U.S. Department of Education

Office of Educational Research and Improvement

NATIONAL CENTER FOR EDUCATION STATISTICS

Reading and Mathematics Achievement: Growth in High School

December 1997

The most recent wave of concern over the level of academic

achievement among our nation’s school population began with the

publication of A Nation at Risk in 1983. The report left education

researchers with an important question: How much does student

achievement (for youth who stay in school) grow during different

stages of students’ schooling? To answer the question for the high

school years, data are available describing the academic

achievement of high school students between 8th and 12th grades in

reading and mathematics. It also is important to examine

differences between whites, blacks, and Hispanics in reading and

mathematics achievement over these same years.

Data from the National Education Longitudinal Study of 1988 on

reading and mathematics achievement of students near the end of

8th and 12th grades reveal that:

• Very modest gains in achievement occur over the high school

years compared to the range of achievement existing near the end

of eighth grade.

• White students score higher in both reading and mathematics than

black and Hispanic students at the end of the eighth grade. These

differences do not increase substantively over the next four years.

• All of the significant differences in reading and mathematics

achievement between whites and black and Hispanic minority

groups at the end of 12th grade reflect differences in achievement

between the groups before they enter high school.

Overall Achievement Growth

Both reading and mathematics achievement increase from the spring

of grade 8 to the spring of grade 12 (table 1). The gains from the

spring of grade 8 to the spring of grade 10 are larger than the gains

from the spring of grade 10 to the spring of grade 12. The average

yearly gain over all four years of high school is 0.17 eighth-grade

standard deviations in reading and 0.26 eighth-grade standard

deviations in mathematics. These yearly gains are similar in

magnitude to those reported for the High School and Beyond survey

(Alexander, Natriello, & Pallas 1985) and to those reported in a

number of other studies summarized by Jencks (1985).

Table 1.—Achievement in grades 8–12

*Number correct scores on tests equated across grades 8, 10, and 12 with item

response theory (IRT).

SOURCE: National Education Longitudinal Study of 1988. See Ingels, et. al. (1994).

One way to interpret the size of these gains is to convert 8th-, 10th-,

and 12th-grade achievement scores into their percentile equivalents

among 8th-graders (table 2). Twelfth-graders have mean 12th-grade

reading scores equal to 8th-graders at the 68th percentile and mean

mathematics scores equal to 8th-graders at the 75th percentile. The

average student thus gains 4.5 8th-grade percentiles per year in

reading and 6.2 8th-grade percentiles per year in mathematics.

Table 2.—Average reading and mathematics achievement in grades

8–12 in eighth-grade percentiles

SOURCE: National Education Longitudinal Study of 1988. See Ingels, et. al. (1994).

Many 8th-graders’ scores are higher than those of the average 12thgrader, and many 12th-graders’ scores are below those of the

average 8th-grader. Table 3 shows the percentage of students at

each grade level with achievement scores in each quarter of the

eighth-grade distribution. About 28 percent of 12th-graders have

scores that would put them in the bottom half of 8th-graders in

reading, and about 20 percent of 12th-graders have mathematics

scores in the bottom half of the 8th-grade distribution. These results

suggest considerable overlap in the achievement distributions of 8th-

, 10th-, and 12th-graders.

Table 3.—Percentage of students in grades 8, 10, and 12 with

achievement scores falling in each quarter of the 8thgrade distribution

SOURCE: National Education Longitudinal Study of 1988. See Ingels, et. al. (1994).

Overall, these results show that achievement increases over the high

school years, but that the gains are relatively modest compared to

the range of variation in eighth grade. It is important to note that

these results describe overall changes in the achievement

distributions at each grade, and not the achievement gains of groups,

such as blacks and Hispanics compared to whites.

ISSUE

BRIEF

IRT scores* 8 10 12 8 10 12

 Mean 28.5 32.3 34.4 38.1 46.0 50.5

 Standard deviations 8.4 9.6 9.7 11.6 13.1 13.7

IRT score gains* 8–10 10–12 8–12 8–10 10–12 8–12

 Gains 3.7 2.2 5.9 7.9 4.4 12.3

 Gains per year in 8th grade

 standard deviations 0.22 0.13 0.17 0.34 0.19 0.26

Reading Mathematics

Subject and grade

8th-grade percentiles 8 1 0 1 2 8 1 0 1 2

 Mean 50.6 61.9 68.4 50.5 67.6 75.3

Gains in 8th-grade percentiles 8–10 10–12 8–12 8–10 10–12 8–12

 Yearly gain 5.7 3.3 4.5 8.6 3.9 6.2

Subject and grade

Reading Mathematics

Percent in each

8th-grade quartile 8 10 12 8 10 12

0–25 24.9 18.2 13.4 24.9 12.3 7.2

26–50 25.2 18.3 14.9 25.2 15.5 12.4

51–75 25.0 20.2 18.8 25.0 23.0 19.5

76–100 24.9 43.3 52.8 24.9 49.2 60.9

Subject and grade

Reading Mathematics
This Issue Brief was prepared by John Ralph of the National Center for Education Statistics and James Crouse, professor of Educational Studies at the University of

Delaware in Newark, DE. For more information about this Issue Brief, contact John Ralph at (202) 219-2270 or John_Ralph@ed.gov. To order additional copies of this

Issue Brief or other NCES publications, call 1-800-424-1616. It may also be found on the Internet at http://www.ed.gov/NCES/pubs/.

