Statistics

in Brief

October 2010

U.S. Department of Education

NCES 2010–016

Authors

Jill Walston

Education Statistics

Services Institute – 

American Institutes for 

Research

Jill Carlivati McCarroll

National Center for 

Education Statistics

Contents

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

Focus of This Statistics 

in Brief............................. 2

The ECLS-K Cohort.............. 2

Mathematics Course 

Enrollment....................... 3

Eighth-Grade Algebra Enrollment in the Schools.......... 3

Fifth-Grade Mathematics 

Performance and Enjoyment of Mathematics....... 6

Eighth-Grade Mathematics 

Performance..................... 6

Enjoyment of Mathematics 

and Educational Expectations in the Eighth Grade . 9

Summary............................. 10

Methodology and 

Technical Notes.............. 11

Glossary: Constructs and 

Variables Used in the 

Analysis ......................... 13

References........................... 15

Appendix A. Standard 

Error Tables................... 17

For more information, contact 

Jill Carlivati McCarroll, 

National Center for Education 

Statistics, (202) 219-7002, 

jill.mccarroll@ed.gov

This report was prepared in part 

under Contract No. ED-05-

CO-0044 with Education Statistics Services Institute – American 

Institutes for Research. Mention 

of trade names, commercial 

products, or organizations does 

not imply endorsement by the 

U.S. Government.

Eighth-Grade Algebra: Findings From the EighthGrade Round of the Early Childhood Longitudinal 

Study, Kindergarten Class of 1998–99 (ECLS-K)

Introduction

Algebra is considered a “gateway” course for the sequence of mathematics and science 

courses that prepares students for success in later schooling (Matthews and Farmer 

2008). Mathematics courses are typically organized sequentially with enrollment in 

progressively more advanced courses dependent upon the successful completion of 

prerequisite courses. The earlier a student proceeds successfully through algebra, and 

then on to courses such as geometry and algebra II, the more opportunities he or she 

has for reaching higher level mathematics courses (e.g., trigonometry, precalculus, and 

calculus) in high school and completion of higher-level mathematics courses is related 

to a higher likelihood of entering a 4-year college or university (Schneider, Swanson, 

and Riegle-Crumb 1998). Recent research has related completion of advanced 

mathematics courses in high school with entering into science, technology, engineering, 

and mathematics majors in college (Chen 2009). Algebra may be integral to preparing 

students for success in college and the labor force, including careers in competitive 

mathematics- and science-related disciplines. The National Mathematics Advisory 

Panel (2008) noted that completing algebra II coursework during high school correlates 

positively with college graduation and employment income. The panel suggested that 

elementary and middle school mathematics curricula should put students on a path 

to learn algebra and have more students prepared to enroll in algebra by the eighth 

grade. Looking at international data, Schmidt (2004) reported that algebra concepts 

are commonly taught in the eighth grade in many other countries and suggested that 

U.S. students would benefit from increased opportunities for algebra instruction in the 

eighth grade. 

Eighth-grade algebra enrollment in the United States has been on the rise. While 

approximately 16 percent of all U.S. 13-year-olds (the age at which many students are 

in eighth grade) were enrolled in algebra in 1986, this figure rose to 22 percent in 1999 

and to 29 percent in 2004 (Perie, Moran, and Lutkus 2005). This trend affects the 

average level of mathematics course attainment students have achieved by graduation. 

An example of this trend is provided by Dalton et al. (2007), who compared coursetaking information from high school transcripts gathered from three nationally 

representative studies: the High School and Beyond (HS&B) Longitudinal Study, 

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

Longitudinal Study of 2002 (ELS:2002). They found an increase between 1982 and 

2004 in the number of high school graduates taking advanced mathematics courses and 

a concurrent drop in the percentage of students finishing high school having completed 

only lower level mathematics courses (e.g., algebra I and plane geometry). 

While the overall number of students in advanced mathematics courses is increasing, 

there are differences between the populations of students who do and who do not take 

advanced mathematics courses in high school. For example, using the ELS:2002 data, 

Bozick and Ingels (2008) found that advanced high school mathematics courses (i.e., 

classes that are part of course sequences containing precalculus) were being taken by 

larger percentages of Asian students, White students, students of high socioeconomic 
2 NCES 2010-016

status (SES), students living in two-parent households, 

students attending Catholic and other private schools, 

and students expecting to earn a bachelor’s degree than by 

other students. Similar differences in mathematics course 

participation (e.g., differences by race/ethnicity and SES) 

were also found by Dalton et al. in their 2007 study. 

Furthermore, students who enter seventh grade with higher 

mathematics achievement have been found to be more 

likely to take advanced mathematics courses earlier than 

their grade-level peers (Ma and Wilkins 2007). The present 

Brief examines how various characteristics are related to 

enrollment in algebra or higher in the eighth grade. 

Eighth-grade mathematics course offerings and placement 

policies differ from school to school (Cogan, Schmidt, 

and Wiley 2001). Some schools enroll only those with the 

highest mathematics achievement in algebra by the eighth 

grade while some schools aim to provide algebra to all 

eighth-grade students regardless of prior ability level.1

The implications of different policies related to algebra 

enrollment for students with various ability levels have 

been discussed and studied. Loveless (2008) reported that 

the percentage of low achievers—those at or below the 

10th percentile on the eighth-grade National Assessment 

of Educational Progress (NAEP) mathematics test—in 

advanced mathematics classes increased between 2000 

and 2005. Burris, Heubert, and Levin (2006) found 

that the percentage of students who completed various 

advanced mathematics courses in high school increased 

after middle schools in one school district eliminated 

the “tracking” strategy that placed only the highest 

performing students in algebra in the eighth grade and 

instead prepared all students for algebra in that grade. 

The increase in participation in advanced mathematics 

courses in high school was found for all groups of students 

within the district, including Black and Hispanic students, 

low-income students, and students who had relatively low 

mathematics scores in fifth grade. Ma (2005) reported that 

low-achieving students placed in algebra showed greater 

growth in mathematics achievement than either their lowor high-achieving peers in lower level classes. Additionally, 

Gamoran and Hannigan’s (2000) analysis of national 

survey data found that algebra enrollment was associated 

with higher mathematics achievement growth for all 

students, although the advantage was less pronounced for 

students with lower initial achievement levels compared 

with their higher achieving peers. 

This Brief examines some of these issues by looking at 

mathematics performance at the end of eighth grade by 

algebra enrollment and other characteristics, including 

prior mathematics ability and schools’ level of eighth-grade 

algebra enrollment. Not all relationships between the 

variables are fully investigated and readers are cautioned 

not to draw causal inferences based on the results presented. 

1

 For example, the California Department of Education has been working 

on issues related to preparing all students for algebra I in the eighth grade 

(California Department of Education, 2008).

Additionally, it is important to note that there may be 

variables related to algebra enrollment and mathematics 

achievement that are not examined in this report.

Focus of This Statistics in Brief

This Brief is intended to provide descriptive statistics 

about various aspects of algebra enrollment in the 

eighth grade. The first analyses describe who is taking 

algebra in the eighth grade; findings compare eighthgrade course enrollment percentages for students with 

different demographic, family, geographic, and school 

characteristics (table 1). The second set of findings looks 

at eighth-grade algebra enrollment levels in the schools 

and reports the percentage of students who attend 

schools with relatively low, medium, and high levels of 

eighth-grade algebra enrollment by demographic, family, 

geographic, and school characteristics (table 2). The next 

set of findings incorporates data collected at the end of 

fifth grade. Enrollment in algebra or higher is compared 

by varying levels of fifth-grade mathematics achievement 

(figure 1), and among students with relatively strong 

fifth-grade mathematics scores, enrollment is compared 

by sex and race/ethnicity (figure 2). Enrollment in algebra 

or higher in eighth grade is also compared for students 

with varying views about mathematics as self-reported in 

the fifth grade (figure 3). The final set of findings describe 

mathematics achievement scores and other student 

measures from the end of eighth grade for students not 

yet in algebra and those in algebra or higher. First, the 

eighth-grade mathematics scores for those in algebra by 

the eighth grade and those not yet in algebra are broken 

down by demographic, family, geographic, and school 

characteristics (table 3), and by fifth-grade mathematics 

score quintiles (figure 4). Findings are then presented 

that look at student-reported enjoyment of mathematics 

(figure 5) and future educational expectations (figure 6) by 

course enrollment. 

The ECLS-K Cohort

Data for this Statistics in Brief are drawn from the Early 

Childhood Longitudinal Study, Kindergarten Class of 

1998–99 (ECLS-K). This Brief focuses on the experiences 

of a cohort of children who were in first grade during the 

1999–2000 school year and who were in eighth grade 

during the 2006–07 school year. That is, it studies students 

who progressed on schedule through schools in the United 

States from first grade to eighth grade, excluding students 

who had been retained in a grade between the first and 

eighth grades and therefore were not yet in eighth grade 

in spring 2007 (about 13 percent of the first-grade class of 

1999–2000) as well as students who had been promoted 

ahead of schedule and were beyond the eighth grade in 

spring 2007 (about 0.3 percent of the first-grade class of 

1999–2000). 
NCES 2010-016 3

The cohort studied in this Brief does not fully represent 

all eighth-grade students in the 2006–07 school year. 

