. The skills

or abilities needed to correctly answer questions that were used

as indicators for each level do not depend on participation in a

particular course. Instead, they transcend such knowledge by

tapping into broader conceptual understandings of science

and related problem-solving skills.

16. By forcing all students into a few groups, students with

differing degrees of understanding of science are combined into

a single level. The aim was to create measures of science

proficiency with more practical utility than alternative continuous

measurements such as ones created using Item Response Theory

(IRT). Some students may increase (or decrease) in science

proficiency during high school and yet not change their level of

science proficiency. See the appendix for a discussion of the

reliability of the proficiency levels.

17. U.S. Department of Education, Office of Research 1992.

18. Cusik 1973.

19. U.S. Department of Education, Office of Research 1994;

Goldman 1985.

20. The National Education Goals Report 1993; Feldman and

Atkin 1993.

21. The relatively lower chances of gaining for those at the

top level of proficiency in eighth grade was not due to a

ceiling effect. The 1992 science test included questions that

covered proficiency one level higher than the highest one

covered by questions on the 1988 eighth grade test.

22. Regression to the mean has a special statistical

interpretation. The lack of perfect reliability in measuring

ability means that in the absence of any changes in

underlying true ability, persons who scored far from their true

score are likely to score closer to the true score when retested, so that high scores will tend to go down and low

scores will tend to go up.

23. See for instance Epstein 1991 or Lee et. al. 1995. Note that

this is not the case with Rock, Owings and Lee’s (1994) findings,

perhaps because in their analysis students in the lowest two

categories of eighth-grade proficiency were combined and

students were only tracked until 10th grade. In the future,

researchers might want to explore this issue in more detail.

24. A breakdown of the science proficiency level of students

in 1992, when they are about to leave high school, by course

taking and demographic characteristics is reported in

appendix table A6.

25. Course taking in science is limited to a few broad areas.

Descriptive frequencies indicate that relatively few students


take physics (roughly one-fourth), nearly half take chemistry,

and over 80 percent take biology. Earth science is taken by

a little more than one-fifth of students. Approximately 60

percent of students take courses outside these areas of

science with only 8 percent of such students taking more

than 2 courses. See the second followup transcript

component data file user’s manual for exact figures (U.S.

Department of Education 1994).

The breakdown used here of the types of science courses

taken by students probably reflects the most common

sequence of courses taken in science. It is a parsimonious

breakdown which facilitates exploring how course taking is

related to gains in achievement. More detailed breakdowns

are possible, such as one which encompasses AP biology or

zoology course taking. However, students who take physics

are probably the ones taking such courses and would be

picked up in this analysis. At any rate, pursuing detailed

breakdowns in future research might further enrich our

understanding of how course taking is related to gains in

achievement.

Based primarily on the fact that they are offered later in the

high school curriculum and fewer students take them,

physics and chemistry are assumed to be more rigorous than

other types of science courses.

26. The percentage of high school seniors who have taken

physics has increased by 11 percentage points from the

beginning of the 1980s (U.S. Department of Education, NCES,

1995). One might attribute part of this increase to the fact

that states have been increasing their science requirements

(Suter 1993).

27. Two semesters of science equal one Carnegie unit of

science. A Carnegie unit represents one credit for the

completion of a 1-hour per day/5 days per week, 1-year course.

Twenty-seven percent of NELS:88 students took 8 or more

semesters of science.

28. The reader is cautioned about interpreting the comparison

between students at level 2 in eighth grade who took 6–7.99

semesters of science versus those who took 0–3.99 semesters and

increases in science proficiency level. The cell representing

students at level 2 in eighth grade who took 0–3.99 semesters of

science contains a small number of cases. This leads to a large

standard error for the estimated percent of these students who

increased in science proficiency level. Consequently, finding a

significant difference when making comparisons involving this

group is difficult. This caution applies also to other parts of this

analysis where relatively large standard errors were generated.

29. Note that in table 3 curriculum also is related to both

number and type of science courses taken.