NCES 98–038

Race/ethnicity and Achievement Gains

On average, blacks and Hispanics score lower than whites in reading

and mathematics at the end of 8th grade (table 4, row 1) and at the

end of 12th grade (row 2). The black and Hispanic differences from

whites at the end of 12th grade are statistically the same size as at

the end of 8th grade (row 2 compared to row 1). These results

suggest that the reading and mathematics achievement differences

between white students and minority black and Hispanic students do

not increase over the high school years.

Table 4.—Black–white and Hispanic–white differences in 8th and

12th grade reading and mathematics achievement1

1Number correct scores on tests equated across grades 8, 10, and 12 with item

response theory (IRT).

2

p<0.01.

SOURCE: National Education Longitudinal Study of 1988. See Ingels, et. al. (1994).

While these results tell us that the race/ethnicity gap in reading and

mathematics achievement at the end of 12th grade is no different

statistically than at the end of 8th grade, they do not tell us how

much of a race/ethnicity gap would exist at 12th grade among white,

black, and Hispanic students with the same 8th grade achievement.

The 12th-grade race/ethnicity gap reflects the fact that, on average,

black and Hispanic students enter high school with different

achievement levels than whites; that is, because the race/ethnicity

gap exists at the end of 8th grade. Among students with the same

8th-grade achievement, the black and the Hispanic disadvantages in

12th-grade reading and mathematics vanish statistically (row 3).

Thus, the racial disparities in 12th-grade achievement reflect

differences in achievement prior to entering high school. These

results suggest that if blacks and Hispanics entered high school with

the same achievement levels as whites, their differences from whites

in 12th-grade reading and mathematics achievement would be

extremely small and statistically insignificant.

Table 5 shows the race/ethnicity differences from table 4 divided by

the average yearly growth in achievement scores from the end of

grade 8 through grade 12. More intuitively, table 5 shows the

number of years apart the race/ethnicity groups are in terms of

achievement growth. At the end of the 12th grade, blacks are about

3–4 years of achievement growth behind whites, and Hispanics are

about 2–3 years behind whites (line 1). Among students with the

same 8th-grade achievement, however, the 12th-grade race/ethnicity

differences after four years of high school are a half a year or less

and are statistically insignificant (line 2).

Table 5.—Race/ethnicity differences at the end of 12th grade

divided by average yearly growth from end of 8th grade

to end of 12th grade

SOURCE: National Education Longitudinal Study of 1988. See Ingels, et. al. (1994).

Conclusions

Overall, data from the National Education Longitudinal Study of

1988 support two conclusions. The first is that without regard to

students’ race or ethnicity, achievement growth over the high school

years in reading and mathematics is relatively modest compared to

the range of achievement that exists at the beginning of high school.

Achievement of 12th-graders as a group is not dissimilar to the

achievement of 8th-graders.

The second conclusion is that the high school years do not contribute

significantly to race/ethnicity differences in reading and

mathematics achievement. Despite differences in the high schools

attended by black, Hispanic, and white students, the 12th-grade

reading and mathematics achievement differences between these

groups reflects differences in how much they knew when they

entered high school, and not on their race or ethnicity per se.

References

Alexander, K., Natriello, G., & Pallas, A. (1985). “For Whom the

Bell Tolls: The Impact of Dropping Out on Cognitive Performance.”

American Sociological Review, 50, 409-420.

Ingels, S.J., Dowd, K. L., Baldridge, J.D., Stipe, J.L., Bartot, V.H.,

Frankel, M. R., Owings, J., & Quinn, P. (1994). National

Education Longitudinal Study of 1988. Second Follow-Up: Student

Component Data File User’s Manual. Washington: U.S.

Department of Education, Office of Educational Research and

Improvement, National Center for Education Statistics.

Jencks, C. (1985). “How Much Do High School Students Learn?”

Sociology of Education, 58, 128-135.

Reading Math Reading Math

1. Eighth-grade differences -5.2 2

-9.0 2 -4.2 2-6.4 2

2. Twelfth-grade differences -6.1 2-10.3 2 -4.1 2 -6.4 2

3. Twelfth-grade differences

 among students with the 

 same eighth-grade scores -0.8 -1.3 0.1 0.2

Race difference and subject

Black–white Hispanic–white

Reading Math Reading Math

1. End of twelfth grade for

 all students -4.2 -3.3 -2.8 -2.1

2. End of twelfth grade for 

 students with the same

 eighth grade test scores -0.5 -0.4 0.1 0.1

Race difference and subject

Black–white Hispanic–white