Specifically, it does not represent eighth-grade students in 

2006–07 who started first grade before the fall of 1999 

and were retained in a later grade, who immigrated to the 

United States after first grade, or who were home-schooled 

until after first grade. The cohort represents approximately 

80 percent of all eighth-grade students in the 2006–07 

school year (Tourangeau et al. 2009b).

Mathematics Course Enrollment 

Table 1 shows the distribution of mathematics course 

enrollment for the eighth-grade students in this cohort. 

Thirty-three percent were enrolled in an algebra class in the 

eighth grade and 6 percent were enrolled in an advanced 

mathematics course other than algebra (i.e., algebra 

II, geometry, or integrated or sequential mathematics). 

Forty-four percent were taking an introduction to algebra 

or pre-algebra class, and 17 percent were in a general 

mathematics course, which is typically intended for 

students who are not yet ready for pre-algebra. Many of 

the findings presented in this report look at students in 

algebra and students in another advanced mathematics 

course grouped together (39 percent of the cohort) and 

students in a general mathematics course or a pre-algebra 

class grouped together (61 percent of the cohort). Much 

of the policy discussion about algebra courses focuses on 

students taking algebra by the eighth grade, so many of 

the findings presented here consider students who took 

algebra or moved into a course beyond algebra in the 

eighth grade as a single analytic group of interest. 

Mathematics course enrollment varied by students’ race/

ethnicity. A larger percentage of Asian students were 

enrolled in algebra or a course more advanced than algebra 

(67 percent) than were students in each of the other race/

ethnicity groups (19 to 45 percent). A larger percentage 

of White (45 percent) and Hispanic (38 percent) students 

were in algebra or higher than were Black students (19 

percent), and a larger percentage of White students were 

in algebra or higher than were students in the “Other” 

racial/ethnic category2

 (30 percent).

Mathematics course enrollment also differed by poverty 

status, mother’s education, and family type.3

 Compared 

with students living in households below the poverty 

threshold, a larger percentage of students living in 

households at or above the poverty threshold were 

enrolled in algebra or higher (43 vs. 23 percent). A larger 

2

 Here, and throughout this report, “Other” refers to Native Hawaiians, 

Pacific Islanders, American Indians, Alaska Natives, and other non-Hispanic 

students of two or more races. Collectively, these students make up about 4 

percent of the cohort represented in this report.

3

 The apparent difference between the percentage of females and the 

percentage of males enrolled in algebra or higher was not detectably different 

when statistical tests of difference were applied.

percentage of students whose mothers had a bachelor’s 

degree or higher were enrolled in algebra or higher (56 

percent) than were students whose mothers had less than 

a 4-year college degree (23 to 36 percent). Also, a larger 

percentage of students whose mother had some college 

(36 percent) were in algebra or higher than were students 

whose mother’s highest education level was a high school 

diploma or the equivalent (28 percent) or who did not 

complete high school (23 percent). Additionally, a larger 

percentage of students in two-parent households were 

enrolled in algebra or higher (43 percent) than were those 

in single-parent homes (31 percent). 

Mathematics course enrollment varied in different regions 

of the country.4 Enrollment in algebra or a course more 

advanced than algebra was least prevalent in the South. 

Thirty percent of the students in the South were enrolled 

in algebra or higher, compared with 38 percent in the 

Midwest, 46 percent in the Northeast, and 54 percent in 

the West. Additionally, the percentage of students in the 

West who were in algebra or higher was larger than those 

in the Midwest (54 vs. 38 percent).5

Mathematics course enrollment was also found to differ 

by school type (i.e., public or private). A larger percentage 

of private school students were enrolled in algebra or a 

course more advanced than algebra (52 percent) than were 

public school students (38 percent).

Eighth-Grade Algebra Enrollment in the 

Schools

This section looks at students who attend schools with 

low, medium, and high levels of eighth-grade algebra 

enrollment to consider differences associated with access 

to algebra at the student’s school. Whether or not a student 

takes algebra by the eighth grade is associated with the 

overall level of algebra enrollment at the school a student 

attends. School principals indicated the percentage of all 

eighth-grade students at the school who were enrolled in 

algebra.6 Table 2 shows the percentage of students in the 

cohort who attended schools with eighth-grade algebra 

enrollment of less than 25 percent, between 25 and 74 

percent, and 75 percent or more, by student, family, and 

school characteristics.

4

 States and jurisdictions included in each region are as follows: the Northeast 

includes CT, ME, MA, NH, RI, VT, NJ, NY, and PA; the Midwest includes 

IL, IN, MI, OH, WI, IA, KS, MN, MO, NE, ND, and SD; the South includes 

DE, DC, FL, GA, MD, NC, SC, VA, WV, AL, KY, MS, TN, AR, LA, OK, and 

TX; and the West includes AZ, CO, ID, MT, NV, NM, UT, WY, AK, CA, HI, 

OR, and WA.

5

 The apparent differences between the Northeast and the Midwest and 

between the Northeast and the West were not detectably different when 

statistical tests of difference were applied.

6

 The principals were asked about eighth-grade algebra enrollment, but were 

not asked about eighth-grade enrollment in a course more advanced than 

algebra.
4 NCES 2010-016

Table 1. ercentage distribution of mathematics course enrollment of ECLS-K spring 2000 first-grade cohort eighth-graders, by P

student, family, and school characteristics: Spring 2007

Characteristic

Mathematics course

General 

mathematics

Introduction 

to algebra/ 

pre-algebra

Algebra or a course more advanced

than algebra

Total Algebra

An advanced 

course other 

than algebra1 

Total2 17 44 39 33 6

Sex 

Male 18 45 37 31 6

Female 15 43 42 35 7

Race/ethnicity3

White, not Hispanic 14 42 45 37 8

Black, not Hispanic 25 56 19 17 ‡

Hispanic 18 44 38 34 4 !

Asian, not Hispanic 16 ! 16 67 51 16

Other, not Hispanic 25 44 30 25 5 !

Poverty status4

Below federal poverty level 25 52 23 21 ‡

At or above federal poverty level 15 42 43 36 7

Mother’s education

Less than high school 25 52 23 22 ‡

High school diploma or equivalent 19 53 28 25 3 !

Some college or vocational technical degree 19 45 36 31 6

Bachelor’s degree or higher 10 35 56 44 11

Family type5

Two parents 16 42 43 36 7

Single parent 20 49 31 27 4

Region6

Northeast 11 43 46 36 10

Midwest 18 44 38 34 4

South 22 49 30 25 5

West 10 36 54 46 9

School type

Public school 18 44 38 32 6

Private school 8 ! 40 52 47 5 !

! Interpret data with caution. Coefficient of variation is greater than 30 percent.

‡ Estimate does not meet reporting standards.

1

 “An advanced course other than algebra” includes integrated or sequential mathematics, algebra II, and geometry.

2

 The total represents all U.S. students who attended first grade in the spring of 2000 and then were in a U.S. eighth grade in the 2006–07 school year.

3

 Black, not Hispanic includes African American. Hispanic includes Latino. Other, not Hispanic includes Native Hawaiians, Pacific Islanders, American 

Indians, Alaska Natives, and non-Hispanic students of two or more races.

4

 Poverty status is a function of household size and household income. Based on 2006 census information, a household of four with a total income below 

$20,615 was considered to be below the federal poverty threshold. 

5

 Children who live with one or more guardians, rather than a parent, are not included because there are too few students in the sample with this family 

type to produce stable estimates. 

6

 States and jurisdictions included in each region are as follows: the Northeast includes CT, ME, MA, NH, RI, VT, NJ, NY, and PA; the Midwest includes IL, 

IN, MI, OH, WI, IA, KS, MN, MO, NE, ND, and SD; the South includes DE, DC, FL, GA, MD, NC, SC, VA, WV, AL, KY, MS, TN, AR, LA, OK, and TX; and the West 

includes AZ, CO, ID, MT, NV, NM, UT, WY, AK, CA, HI, OR, and WA.

NOTE: Estimates were weighted by C7CPTM0. Detail may not sum to total due to rounding.

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Kindergarten–Eighth Grade Full Sample Public-Use Data File.

A larger percentage of Asian (24 percent) and Hispanic 

students (19 percent) attended a school where more than 

75 percent of the eighth-grade students were enrolled in 

algebra than did White, Black, or “Other” students (7 to 

8 percent). A larger percentage of Black (70 percent) and 

“Other” students (64 percent) were in a school where less 

than 25 percent of the eighth-grade students were in algebra 

than were White (49 percent), Hispanic (46 percent), or 

Asian students (36 percent); a larger percentage of White 

students were in one of these schools than were Asian 

students (49 vs. 36 percent). 