30. Results from an overall regression (all students combined)

which includes 1988 proficiency level as a predictor can be

found in the appendix (table A10). Except for a small loss of

detail, the results generally reflect the relationships described in

table 4. In addition, they also indicate that, with all other

variables controlled, students who started at lower initial

proficiency levels were more likely to increase than those who

started at higher levels.

31. When a set of inferences come from the same set of

sample data they are not independent. Thus, determining

the probability of the set of estimates being correct is more

difficult than in the case when there is only one inference.

The Bonferoni procedure, a general procedure for making

inferences in this situation, involves adjusting the statement

confidence coefficients for each inference to reflect the

probability that after repeated sampling the entire set of

coefficients would be correct (Neter, Wasserman, and

Kutner 1990). Applying this logic to all possible inferences

that could be made about the relationship between the four

categories of number of science courses taken and chances

of increasing in science proficiency level (from results of the

multiple logistic regression analysis), the necessary critical tvalue for testing inferences would be 2.64. Using this value

would lead one to conclude that only one in the set of six

inferences for students who started below level 1 and only

two for those who started at level 1 indicate a significant

relationship between number of courses and increasing. This

would lead to a slightly different interpretation of the

relationship, mainly that evidence of a positive relationship is

not so strong. In practice, however, few researchers make

any type of adjustment (Johnson and Wichern 1988).

32. Some caution should be exercised in interpreting this

coefficient. For example, adjusting the significance level to

account for multiple comparisons, as described in footnote

31, would lead one to accept the null hypothesis of no

relationship.

33. To determine whether changes in the coefficients in

table 5 were statistically significant would require applying

sophisticated statistical tests (see Clogg et al 1995; Clogg

and Petkova 1995; Allison 1995) that are beyond the scope

of this report. Instead, a simple rule of thumb is used to

determine if the change is important: if the coefficient

changed by at least 15 percent, the change is deemed to

be of substantive interest.

34. Based on regressions not reported here but available upon

request from the author.

35. Based on regressions not reported here but available upon

request from the author.

36. See, for example, Gamoran et. al. 1995, Oakes 1985 and Rist

1970.

37. Gamoran and Mare 1989 found somewhat similar results in

their analysis of the effects of tracking on math achievement in

the High School and Beyond survey data. Blacks and females

were more likely than non-Blacks and males respectively to be

found in the academic track when initial achievement, SES, and

other variables were controlled. This tended to compensate for

the disadvantage associated with the gross (i.e., without

adjustments for initial achievement, SES, etc.) higher probability

of blacks and females not to be in the academic track.

Compensation of this type was not found for students from low

SES backgrounds, however. Tracking reinforced initial

differences in achievement among students from various SES

backgrounds.

38. In real life this relationship could go in both directions.

Although I have not tested whether gains cause course

taking, I have shown that course taking is related to gains,

controlling for initial achievement. This is an important

finding to note, especially if one is inclined to believe that

the only explanation for the relationship between

achievement and course taking is that smarter students take

more courses.


Appendix A

Table A1.—Standard errors for table 1

School and student Change in science proficiency level

characteristics Decrease Same Increase

 Total 0.6 0.8 0.9

Gender

 Male 0.9 1.2 1.3

 Female 0.6 1.0 1.0

Race-ethnicity

 Asian 1.8 2.7 2.9

 Hispanic 1.4 2.6 2.4

 Black 3.6 2.8 2.7

 White 0.5 0.9 1.0

 American Indian 6.3 6.7 6.2

SES quartile

 Low 1.3 1.8 1.7

 Low-medium 1.6 1.6 1.6

 Medium-high 0.8 1.3 1.3

 High 0.5 1.7 1.7

Type of school

 Public 0.6 0.9 0.9

 Catholic 1.5 3.4 3.2

 Other private 1.2 4.5 4.7

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


Table A2.—Standard errors for table 2

Science courses taken

No

School and Number of semesters of science chemistry- Chemistrystudent characteristics 0.0–3.99 4.0–5.99 6.0–7.99 8.0 or more physics no physics Physics