School algebra enrollment also differed by poverty 

status, mother’s education level, and family type. A larger 

percentage of students from households below the poverty 

threshold attended a school with less than 25 percent 

eighth-grade algebra enrollment than did those at or 

above the poverty threshold (59 vs. 50 percent). A smaller 
NCES 2010-016 5

Table 2. Percentage distribution of ECLS-K spring 2000 first-grade cohort eighth-graders who attended schools with various levels of 

eighth-grade student enrollment in algebra, by student, family, and school characteristics: Spring 2007

Characteristic

Principals’ report of the percentage of all eighth-grade students 

at the school enrolled in algebra

Less than 25 percent 25 to 74 percent 75 percent or more

Total1 51 38 10

Sex 

Male 51 38 12

Female 52 39 9

Race/ethnicity2

White, not Hispanic 49 43 8

Black, not Hispanic 70 22 8 !

Hispanic 46 36 19

Asian, not Hispanic 36 40 24

Other, not Hispanic 64 29 7 !

Poverty status3

Below federal poverty level 59 28 13

At or above federal poverty level 50 40 10

Mother’s education

Less than high school 51 32 18

High school diploma or equivalent 58 35 8

Some college or vocational technical degree 58 33 9

Bachelor’s degree or higher 40 49 12

Family type4

Two parents 49 40 10

Single parent 57 32 11

Region5

Northeast 41 49 10

Midwest 55 36 9

South 62 34 4

West 37 40 24

School type

Public school 54 37 9

Private school 29 48 24

! Interpret data with caution. Coefficient of variation is greater than 30 percent.

1

 The total represents all U.S. students who attended first grade in the spring of 2000 and then were in a U.S. eighth grade in the 2006–07 school year.

2

 Black, not Hispanic includes African American. Hispanic includes Latino. Other, not Hispanic includes Native Hawaiians, Pacific Islanders, American 

Indians, Alaska Natives, and non-Hispanic students of two or more races.

3

 Poverty status is a function of household size and household income. Based on 2006 census information, a household of four with a total income below 

$20,615 was considered to be below the federal poverty threshold. 

4

 Children who live with one or more guardians, rather than a parent, are not included because there are too few students in the sample with this family 

type to produce stable estimates. 

5

 States and jurisdictions included in each region are as follows: the Northeast includes CT, ME, MA, NH, RI, VT, NJ, NY, and PA; the Midwest includes IL, 

IN, MI, OH, WI, IA, KS, MN, MO, NE, ND, and SD; the South includes DE, DC, FL, GA, MD, NC, SC, VA, WV, AL, KY, MS, TN, AR, LA, OK, and TX; and the West 

includes AZ, CO, ID, MT, NV, NM, UT, WY, AK, CA, HI, OR, and WA.

NOTE: Estimates were weighted by C7CPTM0. Detail may not sum to total due to rounding.

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Kindergarten–Eighth Grade Full Sample Public-Use Data File. 

percentage of students whose mothers had a bachelor’s 

degree were in a school where less than 25 percent of their 

fellow eighth-grade students were in algebra (40 percent) 

than were those whose mothers had some college (58 

percent) or whose highest level of education was a high 

school diploma or the equivalent (58 percent). Contrary 

to what might be expected given the finding from table 

1 that mother’s education is generally positively related 

to enrollment in algebra or higher, a larger percentage of 

students whose mothers did not complete high school were 

in a school where 75 percent or more of the eighth-grade 

students were in algebra (18 percent) than students whose 

mother’s highest level of education was a high school 

diploma or the equivalent (8 percent); however, there 

was no detectable difference in enrollment levels in these 

schools between those whose mothers did not complete 

high school and those whose mothers had a bachelor’s 

degree (12 percent). Fifty-seven percent of students from a 

single-parent home were in a low-algebra school compared 

with 49 percent of students from two-parent homes. 

The level of algebra enrollment in the schools the eighthgrade students attended also differed by geographical 

region and school type. Twenty-four percent of students 

in the West attended a school that had a relatively high 

eighth-grade algebra enrollment (i.e., 75 percent or more) 
6 NCES 2010-016

compared with 10 percent of those in the Northeast, 9 

percent in the Midwest, and 4 percent in the South.7

 A 

larger percentage of students in the South (62 percent) and 

the Midwest (55 percent) attended a school where less than 

25 percent of the eighth-grade students were in algebra 

than did students in the Northeast (41 percent) or the West 

(37 percent). A larger percentage of students attending a 

private school were in a school with a high level of eighthgrade algebra enrollment than were public school students 

(24 vs. 9 percent). Conversely, a smaller percentage of 

private school students were in a low-algebra school than 

were students in public schools (29 vs. 54 percent).

Fifth-Grade Mathematics Performance 

and Enjoyment of Mathematics 

Data collected from these students 3 years earlier—at 

the end of the fifth grade—were used to look at how 

prior mathematics performance and prior feelings about 

mathematics may be related to eighth-grade mathematics 

course placement.8

 Students’ scores on the ECLS-K 

mathematics assessment given at the end of fifth grade 

were used to create five quintiles. As shown in figure 1, 

higher performance on the fifth-grade assessment was 

associated with enrollment in algebra or higher in eighth 

grade. Starting with the students who scored in the lowest 

20 percent of the fifth-grade score distribution, each 

ascending quintile had a larger percentage of students who 

were in algebra or higher in the eighth grade (13, 24, 37, 

7

 The western region of the country includes California, which has a statewide 

initiative regarding eighth-grade algebra. 

8

 ECLS-K data were not collected between the end of fifth grade and the end of 

eighth grade. See “Direct cognitive mathematics assessments” in the glossary 

of this report for more details about the fifth-grade mathematics assessment.

Figure 1. Percentage of ECLS-K spring 2000 first-grade 

cohort eighth-graders enrolled in algebra or a 

course more advanced than algebra, by 

fifth-grade mathematics score quintiles: Spring 

2004 and spring 2007

NOTE: The estimates represent all U.S. students who attended first grade in the spring 

of 2000 and then were in a U.S. eighth grade in the 2006–07 school year. “Algebra 

or a course more advanced than algebra” includes algebra I, integrated or 

sequential mathematics, algebra II, and geometry. Estimates were weighted by 

C7CPTM0. Standard errors are available upon request. 

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

Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K), 

Kindergarten–Eighth Grade Full Sample Public-Use Data File. 

Fifth-grade mathematics score quintiles 

1 (lowest) 2 3 4 5

Percent

0

20

40

60

80

100

13

24

37

49

75

49, and 75 percent, respectively). This finding is consistent 

with research showing that schools are more likely to 

place students who begin seventh grade with stronger 

mathematics skills on a track that will lead toward algebra 

by the eighth grade (Ma and Wilkins 2007). However, 

about a quarter of the students who had been in the very 

highest quintile of fifth-grade mathematics scores and 

about half of the students in the next highest fifth-grade 

quintile had not moved on to an algebra class by the 

eighth grade.

Among students in the top two fifth-grade mathematics 

score quintiles, of which 62 percent went on to algebra 

by the eighth grade, there were notable differences by sex 

and race/ethnicity (figure 2). Seventy percent of the girls 

in this group went on to algebra or higher in the eighth 

grade, compared with 56 percent of the boys. Among 

these students with high fifth-grade mathematics scores, a 

smaller percentage of Black students went on to algebra by 

the eighth grade (35 percent) than did Asian (94 percent), 

Hispanic (68 percent), or White (63 percent) students. A 

larger percentage of Asian students from this group moved 

on to algebra or higher by the eighth grade (94 percent) 

than did students from each of the other race/ethnicity 

groups (35 to 68 percent). 

Fifth-grade students also responded to a series of 

statements by indicating how true each statement was 

for them: not at all true, a little bit true, mostly true, or 

very true. Students who indicated in the fifth grade that 

the statement “I like math” was “very true” for them 

were more likely to have gone on to algebra or higher 

in the eighth grade (43 percent) than were students who 

responded “not at all true” (33 percent) or “a little bit 

true” (35 percent) (figure 3).

The following sections look at how students who were in 

algebra or higher in the eighth grade differed from those 

not in algebra on eighth-grade mathematics performance, 

enjoyment of mathematics, and future educational 

expectations, each measured at the end of the eighth grade.

Eighth-Grade Mathematics Performance 

Students taking more advanced mathematics courses 

scored higher on the ECLS-K mathematics assessment9

given at the end of the eighth-grade year than did students 

in less advanced classes. Students in a general mathematics course had the lowest average score, 128 points; 

those in pre-algebra scored, on average, 138 points; and 

those in algebra had a higher average score, 153 points. 

The highest average score (158 points) was obtained by 

students taking an advanced mathematics course other 

than algebra (data not shown). As seen in table 3, students 

9

 The ECLS-K mathematics assessment measured broad-based achievement in 

mathematics; it included algebra concepts, but was not designed as an algebra 

assessment. See “Direct cognitive mathematics assessments” in the glossary of 

this report for more details. 
NCES 2010-016 7

who were in algebra or a course more advanced than 

algebra scored higher than those who were not yet in 

algebra (154 vs. 135 points).10

Higher eighth-grade mathematics scores were obtained by 

students who were in algebra or higher than by those not 

yet in algebra within each subgroup category (sex, race/

10 This difference of 19 points is equal to .86 of the standard deviation 

associated with the eighth-grade mathematics scores for the cohort of eighthgrade students represented in this report (SD = 21.6).

ethnicity, poverty status, mother’s education, family type, 

region, percentage of algebra enrollment in school, and 

school type). For example, enrollment in algebra or higher 

was associated with higher scores for Black students (140 

vs. 130 points), Hispanic students (146 vs. 129 points), 

students living in homes with incomes below the poverty 

threshold (142 vs. 126 points), and students whose mother 

did not complete high school (136 vs. 121 points) or whose 

highest level of education was high school completion 

(150 vs. 132 points). 

Overall differences in eighth-grade mathematics 

achievement (averaged across students in all mathematics 

courses) were related to many student and family 

characteristics. For example, Asian (150 points) and White 

(147 points) students scored higher, on average, than 

Black (131 points) and Hispanic (135 points) students; 

students living in poverty scored lower, on average, 

than students from homes with incomes at or above 

the federal poverty threshold (129 vs. 145 points); and 

average scores increased as levels of maternal education 

increased (less than a high school credential, 126 points; 

a high school credential, 136 points; some college or a 

vocational technical degree, 142 points; and a bachelor’s 

degree or higher, 152 points). The patterns of differences 

among students in all mathematics courses were generally 

mirrored among students in algebra or higher as well 

as among students not yet in algebra. However, among 

students not yet in algebra, Asian students (128 points) 

did not score higher than Black (130 points) or Hispanic 

students (129 points), and among students in algebra 

or higher, the average score for students whose mother 

attended some college (151 points) was not measurably 

different from that for students whose mother’s highest 

Figure 2. Percentage of the ECLS-K spring 2000 first-grade cohort in the top two fifth-grade mathematics score quintiles who 

were enrolled in algebra or a course more advanced than algebra in the eighth grade, by sex and race/ethnicity: 

Spring 2004 and spring 2007

1

 Black, not Hispanic includes African American. Hispanic includes Latino. Other, not Hispanic includes Native Hawaiians, Pacific Islanders, American Indians, Alaska Natives, 

and non-Hispanic students of two or more races. 

NOTE: The estimates represent all U.S. students who attended first grade in the spring of 2000 and then were in a U.S. eighth grade in the 2006–07 school year. “Algebra or a 

course more advanced than algebra” includes algebra I, integrated or sequential mathematics, algebra II, and geometry. Estimates were weighted by C7CPTM0. Standard 

errors are available upon request. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K), KindergartenEighth Grade Full Sample Public-Use Data File. 

Sex Race/ethnicity1

Total Male Female White,

not

Hispanic

Black,

not

Hispanic

Hispanic Asian,

not

Hispanic

Other,

not

Hispanic

Percent

0

20

40

60

80

100

62

56

70

63

35

68

94

53

Figure 3. Percentage of ECLS-K spring 2000 first-grade cohort 

eighth-graders enrolled in algebra or a course 

more advanced than algebra, by fifth-grade 

enjoyment of mathematics: Spring 2004 and 

spring 2007

NOTE: The estimates represent all U.S. students who attended first grade in the spring 

of 2000 and then were in a U.S. eighth grade in the 2006–07 school year. “Algebra or 

a course more advanced than algebra” includes algebra I, integrated or 

sequential mathematics, algebra II, and geometry. Estimates were weighted by 

C7CPTM0. Standard errors are available upon request. 

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

Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K), 

Kindergarten–Eighth Grade Full Sample Public-Use Data File, and the Kindergarten 

Through Fifth Grade Approaches to Learning and Self-Description Questionnaire 

Supplemental Data File. 

Fifth-grade student responses to “I like math”

Not at all true A little bit true Mostly true Very true

Percent

0

20

40

60

80

100

33 35

41 43
8 NCES 2010-016

level of education was a high school diploma or the 

equivalent (150 points). 

Among students taking algebra or higher in the eighth 

grade, those attending schools where 75 percent or 

more of the eighth-graders were taking algebra scored 

lower (148 points) than those in schools with less than 

25 percent (155 points) or between 25 and 74 percent 

eighth-grade algebra enrollment (156 points). This reflects 

the fact that schools with higher algebra enrollment often 

enroll students with a much broader range of mathematics 

ability levels in their algebra classes. Among students with 

relatively strong fifth-grade mathematics scores (i.e., in the 

top two quintiles) who went on to algebra by the eighth 

grade, there were no differences detected in the average 

eighth-grade mathematics scores for students attending 

Table 3. Average ECLS-K spring 2000 first-grade cohort’s eighth-grade mathematics scores, by mathematics course, student, family, 

and school characteristics: Spring 2007

Characteristic Total

Eighth-grade mathematics course

Not in algebra1

Algebra or a course more 

advanced than algebra2

Total3 142 135 154

Sex 

Male 144 137 156

Female 141 133 152

Race/ethnicity4

White, not Hispanic 147 139 157

Black, not Hispanic 131 130 140

Hispanic 135 129 146

Asian, not Hispanic 150 128 161

Other, not Hispanic 143 138 158

Poverty status5

Below federal poverty level 129 126 142

At or above federal poverty level 145 138 155

Mother’s education

Less than high school 126 121 136

High school diploma or equivalent 136 132 150

Some college or vocational technical degree 142 137 151

Bachelor’s degree or higher 152 144 159

Family type6

Two parents 145 137 155

Single parent 137 133 148

Region7

Northeast 146 138 156

Midwest 143 136 156

South 141 135 156

West 141 132 149

School’s eighth-grade algebra enrollment

Less than 25 percent 141 135 155

25 to 74 percent 146 136 156

75 percent or more 143 133 148

School type

Public school 142 135 154

Private school 147 140 154

1

 “Not in algebra” includes students in a general eighth-grade mathematics course, introduction to algebra, or pre-algebra.

2

 “Algebra or a course more advanced than algebra” includes algebra I, integrated or sequential mathematics, algebra II, and geometry.

3

 The total represents all U.S. students who attended first grade in the spring of 2000 and then were in a U.S. eighth grade in the 2006–07 school year.

4

 Black, not Hispanic includes African American. Hispanic includes Latino. Other, not Hispanic includes Native Hawaiians, Pacific Islanders, American 

Indians, Alaska Natives, and non-Hispanic students of two or more races. 

5

 Poverty status is a function of household size and household income. Based on 2006 census information, a household of four with a total income below 

$20,615 was considered to be below the federal poverty threshold.

6

 Children who live with one or more guardians, rather than a parent, are not included because there are too few students in the sample with this family 

type to produce stable estimates. 

7

 States and jurisdictions included in each region are as follows: the Northeast includes CT, ME, MA, NH, RI, VT, NJ, NY, and PA; the Midwest includes IL, 

IN, MI, OH, WI, IA, KS, MN, MO, NE, ND, and SD; the South includes DE, DC, FL, GA, MD, NC, SC, VA, WV, AL, KY, MS, TN, AR, LA, OK, and TX; and the West 

includes AZ, CO, ID, MT, NV, NM, UT, WY, AK, CA, HI, OR, and WA. 

NOTE: Estimates were weighted by C7CPTM0. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Kindergarten–Eighth Grade Full Sample Public-Use Data File. 
NCES 2010-016 9

schools with various levels of algebra enrollment (the 

average score was 162 for each category of school algebra 

enrollment (<25 percent, 25 to 74 percent, and 75 or more 

percent)). Overall differences in eighth-grade mathematics 

achievement were also related to school type. Students in 

private schools scored higher than those in public schools 

(147 vs. 142 points). Among students who were not yet 

in algebra by the eighth grade, students in private schools 

also scored higher than those in public schools (140 vs. 

135 points). However, eighth-grade students in public 

schools taking algebra or higher and eighth-grade students 

in private schools taking algebra or higher both had an 

average mathematics score of 154 points. 

Figure 4 illustrates the eighth-grade scores for students 

who were in algebra and those not in algebra by the 

eighth grade within fifth-grade score quintiles. Higher 

average scores were obtained by students who had moved 

to algebra by the eighth grade compared to students who 

were not yet in algebra in the eighth grade for students 

within each of the fifth-grade mathematics score quintiles 

except the very lowest quintile.11

11 The apparent difference in eighth-grade mathematics scores between those 

in algebra and those not in algebra by the eighth grade for students in the 

lowest quintile is not statistically significant. This is due to the relatively large 

standard error for the estimate for students in this group who were in algebra 

or higher. 