 Total 0.4 1.0 0.8 1.0 1.0 0.9 1.0

Gender

 Male 0.5 1.4 1.2 1.2 1.4 1.3 1.3

 Female 0.5 1.1 1.0 1.1 1.1 1.2 1.1

Race-ethnicity

 Asian 1.3 4.0 2.7 3.8 3.5 3.6 4.0

 Hispanic 1.8 2.6 2.2 2.1 3.0 2.9 2.0

 Black 1.3 3.5 2.5 2.6 3.4 2.8 2.5

 White 0.5 1.1 1.0 1.1 1.0 1.0 1.1

 American Indian 3.9 6.4 7.1 4.1 7.9 5.9 6.6

SES quartile

 Low 1.3 1.9 2.0 1.1 1.8 1.7 1.0

 Low-medium 0.8 1.8 1.3 1.2 1.7 1.6 1.2

 Medium-high 0.6 1.4 1.4 1.6 1.4 1.5 1.3

 High 0.4 1.3 1.7 1.8 1.2 1.9 2.0

Type of school

 Public 0.5 1.0 0.8 0.9 1.0 0.9 0.9

 Catholic 0.8 3.6 3.7 4.4 2.9 3.8 4.4

 Other private 1.9 4.7 6.0 7.6 4.7 6.0 7.9

Curriculum

 Academic 0.3 1.1 1.3 1.5 0.8 1.4 1.5

 General 0.8 1.5 1.2 1.0 1.5 1.2 1.0

 Vocational 1.6 2.5 2.2 1.4 2.3 2.1 1.4

Science courses

 No chemistry-or physics 1.0 1.5 1.1 0.4 — — —

 Chemistry-no physics 0.2 1.4 1.6 1.4 — — —

 Physics 0.3 0.7 1.6 1.8 — — —

1988 proficiency level

 Below 1 1.1 1.8 1.9 1.1 1.9 1.9 1.1

 Level 1 0.5 1.3 1.2 1.1 1.3 1.2 1.2

 Level 2 0.4 1.3 1.3 1.6 1.1 1.5 1.6

— Not applicable.

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


Table A3.—Standard errors for table 3

Course taking and Proficiency level in 1988

curriculum Below 1 Level 1 Level 2

 Total 1.9 1.2 1.6

Semesters of science

 0.0–3.99 5.0 3.7 7.0

 4.0–5.99 2.1 2.0 2.9

 6.0–7.99 4.5 1.8 2.4

 8.0 or more 2.8 2.0 2.5

Curriculum

 Academic 4.4 1.4 2.0

 Vocational 3.6 3.3 3.6

 General 2.0 2.0 2.6

Science courses

 No chemistry-or physics 1.9 1.8 2.2

 Chemistry-no physics 4.9 1.7 2.5

 Physics 2.7 1.8 2.0

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


Table A4.—Data for Figure 1: Percent of NELS students at different levels of science

 proficiency: 1988 and 1992

Table A5.—Standard errors for table A4

Proficiency level

Year Below 1 Level 1 Level 2 Level 3

1988 8th-grade 22 47 31 —

1992 15 29 32 24

— Not applicable.

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

Proficiency level

Year Below 1 Level 1 Level 2 Level 3

1988 8th-grade 0.8 0.8 0.8 —

1992 0.7 0.7 0.8 0.7

— Not applicable.

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


Table A6.—Percent of NELS students at various levels of science proficiency in 1992

School and student At or above:

characteristics Below level 1 Level 1 Level 2 Level 3

 Total 15 (0.7) 85 (0.7) 56 (0.9) 24 (0.7)

Gender

 Male 13 (1.1) 87 (1.1) 59 (1.3) 28 (1.0)

 Female 17 (0.8) 83 (0.8) 53 (1.1) 19 (0.8)

Race-ethnicity

 Asian 12 (1.7) 88 (1.7) 61 (3.5) 32 (3.1)

 Hispanic 22 (1.8) 78 (1.8) 43 (2.4) 13 (1.7)

 Black 35 (3.5) 65 (3.5) 29 (2.8) 6 (0.9)

 White 11 (0.7) 89 (0.7) 61 (0.9) 27 (0.8)

 American Indian 31 (7.1) 69 (7.1) 27 (6.1) 12 (3.9)