Figure 4. Average ECLS-K spring 2000 first-grade cohort's 

eighth-grade mathematics scores, by 5th-grade 

mathematics score quintile and eighth-grade 

mathematics course: Spring 2004 and spring 2007

NOTE: The estimates represent all U.S. students who attended first grade in the spring 

of 2000 and then were in a U.S. eighth grade in the 2006–07 school year. “Not in 

algebra” includes students in a general eighth-grade mathematics course, 

introduction to algebra, or pre-algebra. “Algebra or a course more advanced than 

algebra” includes algebra I, integrated or sequential mathematics, algebra II, and 

geometry. Estimates were weighted by C7CPTM0. Standard errors are available 

upon request. 

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

Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K), 

Kindergarten–Eighth Grade Full Sample Public-Use Data File. 

Fifth-grade mathematics score quintiles 

1 (lowest) 2 3 4 5

Eighth-grade score

0

20

40

60

80

180

160

140

120

100

13

24

37

49

75

113 117

133 139 145 147 153 157 160 165

Not in algebra In algebra or a course more

advanced than algebra

Enjoyment of Mathematics and 

Educational Expectations in the Eighth 

Grade 

Past research has found that eighth-grade students’ future 

educational expectations (Bui 2007) and enjoyment of 

mathematics (Beaton et al. 1996) are important educational 

variables. These next two sections investigate how these 

two student characteristics compare for those students 

who are enrolled in algebra by the eighth grade and those 

who are not yet enrolled in algebra. Figure 5 shows the 

responses made when students were near the end of the 

eighth grade to the statement, “I like math,” for those in 

algebra or higher and those not yet in algebra. Compared 

with those not yet in algebra, a larger percentage of 

students in algebra or higher responded that this statement 

was “mostly true” for them (31 vs. 25 percent) and a 

smaller percentage indicated that this statement was “not 

at all true” (16 vs. 24 percent).

The eighth-grade students were also asked to report 

the level of education they expected to attain. Figure 6 

illustrates the differences in educational expectations for 

students who were enrolled in algebra or higher by the 

eighth grade and those not enrolled in algebra. A larger 

percentage of students in algebra or higher envisioned 

themselves with an advanced degree than did students 

not in algebra (49 vs. 28 percent). A smaller percentage 

of those in algebra or higher reported that they would 

not complete a 4-year college degree (7 vs. 17 percent) or 

selected “don’t know” (10 vs. 18 percent) as their response 

to the question about their educational expectations than 

did students not in algebra.

Figure 5. Percentage distribution of ECLS-K spring 2000 

first-grade cohort eighth-grade students, by 

enjoyment of mathematics and eighth-grade 

mathematics course enrollment: Spring 2007

NOTE: The estimates represent all U.S. students who attended first grade in the spring 

of 2000 and then were in a U.S. eighth grade in the 2006–07 school year. “Not in 

algebra” includes students in a general eighth-grade mathematics course, 

introduction to algebra, or pre-algebra.“Algebra or a course more advanced than 

algebra” includes algebra I, integrated or sequential mathematics, algebra II, and 

geometry. Estimates were weighted by C7CPTM0. Standard errors are available 

upon request. 

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

Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K), 

Kindergarten–Eighth Grade Full Sample Public-Use Data File. 

Eighth-grade student responses to “I like math”

Not at all true A little bit true Mostly true Very true

Percent

0

20

40

60

80

100

Not in algebra In algebra or a course more

advanced than algebra

24

16

26 26 25

31

25 27
10 NCES 2010-016

Figure 6. Percentage distribution of ECLS-K spring 2000 first-grade cohort as eighth-grade students, by future educational 

expectations and eighth-grade mathematics course enrollment: Spring 2007

NOTE: The estimates represent all U.S. students who attended first grade in the spring of 2000 and then were in a U.S. eighth grade in the 2006–07 school year. “Not in algebra” 

includes students in a general eighth-grade mathematics course, introduction to algebra, or pre-algebra. “Algebra or a course more advanced than algebra” includes 

algebra I, integrated or sequential mathematics, algebra II, and geometry. Estimates were weighted by C7CPTM0. Standard errors are available upon request. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 (ECLS-K), KindergartenEighth Grade Full Sample Public-Use Data File. 

Eighth-grade student responses to “How far in school do you think you will get?”

Don’t know Less than a 4-year 

college degree

A 4-year college

degree

Not in algebra In algebra or a course more advanced than algebra

An advanced degree

(e.g., master’s, Ph.D., or M.D.)

Percent

0

20

40

60

80

100

18

10

17

7

37 34

28

49

Summary

Some policymakers and researchers have recommended 

advancing more students to algebra classes by the eighth 

grade, placing these students on a mathematics course 

trajectory that would prepare them for the challenging 

college coursework necessary for science, technology, 

engineering, and mathematics degrees, which in turn are 

associated with high income careers (e.g., Riley 1997). 

This would also result in U.S. students being placed in 

mathematics course trajectories more like those of many of 

their international peers (e.g., Schmidt 2004). The present 

report finds that among the cohort of students in the firstgrade class of 1999–2000 who had progressed to eighth 

grade in the 2006–07 school year (representing about 80 

percent of the eighth-grade class of 2006–07), nearly 4 in 

10 were enrolled either in algebra or a higher mathematics 

course in the eighth grade. Consistent with other studies’ 

findings (e.g., Bozick and Ingels 2008; Dalton et al. 

2007), algebra enrollment was more common for Asian 

students, students not living in poverty, students whose 

mother had a bachelor’s degree or higher, students living 

in a two-parent home, and private school students than 

their respective counterparts. In some schools, eighthgrade algebra coursework was relatively common (i.e., 

more than 75 percent of the school’s eighth-graders were 

enrolled in algebra); students living in the western region 

of the country were more likely to be attending one of 

these schools than students in other regions of the country. 

Algebra enrollment was also related to prior mathematics 

ability; higher scores on the ECLS-K mathematics 

assessment in the fifth grade were associated with higher 

levels of algebra enrollment by the eighth grade. However, 

about a quarter of the students who had been in the 

very highest quintile of fifth-grade mathematics scores 

and about half of the students in the next highest fifthgrade quintile had not moved on to an algebra class by 

the eighth grade. Furthermore, among students in these 

top two fifth-grade mathematics score quintiles, male 

students and Black students proceeded on to algebra by 

the eighth grade at lower rates than their counterparts. 

These findings suggest that some students with relatively 

strong mathematics skills at the end of elementary school 

are not in algebra by the eighth grade. 

Additionally, enrollment in algebra or higher was associated 

with higher mathematics scores on the assessment given at 

the end of the eighth grade, and this was true within each 

subgroup category—sex, race/ethnicity, poverty status, 

mother’s education, family type, region, school type, and 

school’s algebra enrollment (e.g., Black students in algebra 

or higher courses outperformed Black students not in 

algebra). Higher average eighth-grade mathematics scores 

for students in algebra or higher compared to students in 

other classes were found within each of the fifth-grade 

mathematics score quintiles except the lowest fifth-grade 

quintile. Students in algebra by the eighth grade in schools 

where this was commonplace (i.e., more than 75 percent 

of the eighth-grade students in the school were taking 

algebra) had lower average scores than algebra students 

in schools where algebra in the eighth grade was less 

common. However, among students with relatively strong 

mathematics skills at the end of fifth grade, there were no 

differences in average eighth-grade mathematics scores by 

school algebra level. 

The overall mathematics achievement gaps found among 

eighth-grade students were generally also found among 

students in algebra or higher and among students not yet 
NCES 2010-016 11

in algebra. However, there were some exceptions: private 

school students taking algebra or higher coursework did 

not have higher scores than public school students taking 

algebra or higher coursework. Additionally, among those 

not in algebra, Asian students did not score higher than 

Black or Hispanic students.

In addition to higher average mathematics scores, students 

taking algebra by the eighth grade had higher expectations 

about their own future educational attainment and liked 

mathematics more than those not in algebra classes by the 

eighth grade.

Methodology and Technical Notes

Overview of the ECLS-K

The ECLS-K is sponsored by the National Center for 

Education Statistics (NCES), which is part of the Institute 

of Education Sciences within the U.S. Department of 

Education. The purpose of the ECLS-K is to provide 

detailed information on the school achievement and 

experiences of students from kindergarten entry to middle 

school. Westat, Inc. assisted with the design of the study 

and collected the data upon which this report is based. 

The students participating in the ECLS-K were followed 

longitudinally from kindergarten in the fall of 1998 

through the spring of 2007 when most were in eighth 

grade. The sample was freshened for first grade in the 

spring of 2000. About 87 percent of the students were in 

the eighth grade in the 2006–07 school year; 13 percent 

were enrolled below eighth grade because they had been 

retained at least once since they were in kindergarten in 

1998–99.12 About one-third of 1 percent of the students 

had, at some time, been promoted a grade ahead of 

schedule and were above eighth grade in the 2006–07 

school year. The cohort referred to in this report represents 

approximately 80 percent of all eighth-grade students in 

the 2006–07 school year. Estimates in this report are based 

on data collected from about 3,750 students who were in 

eighth grade in the spring of 2007 and who had complete 

mathematics assessment data, parent interview data, and 

mathematics teacher questionnaire data. When properly 

weighted, information about these students represents 

all students who were in first grade in the 1999–2000 

school year and the eighth grade in the 2006–07 school 

year. Information about obtaining the ECLS-K data and 

publications can be found at the ECLS-K website, http://

nces.ed.gov/ecls/kindergarten.asp.

Sample design

A nationally representative sample of 21,260 students 

enrolled in 944 kindergarten programs during the 1998–99 

school year participated in the ECLS-K. To improve the 

12 The kindergarten 1998–99 data collection also included students who were 

in their second year of kindergarten during that school year and because of the 

sample freshening in first grade, the sample includes those who were repeating 

first grade in 1999–2000. These repeaters are included in the analyses in this 

report if they did not repeat another school year (i.e., if they were in eighth 

grade in the 2006–07 school year).

precision of estimates for these students, oversamples 

of Asians/Pacific Islanders and kindergartners attending 

private schools were built into the study.

Sampling for the ECLS-K involved a dual-frame, 

multistage sampling design. The first stage of sampling 

involved the selection of 100 primary sampling units 

(PSUs) from a national sample of PSUs. The PSUs were 

counties and county groups. Public and private schools 

were then selected within the PSUs, and students were 

sampled from the selected schools. Approximately 23 

kindergartners were selected in each of the sampled 

schools. In the spring of first grade, the sample was 

freshened to obtain a nationally representative sample of 

first-graders by bringing into the study first-graders who 

were not enrolled in kindergarten during the 1998–99 

school year and therefore did not have an opportunity 

for selection in the base year. Freshening was carried out 

during the first-grade year because a small, but significant, 

number of children began formal schooling in first grade 

as opposed to kindergarten when the cohort was initiated. 

The sample was not freshened in grades 3, 5, or 8.

All students still enrolled in their previous-year schools 

were recontacted for subsequent rounds of data collection, 

while students who had transferred from their previousyear schools were subsampled in grades 1, 3, and 5. In the 

eighth-grade collection, ineligible students were those who 

had moved out of the country, who were deceased, or who 

had moved to another school and were not subsampled for 

follow-up in an earlier grade. In eighth grade, there was 

no subsampling of movers for follow-up as in previous 

rounds since the majority of students did not remain in 

the same school from fifth through eighth grade (having 

moved out of elementary school into middle school).

For information on the sampling design and sampling 

procedures at each round from kindergarten through 

eighth grade, refer to the Early Childhood Longitudinal 

Study, Kindergarten Class of 1998–99 (ECLS-K), 

Combined User’s Manual for the ECLS-K Eighth-Grade 

and K–8 Full Sample Data Files and Electronic Codebooks

(Tourangeau et al. 2009b). 

Data collection

The data used in this report come from the fifth- and 

eighth-grade direct mathematics assessments, the fifthand eighth-grade student questionnaires, the eighth-grade 

mathematics teacher questionnaires, the eighth-grade 

school administrator questionnaire, and the eighth-grade 

parent interviews. Spring fifth-grade data were collected 

from February through June 2004, with over 75 percent of 

the student assessments completed by the end of April; the 

eighth-grade direct student assessments were conducted 

from March through early June 2007, with about 81 

percent of the eighth-grade assessments completed between 

March and April. In the eighth-grade data collection, 

students completed a student questionnaire during their 
12 NCES 2010-016

assessment time. The student questionnaire covered many 

topics related to the students’ school experiences, schoolsponsored and out-of-school activities, self-perceptions 

of social and academic competence and interests, weight 

and exercise, and diet. Eighth-graders’ teachers were given 

questionnaires in the spring that covered information 

about themselves, their students, and their classrooms. 

All students’ English teachers received a questionnaire, 

but due to limited resources, a random half of the 

students’ mathematics teachers received questionnaires 

and the other half of the students’ science teachers 

received questionnaires. School administrators completed 

questionnaires in the spring and provided details about the 

students and programs at their school. In the eighth-grade 

data collection during the fall and winter of 2006, parents 

completed a computer-assisted telephone interview that 

focused on a range of topics including sociodemographic 

characteristics and home activities.

Response rates and nonresponse bias analysis

A total of 944 of the 1,277 originally sampled schools 

participated during the base year of the study. This 

translates into a weighted response rate (weighted by the 

base weight) of 74 percent for the base year of the study. 

The weighted student base-year survey response rate was 

88 percent (i.e., 88 percent of the students were assessed 

at both rounds in kindergarten). The weighted parent 

base-year unit response rate was 84 percent (i.e., a parent 

interview was completed at both rounds in kindergarten) 

(Tourangeau et al. 2009b). Thus, the overall base-year 

response rate for students was 65 percent (i.e., 74 percent 

of schools x 88 percent of sampled students), and the 

overall base-year response rate for the parent interview 

was 62 percent (i.e., 74 percent of schools x 84 percent 

of parents of sampled students). About 87 percent of the 

students and 84 percent of students’ parents eligible for 

the first-grade data collection (spring 2000) participated; 

about 80 percent of students and 77 percent of students’ 

parents eligible for the third-grade data collection (spring 

2002) participated; about 84 percent of the students and 

88 percent of students’ parents eligible for the fifth-grade 

data collection (spring 2004) participated; and about 75 

percent of students and 71 percent of students’ parents 

eligible for the eighth-grade data collection (spring 2007) 

participated (Tourangeau et al. 2009b). The overall 

eighth-grade response rate for students was 55 percent 

and the overall response rate for the parent interview was 

53 percent. 

A nonresponse bias analysis was conducted to determine 

if substantial bias was introduced as a result of the 

base-year school nonresponse. Findings from this analysis 

suggest that there was not a substantial bias due to 

nonresponse. For information on the nonresponse bias 

analysis, refer to the ECLS-K, Base Year Public-Use 

Data File, Kindergarten Class of 1998–99: Data Files 

and Electronic Code Book (Child, Teacher, School Files), 

and User’s Manual (U.S. Department of Education 

2001). As in most longitudinal surveys, nonresponse 

in the ECLS-K generally increased as the sample aged. 

Chapter 6 of the Early Childhood Longitudinal Study, 

Kindergarten Class of 1998–99 (ECLS-K), Eighth-Grade 

Methodology Report (Tourangeau et al. 2009a) and the 

Early Childhood Longitudinal Study, Kindergarten Class 

of 1998–99 (ECLS-K), Fifth-Grade Methodology Report

(Tourangeau, Lê, and Nord 2005) include an examination 

of the potential for nonresponse bias using three methods: 

(1) a comparison of respondents and nonrespondents using 

data available from the sampling frame, (2) a multivariate 

analysis to identify the characteristics of cases most likely 

to respond, and (3) an analysis of attrition bias applicable 

to longitudinal studies. Nonresponse bias of the estimates 

from the fifth- and eighth-grade samples was present, but 

small, and was corrected, at least in part, through weight 

adjustments. 

The item nonresponse rates for the variables used in this 

report are low, ranging from 0 to about 2.5 percent for 

the analysis sample. A few of the variables were imputed 

to replace missing data (e.g., mother’s education). More 

information on item nonresponse can be found in the 

Early Childhood Longitudinal Study, Kindergarten Class 

of 1998–99 (ECLS-K), Combined User’s Manual for the 

ECLS-K Eighth-Grade and K–8 Full Sample Data Files 

and Electronic Codebooks (Tourangeau et al. 2009b).

Weighting, variance estimation, and tests of 

significance

The ECLS-K data are weighted to account for unequal 

probabilities of selection at each sampling stage and to 

adjust for the effects of school, student, teacher, and parent 

nonresponse. A brief description of the weighting process 

follows. The first stage of the weighting process assigns 

weights to the sampled PSUs that are equal to the inverse 

of their probability of selection.13 The second stage of the 

weighting process assigns weights to the schools sampled 

within PSUs. The base weight for each sampled school is 

the PSU weight multiplied by the inverse of the school’s 

probability of selection. The base weights for eligible 

schools are adjusted for nonresponse. These adjustments 

are made separately for public and private schools.

The base weight for each student in the sample is the 

school nonresponse-adjusted weight for the school the 

student attends multiplied by a poststratified within-school 

student weight (total number of students in the school 

divided by the number of students sampled in the school). 