SES quartile

 Low 27 (1.6) 73 (1.6) 33 (1.7) 9 (1.0)

 Low-medium 18 (1.6) 82 (1.6) 47 (1.6) 17 (1.1)

 Medium-high 13 (0.9) 87 (0.9) 58 (1.4) 23 (1.2)

 High 7 (1.4) 93 (1.4) 74 (1.5) 38 (1.5)

Type of school

 Public 15 (0.8) 85 (0.8) 55 (1.0) 23 (0.7)

 Catholic 10 (1.9) 90 (1.9) 64 (3.4) 30 (3.1)

 Other private 9 (3.7) 91 (3.7) 71 (5.3) 35 (5.0)

Semesters of science

 0.0–3.99 31 (0.4) 69 (0.4) 26 (2.3) 7 (1.4)

 4.0–5.99 22 (1.3) 78 (1.3) 39 (1.4) 11 (0.8)

 6.0–7.99 13 (1.3) 87 (1.3) 59 (1.5) 23 (1.2)

 8.0 or more 5 (0.6) 95 (0.6) 80 (1.1) 44 (1.7)

Curriculum

 Academic 8 (0.9) 92 (0.9) 70 (1.1) 34 (1.1)

 Vocational 23 (1.8) 77 (1.8) 36 (2.1) 7 (1.1)

 General 21 (1.2) 79 (1.2) 44 (1.3) 15 (1.0)

Science courses

 No chemistry-no physics 26 (1.2) 74 (1.2) 34 (1.2) 7 (0.6)

 Chemistry-no physics 12 (1.3) 88 (1.3) 61 (1.5) 23 (1.1)

 Physics 4 (0.5) 96 (0.5) 81 (1.1) 46 (1.6)

1988 proficiency level

 Below 1 37 (1.9) 63 (1.9) 23 (1.2) 4 (0.5)

 Level 1 12 (0.9) 88 (0.9) 55 (1.2) 18 (0.8)

 Level 2 3 (0.5) 97 (0.5) 83 (1.1) 46 (1.6)

NOTE: Standard errors are in parentheses.

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


Table A7.—Percent of 1988 8th-grade students whose science proficiency level decreased,

 remained the same or increased between 1988 and 1992

Course-taking, curriculum, and Change in science proficiency level

1988 science proficiency level Decreased Same Increased

 Total 11 (0.6) 35 (0.8) 54 (0.9)

Semesters of science

 0.0–3.99 14 (1.9) 46 (3.1) 40 (3.1)

 4.0–5.99 15 (1.2) 42 (1.4) 44 (1.3)

 6.0–7.99 11 (0.8) 35 (1.4) 55 (1.4)

 8.0 or more 7 (0.7) 26 (1.5) 68 (1.6)

Science courses

 No chemistry-no physics 16 (1.1) 42 ( 1.2) 42 (1.2)

 Chemistry-no physics 9 (0.8) 36 (1.5) 54 (1.5)

 Physics 6 (0.6) 24 (1.2) 70 (1.3)

Curriculum

 Academic 8 (0.5) 31 (1.2) 62 (1.2)

 Vocational 16 (1.9) 40 (2.2) 43 (2.2)

 General 14 (1.1) 39 (1.2) 47 (1.3)

1988 proficiency level

 Below 1 — 37 (1.9) 63 (1.9)

 Level 1 12 (0.9) 33 (1.0) 55 (1.2)

 Level 2 17 (1.1) 37 (1.5) 46 (1.6)

— Not applicable.

NOTE: Standard errors are in parentheses.

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


Table A8.—Estimated logistic regression coefficients for the regression of increase in science

 proficiency level between 1988 and 1992 on student, school, and course-taking

characteristics

 Intercept 0.71 * (0.10)

Gender (vs. female)

Male 0.28 * (0.08)

Race-ethnicty (vs. white)

Asian -0.02 -0.14

Hispanic -0.20 -0.12

Black -0.78 * (0.12)

American Indian -0.57 -0.32

SES (vs. high)

Low -0.67 * (0.13)

Low-medium -0.50 * (0.11)

Medium-high -0.31 * (0.11)

Type of school (vs. public)