The child cross-sectional weight (C7CPTM0), which is the 

weight used to produce the estimates found in this report, 

is the base-year child weight adjusted for nonresponse to 

the student assessments, the parent interviews, and the 

mathematics teacher questionnaire at the eighth-grade 

13 The approach used to develop weights for the ECLS-K is described in 

the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Combined User’s Manual for the ECLS-K Eighth-Grade and K–8 

Full Sample Data Files and Electronic Codebooks (Tourangeau et al. 2009b).
NCES 2010-016 13

round.14 This weight sums to the population of all students 

who attended kindergarten in the fall of 1998 or first grade 

in the spring of 2000. 

In addition to properly weighting the responses, special 

procedures for estimating the statistical significance of the 

estimates were employed because the data were collected 

using a complex sample design.15 Complex sample 

designs, like that used in the ECLS-K, result in data that 

violate the assumptions that are normally required to 

assess the statistical significance of results. Frequently, 

standard errors of estimates based on complex samples 

are larger than those based on simple random samples. 

Replication methods of variance estimation were used to 

reflect the multistage sample design used in the ECLS-K. 

Using AM statistical software,16 the jackknife replication 

method (JK2) was used with 90 ECLS-K replicate weights 

to compute approximately unbiased estimates of the 

standard errors of the estimates in this report.17

Statistical procedures

Comparisons made in the text were tested for statistical 

significance at the p < .05 level to ensure that the 

differences were larger than might be expected due to 

sampling variation. When comparing estimates between 

categorical groups (e.g., sex, race/ethnicity), t statistics 

were calculated. The formula used to compute the t 

statistic was 

t = Est1

 – Est2 / (SQRT[(se1)

2

 + (se2)

2

])

where Est1 and Est2 are the estimates being compared 

and se1 and se2 are their corresponding standard errors. 

No adjustments were made for multiple comparisons. In 

this report, a “substantive difference” for comparisons 

of percentages is defined as a difference of 5 percentage 

points or greater. Differences discussed in the text of this 

report are both statistically significant and substantive.

It is important to note that many of the variables examined 

in this Brief may be related to one another and to other 

variables not included in the analyses. The complex 

interactions and relationships among the variables were 

not fully explored in this report and warrant more extensive 

analysis. Furthermore, the variables examined here are 

just a few of those that could be examined in these data 

and other variables related to algebra enrollment may not 

14 Students received a valid student assessment weight if they participated in any 

part of the student assessment, such as the height and weight measurements. 

Thus, students who were unable to take the cognitive assessments because of 

a disability could still have a valid student assessment weight.

15 For more details about sampling error and nonsampling error, please see 

the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Combined User’s Manual for the ECLS-K Eighth-Grade and K–8 

Full Sample Data Files and Electronic Codebooks (Tourangeau et al. 2009b).

16 AM statistical software is designed to calculate estimates and appropriate 

standard errors for multistage, stratified, and unequal probability sample 

designs.

17 Details about the paired jackknife replication method are provided in 

the Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Combined User’s Manual for the ECLS-K Eighth-Grade and K–8 

Full Sample Data Files and Electronic Codebooks (Tourangeau et al. 2009b).

be represented in this report. Readers are cautioned not 

to draw causal inferences based on the results presented.

The coefficient of variation (CV) represents the ratio of 

the standard error to the estimate. The CV is an important 

measure of the reliability and accuracy of an estimate. In 

this report, the CV was calculated for all estimates, and in 

cases where the CV was at least 30 percent the estimates 

were noted with a ! symbol (interpret data with caution). 

In cases where the CV was greater than 50 percent, the 

estimate was determined not to meet reporting standards 

and was suppressed.

Standard errors can be found in appendix A.

Glossary: Constructs and Variables Used in 

the Analysis

Direct cognitive mathematics assessments

The ECLS-K fifth- and eighth-grade direct cognitive 

assessment batteries were designed to assess students’ 

academic achievement in reading, mathematics, and science 

in the fifth and eighth grades and to provide a means of 

measuring growth since kindergarten entry.18 The cognitive 

assessments used in the study (for K–1 and grades 3, 5, 

and 8) were administered using two-stage adaptive tests 

with multiple test forms of varying difficulties to maximize 

the accuracy of measurement and reduce administration 

time. Overlapping items for the test forms within a grade 

as well as across grades link the forms to a vertical scale 

for measuring longitudinal gains. The assessments for K–1 

and grades 3 and 5 were individually administered by 

trained assessors using computer-assisted technology and 

small easel test books of the test items. The assessor first 

administered a routing test for a particular content area 

followed by a second-stage test at the level determined by 

the student’s scores on the routing test. In the eighth grade, 

students completed the two-stage assessments in proctored 

groups, with a routing test followed by a second-stage test. 

Unlike the assessments administered at earlier grades, the 

eighth-grade assessments were self-administered paperand-pencil tests. 

The fifth- and eighth-grade mathematics assessments 

included increasingly difficult items that addressed the 

following content strands: number sense, properties, and 

operations; measurement; geometry and spatial sense; 

data analysis, statistics, and probability; and patterns, 

algebra, and functions. Cognitive processes (conceptual, 

procedural, and problem solving) were assessed in each 

of the strands. Some of the items drew upon knowledge 

from more than one strand. For example, an item might 

require that a student apply knowledge about geometry, 

measurement, and number operations to answer the 

question correctly. For some of the analyses in this report, 

the students’ fifth-grade mathematics scores are converted 

18 Science achievement was assessed in third grade as well as in the fifth and 

eighth grades.
14 NCES 2010-016

into quintiles; that is, the weighted distribution of the 

fifth-grade scores is grouped into five ordered groups, each 

representing about 20 percent of the cohort of students 

who were in the eighth grade in 2007. 

School characteristics

Region. The state or jurisdiction of the school was used to 

create a variable to reflect the four geographical regions 

of the country according to the Bureau of the census 

classification scheme. States and jurisdictions included in 

each region are as follows: the Northeast includes CT, ME, 

MA, NH, RI, VT, NJ, NY, PA; the Midwest includes IL, IN, 

MI, OH, WI, IA, KS, MN, MO, NE, ND, SD; the South 

includes DE, DC, FL, GA, MD, NC, SC, VA, WV, AL, KY, 

MS, TN, AR, LA, OK, TX; and the West includes AZ, CO, 

ID, MT, NV, NM, UT, WY, AK, CA, HI, OR, WA.

School type. This variable indicates whether a student 

attended a public or private school in the spring of eighth 

grade. Public schools included Bureau of Indian Education 

and tribal schools, public schools of choice (e.g., charter 

schools), and public schools with magnet programs. 

Private schools included Catholic schools, other religious 

private schools, and nonreligious private schools.

School’s level of algebra enrollment. An item in the school 

administrator questionnaire had school principals indicate 

the percentage of all eighth-grade students at the school 

who were enrolled in algebra. For some analyses presented 

in this paper, this variable was changed from a continuous 

(0 to 100 percent) variable to a categorical variable of 

eighth-grade algebra enrollment levels (i.e., less than 25 

percent, between 25 and 74 percent, and 75 percent or 

more).

Students’ course enrollment, educational 

expectations, and enjoyment of mathematics

Mathematics course enrollment. Students’ mathematics 

teachers indicated the name of the course in which 

the student was enrolled. The options were general 

mathematics, introduction to algebra/pre-algebra, algebra 

I, integrated or sequential mathematics, algebra II, and 

geometry. 

Educational expectations. Students were asked the 

question, “As things stand now, how far in school do 

you think you will get?” The eight response options were 

less than high school graduation; high school graduation 

or GED only; attend or complete a 2-year program in a 

community college or vocational school; attend college, 

but not complete a 4-year degree; graduate from a 4-year 

college; obtain a master’s degree or the equivalent; obtain 

a Ph.D., M.D., or other advanced degree; and don’t know. 

For this report, these responses were collapsed into four 

categories: less than a 4-year college degree; a 4-year college 

degree; beyond a 4-year college degree; and don’t know. 

Enjoyment of mathematics. In both the fifth and eighth 

grades, students responded to a series of questionnaire 

statements by indicating how true each statement was 

for them: not at all true, a little bit true, mostly true, or 

very true. This report analyzes student responses to the 

statement “I like math” at both grades.

Student and family characteristics

A number of the variables used in this report were derived 

by combining information from one or more questions in 

the ECLS-K study instruments. More information on the 

derivation of key variables is contained in chapter 7 of the 

Early Childhood Longitudinal Study, Kindergarten Class 

of 1998–99 (ECLS-K), Combined User’s Manual for the 

ECLS-K Eighth-Grade and K–8 Full Sample Data Files 

and Electronic Codebooks (Tourangeau et al. 2009b).

Grade level of student. To create the grade-level composite, 

two sources of grade-level data were used: information 

from the special education teacher part B questionnaire 

(for those students who had a special education teacher) 

and information collected about each student from the 

schools by the field staff. 