Other private 0.22 -0.17

Catholic -0.20 -0.15

Semesters of science (vs. 8 or more)

0.0–3.99 -0.63 * (0.17)

4.0–5.99 -0.45 * (0.11)

6.0–7.99 -0.32 * (0.10)

Curriculum (vs. academic)

General -0.36 * (0.09)

Vocational -0.28 * (0.12)

Science courses (vs. physics)

No chemistry-or physics -1.05 * (0.10)

Chemistry-no physics -0.58 * (0.09)

1988 proficiency level (vs. 2)

Below 1 1.79 * (0.17)

Level 1 0.91 * (0.09)

* p<.05

NOTE: Standard errors are in parentheses.

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


Table A9.—Estimated odds ratios for the logistic regression coefficients in table 4

Science proficiency level in 1988

Selected characteristics Below 1 Level 1 Level 2

Gener (vs. female)

 Male 1.25 1.25 1.55

Race-ethnicity (vs. white)

 Asian 0.88 0.93 1.28

 Hispanic 0.82 0.76 0.85

 Black 0.49 0.42 0.44

 American Indian 0.74 0.41 1.26

SES (vs. high)

 Low 0.73 0.44 0.48

 Low-medium 1.08 0.46 0.63

 Medium-high 0.86 0.64 0.80

Type of school (vs. public)

 Catholic 1.19 0.67 0.87

 Other private 0.98 1.01 1.72

Semesters of science (vs. 8.0 or more)

 0.0–3.99 0.32 0.49 1.40

 4.0–5.99 0.53 0.55 0.82

 6.0–7.99 0.53 0.72 0.81

Curriculum (vs. academic)

 General 0.96 0.62 0.69

 Vocational 1.26 0.64 0.44

Science courses (vs. physics)

 No chemistry-or physics 0.35 0.46 0.20

 Chemistry-no physics 0.44 0.72 0.51

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



Logistic Regression

The logistic regression model is of the following

form:

log[p/(1-p)]=B0

 + B1x1 + ... + Bixi

An odds ratio is computed by dividing the

probability that an event occurred by the

probability that it did not (p/1-p). In this analysis

the event of interest is whether a student's science

proficiency level increased. The log of the odds

ratio is then taken and used as the outcome

variable in logistic regression. In the above

model, B0

 represents the intercept which can be

interpreted as the log-odds of the outcome

variable when all the explanatory variables are

zero, B1

x1 represents the increase in the log-odds

of the outcome variable accounted for by an

increment in the explanatory variable x1

, and Bixi

represents the increase in the log-odds of the

outcome variable accounted for by an increment

in the explanatory variable xi

. If more than one

explanatory variable is included in the logistic

regression model (as in this analysis), then Bi

xi

represents the effect of xi on the outcome after

adjusting for the effects of the other explanatory

variable(s).

One can determine the change in the odds of

increasing in science proficiency by going from

one category of an independent variable to

another, a statistic easier to interpret than the logodds, by exponentiating the appropriate

coefficient of interest. For example, at initial

proficiency level 1, in terms of odds ratios, males

were 1.25 times more likely than females to

increase in proficiency, controlling for

demographic and course-taking factors.

Likewise, in terms of odds ratios, students from

high SES backgrounds were over two times as

likely to increase in proficiency compared to their

low SES background peers. Among students

who were at level 2 in eighth grade, in terms of

odds ratios, those who took physics were five

times as likely to increase in proficiency level than

those who took neither chemistry nor physics.

See table A9 for the odds ratios of other variables

in table 4.


Appendix B: Technical Notes for NELS:88*

The NELS:88 base year survey comprised a

national probability sample of all regular public

and private 8th-grade schools in the 50 states and

the District of Columbia in the 1987–88 school

year. During the base year data collection,

students, parents, teachers, and school

administrators were selected to participate in the

survey. The total 8th grade enrollment from 1,052

NELS:88 sample schools was 202,996. During the

listing procedures (before 24–26 students were

selected per school), 5.35 percent of students were

excluded because they were identified by school

staff as being incapable of completing the

NELS:88 instruments because of limitations in

their language proficiency or because of mental or

physical disabilities. Ultimately, 93 percent, or

24,599, of the sample students participated in the

base year survey in the spring of 1988.

The NELS:88 second followup survey was

conducted during the spring of 1992. Students,

dropouts, parents, teachers, and school

administrators participated in the followup,

which set a target subsample of 21,188 students.

Some 97 percent of these students were

successfully located. For the current report, data

from base year ineligibles (BYI), students deemed

not capable of answering the questionnaire due to

language or mental difficulties, were not used

because measures that reflect science proficiency

for two points in time (base year and second

followup), a necessary requirement for

determining the progression of science skills of

students, are not available for these students.

The scope of the cohort data presented in this

report is limited to students who were sampled

and attending schools both during the base year

and second followup surveys. Excluded from

this study are sampled eighth graders who

dropped out of school. Also excluded from this

analysis are BYI students and freshened students

(ones in followup surveys who did not have the

opportunity to participate in 1988 for various

reasons including not being in country) who were

not selected in the base year sample. Altogether,

the in-scope sample consists of

14,814 cases. Among them, 7,230 either did not

have complete transcript information (which was

obtained from a special transcript component of

the second followup survey) or did not complete

sufficient numbers of test items so that their

science proficiency could be determined in the

base year and/or the second followup. Due to

the absence of these key pieces of data, they were

treated as missing. Thus, 7,584 cases were used

for this analysis. (Due to decisions that were

made in conducting various parts of the NELS:88

survey, these numbers should not be used to

construct a survey “response rate.”)

A brief sketch of the number of students involved

in NELS:88 and the final number used in this

analysis is as follows:

1) Target base year sample size............. 26,432

Realized sample size...........................24,599

2) Target second followup (F2)

sample size .......................................21,188

Realized sample size.........................20,623

3) Number of realized F2 students

representing the 8th-grade panel......16,489

4) Number of above (3) students who

did not drop out..................................14,814

5) Number of above (4) students with

 base year cognitive tests, second

 followup cognitive tests, and

 complete transcripts (number used

in analyses)............................................ 7,584

The results of these analyses apply to the

population of children who were in 8th grade in

1988 and in 12th grade four years later.

*Parts of these notes can be found in Rock, Owings, and Lee

(1994). In addition, Judy Pollack from Educational Testing

Services in Princeton, N.J. provided technical information on

the psychometric properties of the NELS:88 science

proficiency levels.


Respondents Who Were Missing Key Information

Certain patterns were noted in the types of

students who were missing information. Females

were less likely than males; Hispanics, blacks, and

American Indians were less likely than whites;

and low SES students were less likely than high

SES students to have complete key information

(Appendix Table B1). These groups of students,

therefore, were more likely to be excluded from

the analyses. Aggregate results may tend to overrepresent patterns for whites, males and students

from high SES family backgrounds.

Additional comparisons reveal that the group

without key information was slightly less likely

than the group with such information to: (1) be

classified at a higher proficiency level in the 8th

grade; (2) be classified at a higher proficiency level

in 12th grade; (3) take more science courses; (4)

report being enrolled in an academic curriculum;

and (5) take physics or chemistry as opposed to

neither of these courses.

Because students without key information were

less likely to be proficient at higher levels in

eighth grade, the distribution of the eighth-grade

science proficiency levels reported in this analysis

may be biased upward. Similarly, the

distribution of 12th-grade science proficiency

reported here may also be biased upward.

The estimated effects of these variables in the

analysis sample may or may not differ from their

effect in the full population. If the average

increase in science proficiency level for students

with incomplete data was similar to that of their

counterparts with complete data, the analysis

reported here is not affected by excluding these

students. However, if among students with the

same characteristics, i.e., eigth-grade science

proficiency, sciences courses taken, etc., those

with incomplete data had a substantially different

average increase in science proficiency from those

with complete data, the analysis may under or

overestimate the effects of these variables

depending on the direction of the difference. For

example, if among excluded students with few

science courses taken the average increase in

science proficiency was less than among included

students with few science courses taken, the effect

of courses taken would have been

underestimated.