Student’s sex. This composite is brought forward from 

information originally confirmed in the fall kindergarten 

parent interview. If the parent interview indicated a sex 

different from that in the field management system, the 

parent interview information took priority. 

Student’s race/ethnicity. In the spring of eighth grade, the 

race/ethnicity of the focal student was no longer collected 

in the parent interview; thus, race/ethnicity information 

is based on the race/ethnicity collected in previous parent 

interviews and the field management system. The race/

ethnicity composite is constructed from two parentreported variables: ethnicity and race. Following the 1997 

Office of Management and Budget guidelines, respondents 

were allowed to indicate that their child belonged to more 

than one of the following race categories: White, Black 

or African American, American Indian or Alaska Native, 

Asian, or Native Hawaiian or other Pacific Islander. In 

addition, each respondent was asked to identify whether 

the student was Hispanic. The following are the five 

composite race/ethnicity categories presented in this report: 

White, not Hispanic; Black, not Hispanic; Hispanic; Asian, 

not Hispanic; and Other, not Hispanic (which includes 

Native Hawaiians, Pacific Islanders, American Indians, 

Alaska Natives, and non-Hispanic students of two or 

more races). When race/ethnicity differences are presented 

in this report, White refers to White, not Hispanic; Black 

refers to Black, not Hispanic; Asian refers to Asian, not 

Hispanic; and Other refers to other, not Hispanic. 

Poverty status. The federal poverty-level status composite 

variable is derived from household income and the total 

number of household members. Federal poverty thresholds 

are used to define households below the poverty level. 

Households whose income fell below the appropriate 

threshold based on census information from 2006 were 

classified as living in poverty. For example, if a household 
NCES 2010-016 15

contained four members, and the household income was 

lower than $20,614, the household was considered to be 

below the poverty threshold.

Mother’s highest level of education. This composite is 

derived from parent interview information on the mother’s 

educational attainment. Missing data were imputed using 

hot-deck procedures. The 406 students without a mother 

in the household in the eighth-grade year do not have data 

for this variable and are excluded from analyses related 

to mother’s education. For this report, the composite was 

collapsed into a four-category variable: less than high 

school, high school diploma or the equivalent, some college 

or vocational technical degree, and bachelor’s degree or 

higher. Those with an associate’s degree are included with 

“some college or vocational technical degree.”

Family type. This composite is derived from parent 

interview information on the number of parents in the 

home. For this report, the composite was collapsed into 

a three-category variable: two parents, single parent, and 

other. “Other” households include related and/or unrelated 

guardians. The tables do not include estimates for the 

“other” category because there are too few students in the 

sample with this family type to produce stable estimates.

References

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12). The California Algebra I Success Initiative: A 

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U.S. Department of Education. Washington, DC.

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1998–99 (ECLS-K), Fifth-Grade Methodology Report 

(NCES 2006-037). National Center for Education 

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ecls/. To order additional copies of this Statistics in Brief or other NCES publications, call 1-877-4ED-PUBS or visit http://www.edpubs.

gov. NCES publications are also available on the Internet at http://nces.ed.gov.
NCES 2010-016 17

Appendix A. Standard Error Tables

Table A-1. Standard errors for table 1: Percentage distribution of mathematics course enrollment of ECLS-K spring 2000 first-grade 

cohort eighth-graders, by student, family, and school characteristics: Spring 2007

Characteristic

Mathematics course

General 

mathematics

Introduction 

to algebra/ 

pre-algebra

Algebra or a course more advanced

than algebra

Total Algebra

An advanced 

course other 

than algebra

Total 1.1 1.6 1.3 0.8 1.4

Sex 

Male 1.4 2.2 1.9 1.8 0.8

Female 1.5 2.1 1.9 1.8 1.1

Race/ethnicity

White, not Hispanic 1.0 1.9 2.0 1.8 1.0

Black, not Hispanic 3.3 4.0 3.6 3.4 † 

Hispanic 3.2 3.4 3.1 2.9 1.2

Asian, not Hispanic 6.4 3.4 6.1 5.4 4.1

Other, not Hispanic 6.8 7.8 6.3 5.7 2.6

Poverty status

Below federal poverty level 3.7 3.9 2.6 2.5 † 

At or above federal poverty level 1.0 1.7 1.6 1.5 0.8

Mother’s education

Less than high school 3.5 5.1 3.3 3.3 † 

High school diploma or equivalent 3.0 3.4 2.6 2.3 1.0

Some college or vocational technical degree 1.7 2.4 2.3 2.1 1.2

Bachelor’s degree or higher 1.4 2.4 2.4 2.4 1.5

Family type

Two parents 1.3 1.9 1.8 1.6 0.8

Single parent 1.9 3.3 3.0 2.9 1.3

Region

Northeast 1.7 2.9 3.1 3.0 2.0

Midwest 2.0 3.6 3.1 2.7 0.9

South 2.4 2.6 1.8 1.5 1.4

West 2.4 4.0 3.8 3.7 1.8

School type

Public school 1.2 1.8 1.6 1.4 0.8

Private school 2.8 3.4 3.7 3.8 1.9

† Not applicable.

NOTE: Standard errors were estimated with replicate weights C7CPTM1 through C7CPTM90. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Kindergarten–Eighth Grade Full Sample Public-Use Data File. 
18 NCES 2010-016

Table A-2. Standard errors for table 2: Percentage distribution of ECLS-K spring 2000 first-grade cohort eighth-graders who attended 

schools with various levels of eighth-grade student enrollment in algebra, by student, family, and school characteristics: 

Spring 2007

Characteristic

Principals’ report of the percentage of all eighth-grade students at the 

school enrolled in algebra

Less than 25 percent 25 to 74 percent 75 percent or more

Total 1.9 1.9 1.0

Sex 

Male 2.4 2.5 1.5

Female 2.2 2.1 1.0

Race/ethnicity

White, not Hispanic 2.3 2.3 1.1

Black, not Hispanic 5.7 5.0 2.9

Hispanic 3.3 3.6 2.8

Asian, not Hispanic 6.0 6.2 5.9

Other, not Hispanic 7.1 6.0 3.4

Poverty status

Below federal poverty level 3.4 3.3 2.5

At or above federal poverty level 2.1 2.1 1.0

Mother’s education

Less than high school 6.1 6.1 4.2

High school diploma or equivalent 3.3 2.7 1.8

Some college or vocational technical degree 3.0 2.9 1.6

Bachelor’s degree or higher 2.6 3.0 1.6

Family type

Two parents 2.2 2.2 1.1

Single parent 3.1 2.8 1.7

Region

Northeast 3.6 3.6 2.2

Midwest 3.8 3.1 2.1

South 3.5 3.4 1.1

West 3.1 3.4 3.1

School type

Public school 2.1 2.0 1.1

Private school 4.0 4.1 3.5

NOTE: Standard errors were estimated with replicate weights C7CPTM1 through C7CPTM90. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Kindergarten–Eighth Grade Full Sample Public-Use Data File. 
NCES 2010-016 19

Table A-3. Standard errors for table 3: Average ECLS-K spring 2000 first-grade cohort’s eighth-grade mathematics scores, by 

mathematics course, student, family, and school characteristics: Spring 2007

Characteristic Total

Eighth-grade mathematics course

Not in algebra

Algebra or a course more 

advanced than algebra

Total 0.65 0.84 0.70

Sex 

Male 0.96 1.22 0.86

Female 0.90 1.07 1.08

Race/ethnicity

White, not Hispanic 0.84 1.18 0.70

Black, not Hispanic 1.66 1.83 3.82

Hispanic 1.17 1.30 1.79

Asian, not Hispanic 3.71 7.33 1.79

Other, not Hispanic 3.06 3.39 2.60

Poverty status

Below federal poverty level 1.56 1.79 2.36

At or above federal poverty level 0.61 0.93 0.68

Mother’s education

Less than high school 1.71 1.93 4.08

High school diploma or equivalent 1.45 1.73 1.51

Some college or vocational technical degree 0.91 1.01 1.40

Bachelor’s degree or higher 0.72 1.35 0.72

Family type

Two parents 0.69 0.91 0.65

Single parent 1.36 1.66 1.79

Region

Northeast 1.35 2.06 1.21

Midwest 1.75 1.89 1.16

South 1.14 1.35 1.52

West 1.26 2.00 1.61

School’s eighth-grade algebra enrollment

Less than 25 percent 1.01 1.23 1.35

25 to 74 percent 1.09 1.72 0.83

75 percent or more 1.85 4.51 2.24

School type

Public school 0.67 0.85 0.73

Private school 1.63 2.35 1.77

NOTE: Standard errors were estimated with replicate weights C7CPTM1 through C7CPTM90. 

SOURCE: U.S. Department of Education, National Center for Education Statistics, Early Childhood Longitudinal Study, Kindergarten Class of 1998–99 

(ECLS-K), Kindergarten–Eighth Grade Full Sample Public-Use Data File.
www.ed.gov ies.ed.gov