Table B1.—Percentage of respondents1 who were missing key information, by demographic and

 schooling characteristics

Sampling Errors

Did not have key information

Student and school Unweighted Weighted Standard

characteristics number number Percent2 error

Total 6,786 7,230 49 (0.8)

Gender

Male 3,286 3,563 47 (1.1)

Female 3,500 3,667 50 (1.1)

Race-ethnicity

Asian 407 227 42 (2.9)

Hispanic 890 782 56 (1.9)

Black 771 1,137 60 (2.7)

White 4,621 4,955 46 (1.0)

American Indian 75 98 62 (4.7)

Missing3 32 47 — —

SES quartile

Low 1,571 1,699 57 (1.5)

Low-medium 1,631 1,808 49 (1.4)

Medium-high 1,664 1,877 48 (1.4)

High 1,920 1,846 44 (1.5)

Type of school

Public 5,650 6,112 47 (1.0)

Catholic 330 385 46 (3.7)

Other private 506 291 50 (4.9)

Missing3 461 450 — —

Curriculum

General 2,714 3,249 52 (1.2)

Academic 2,935 2,602 41 (1.2)

Other 717 797 49 (2.1)

Missing3 307 628 — —

Semesters of science

0–3.99 789 937 71 (2.1)

4.0–5.99 1,634 1,592 39 (1.2)

6.0–7.99 1,474 1,289 33 (1.2)

8.0 or more 1,003 766 26 (1.1)

Missing3 1,886 2,646 — —

Science courses

No chemistry-no physics 2,415 2,585 47 (1.2)

Chemistry-no physics 1,347 1,170 31 (1.2)

Physics 1,138 830 28 (1.2)

Missing3 1,886 2,646 — —

1988 proficiency level

Below 1 1,505 1,719 50 (1.4)

Level 1 2,427 2,708 43 (1.2)

Level 2 1,278 1,267 35 (1.4)

Missing3 1,576 1,535 — —

1992 proficiency level

Below 1 506 559 33 (2.0)

Level 1 841 969 31 (1.7)

Level 2 718 747 23 (1.5)

Level 3 446 459 20 (1.6)

Missing3 4,275 4,496 — —

—Not applicable.

1

Out of 14,814 8th-grade longitudinal panel respondents who did not drop out of school. See Appendix B for more information on the sample. Students

were classified as missing key information if they did not have both base year and second followup cognitive tests. In addition, students who were

involved in the transcript component of NELS:88 but did not have complete or only partial traynscript information were classified as missing key data. 2

If students were missing information on a stratification variable such as race or school sector, then they were not used to calculate the percentage without

key information for that particular variable.

3

This variable code represents missing cases on the stratification variable. For example, no student was missing information on gender and 47 were missing

race information. Note that 2,646 respondents were not involved in the transcript study, and show up as missing for the variables Science courses and

Semesters of science. In addition, the number of respondents who were missing 1992 proficiency level information is relatively large because the response

rate on the cognitive tests in the second followup was only 77 percent, as compared to 97 percent in the base year.

NOTE: Frequencies were weighted with a relative weight.

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


The data were weighted using the second

followup panel weight (F2PNLWT) divided by

the average panel weight to reflect the sampling

rates (probability of selection) and adjustments for

unit non-response.*

 The complex sample design

was taken into account when a Taylor series

approximation procedure was used to compute

the standard errors in this report. The standard

error is a measure of the variability of a sample

estimate due to sampling. It indicates, for a given

sample size, how much variance there is in the

population of possible estimates of a parameter.

    	
 	


 
     


 
  

 	
 
 
 	





  
 
 
  
 	

 	
 	  	  	
  

  
 
	 	   
  

	   
 
 
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If all possible samples were selected under similar

conditions, intervals of 1.96 standard errors below

to 1.96 standard errors above a particular statistic

would include the true population parameter

being estimated for about 95 percent of these

samples (i.e., 95 percent confidence interval).

Comparisons noted in this report are significant

at the 0.05 level. Except for results in the logistic

regression section, all comparisons were

determined using Bonferroni adjusted t-tests.

(See the footnote above for a discussion of the

procedures followed in the logistic regression

section.)


Variables Used in Analysis

Science proficiency. Proficiency levels in

science achievement form a hierarchical scale

with each succeeding level characterized by

increased complexity. A proficiency at a given

level implies proficiency at all levels below it.

Each proficiency level is marked by a block of

four items that have similar difficulty. For

example, the level 1 items mostly deal with

knowledge of simple scientific concepts.

Item #1 - Identify components of the solar system.

Item #2 - Read a graph depicting the solubility of

chemicals.

Item #3 - Choose a statement about the source of

the moon's light.

Item #4 - Identify the example of a simple reflex.

In addition to requiring the same cognitive

operations, the items for a particular level exhibit

similar item difficulty parameters. Since the

underlying cognitive demand model is assumed

to be hierarchical, students who are proficient on

the level 2 items should also demonstrate

proficiency on the level 1 items. While four items

may seem like a relatively small number of items,

they do prevent the chances of guessing correctly

at a level and are essentially parallel measures of

the same content or processing skill. The four

items are not a subscale that attempts to

discriminate individuals along a continuous

dimension but are simply used to make a

“know/can do” versus “do not know/cannot do”

determination at a certain point referencing a

specific skill. A full description of the

psychometric properties of the NELS:88 base year

test battery is presented by Rock & Pollack (1991).

Descriptions of followup batteries are available in

forthcoming followup NELS:88 psychometric

reports.

Reliability of proficiency levels. An estimate of

the reliability of a set of hierarchically ordered

proficiency levels must take into account the

hierarchical nature of the underlying cognitive

model and consider the reproducibility of the

response pattern. In a three-level model as used

in science a person who demonstrates proficiency

on two of those levels should show a

response pattern consistent with the hierarchical

nature of the proficiency levels. For instance, a

response pattern where students fail to pass the

lowest level but succeed at the higher levels

would not be consistent with the assumed

cognitive model where the increased difficulty

goes from low to high. Guttman's coefficient of

reproducibility is one measure of the deviation of

response patterns from the ideal when there is an

underlying order hierarchy. Guttman's

coefficient of reproducibility is equal to one - [total

number of deviations from the ideal across all

respondents/(number of respondents) (number

of levels)]. A corrected version of this coefficient

of reproducibility, one which removes those

individuals who had either a perfect score on the

three levels or a zero score since they would have

no opportunity for having deviations from the

ideal response pattern, was found to be .95.

Coefficients over .90 are considered quite high.

However, when the measuring instrument has

only three ordered and well spaced levels there is

less opportunity for errors to occur.

Semesters of science. Measured in Carnegie

units. A Carnegie unit represents one credit for

the completion of a one-hour, one-year course

five days a week. This measure was converted

into semesters by assuming that one Carnegie

unit represents two semesters of science.

Approximately 27 percent (s.e.=.96) of the

students took 8 or more, 34 percent (s.e.=.82) took

at least 6 but fewer than 8, 33 percent (s.e.=.98)

took at least 4 but less than 6, and the rest (6

percent) less than 4 semesters of science.

Science courses. If a student's transcript

indicated that she or he took a physics course,

then they received the value of “3” on this

variable. Students who took chemistry but not

physics received a two and those who took

neither chemistry nor physics received a one.

Curriculum. Categorical variable coded as

general, academic, or vocational from student

self-reports of high school curriculum in 1992.

Students who could not identify their type of

curriculum were included in the general category.

Type of school. Categorical variable created from

responses to the second followup school


questionnaire coded as public, Catholic, and other

private. Other private schools are composed of

both non-Catholic religious and non-religious

private.

Gender. Male and female.

Race-ethnicity. Asian-Pacific Islander, Hispanic,

Black-not Hispanic, White-not Hispanic, and

American Indian.

SES (Socioeconomic status). Base-year parent

data on father's education level, mother's

education level, father's occupation, mother's

occupation, and family income were standardized

and a continuous scale was created. This scale

was then divided into four to create quartiles.

Parent data were used unless parent information

was missing, then student responses to questions

about their parents were used. In a few cases

where data on all five components of SES were

not available, scale scores were constructed based

on the components that were available.


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