U.S. Department of Education

Office of Educational Research and Improvement

NATIONAL CENTER FOR EDUCATION STATISTICS

First-Graders’ Achievement in Top and Bottom Schools

January 1998

Most people believe that schools differ widely from one another in their

students’ achievement, but little is known about the magnitude of these

differences, particularly at the early grades of schooling. Drawing on

data from Prospects: The Congressionally Mandated Study of

Educational Growth and Opportunity, we can now address questions in

this area.

To describe the magnitude of reading and mathematics differences in

top and bottom schools, we ranked a nationally representative sample

of Prospects schools by the test scores of their students at the end of

first grade; then we compared the scores and characteristics of the

students in the top- and bottom-ranked quarters of these schools. Since

there is no single standard way to compare the scores and

characteristics of the students in the top and bottom quarters of these

schools, we make the comparison four ways.

The first method compares the percentile ranks of the average student

in the top and bottom quarters of schools at the end of first grade. The

second approach converts the test score differences between students in

the top and bottom quarters of schools into a widely used measure

called effect size. The third approach determines the number of years

of schooling the bottom school students are behind the top school

students at the end of first grade. The fourth method shows how

students in the bottom quarter rank on average at the end of first grade

relative to students in the top schools and vice versa. We then look at

the educational and economic backgrounds of the students attending the

top and bottom quarters of schools in achievement.

Achievement Differences Between Top and Bottom Schools

Each of the four approaches shows large differences in reading and

mathematics achievement at the end of first grade between students in

the top and bottom scoring schools.

The first comparison shows that the average achievement of students

attending the top quarter of schools equals that of a student at the 71st

percentile in reading and the 70th percentile in mathematics (table 1,

line 1). The average achievement of students attending the bottom

quarter of schools equals that of a student at the 24th percentile in both

reading and mathematics (line 2). Thus, there are 46–47 percentile

point differences in achievement between average students in top and

bottom scoring schools.

The second comparison converts the average test scores of students in

the top and bottom quarters of schools (table 1, lines 1 and 2) into a

measure of the size of the difference called an effect size. The effect

size is the average achievement difference between students in the top

and bottom quarters of schools (line 2 minus line 1) divided by the

standard deviation of all students’ achievement. The effect size for the

achievement difference between students in the top and bottom quarters

of schools is 1.15 in reading and 1.13 in mathematics (line 3). Effect

sizes of 0.8 and greater are generally considered large. An effect size

of 0.8, for example, corresponds to the average difference between the

heights of 13-year-old and 18-year-old girls.

Table 1.—First-graders’ reading and mathematics achievement in

top and bottom schools in spring of first grade

Reading Mathematics

achievement achievement

(and percentile) (and percentile)

1. Average achievement (and 

 percentile) of students attending

 top quarter of schools 598 (71) 556 (70)

2. Average achievement (and

 percentile) of students attending

 bottom quarter of schools 524 (24) 479 (24)

3. Effect size: Achievement difference

 between students in top and 

 bottom quarter of schools divided

 by first grade standard deviation 1.15 1.13

4. Achievement difference between

 students in top and bottom quarter of

 schools divided by average gain

 from spring of first grade to spring

 of second grade 1.10 0.95

NOTE: In reading, the n for top schools is 39 and for bottom schools is 36. In

mathematics, the n for top schools is 36 and for bottom schools is 41.

SOURCE: U.S. Department of Education, Prospects: The Congressionally Mandated

Study of Educational Growth and Opportunity, 1991, 1992.

The third approach to comparing achievement in the top and bottom

schools looks at the difference in achievement between the top and

bottom schools at the end of first grade, compared to the average

achievement growth in reading and mathematics the next year. The

difference in reading achievement between the top and bottom schools

at the end of first grade is 1.1 times as large as the reading gain

experienced by the average student through the end of second grade

(table 1, line 4). The difference in mathematics is 0.95 times as large as

the next year’s gain. These results imply that the average student in the

bottom-ranked schools—if this student gains at the average growth rate

of all students—will not reach, after a full year of second grade, where

students in the top-ranked schools were at the end of their first grade in

reading. By the end of second grade, in the bottom-ranked schools, the

average student will just about equal end-of-first-grade performance in

the top schools in mathematics.

The fourth comparison shows that the average first-grader among all

students achieves at a level exceeding 27 percent of the first-graders in

the top quarter schools, but has a score higher than 75 percent of the

first-graders in the bottom quarter schools (table 2, lines 1 and 2).

Perhaps more striking, the average first-grader in the top schools has

achievement exceeding 88–89 percent of the first-graders in the bottom

schools, while the average student in the bottom schools exceeds 7–9

percent of the students in the top schools (table 2, lines 3 and 4).

ISSUE

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

of Delaware in Newark; and William Thompson of ABT Associates, Inc. Data source: U.S. Department of Education, Prospects: The Congressionally Mandated Study of

Educational Growth and Opportunity. For more information regarding this Issue Brief, please contact John Ralph at (202) 219-2270. 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 98–041

Table 2.—First-graders’ achievement percentiles in top and bottom

schools

Reading Mathematics

achievement achievement

1. Percentile an average student

 overall would have among 

 students in top quarter of schools 27 27

2. Percentile an average student

 overall would have among students

 in bottom quarter of schools 75 75

3. Percentile an average student in

 top quarter of schools would have

 among students in bottom quarter

 of schools 88 89

4. Percentile an average student in

 bottom quarter of schools would have

 among students in top quarter of

 schools 7 9

NOTE: In reading, the n for top schools is 39 and for bottom schools is 36. In

mathematics, the n for top schools is 36 and for bottom schools is 41.

SOURCE: U.S. Department of Education, Prospects: The Congressionally Mandated

Study of Educational Growth and Opportunity, 1991, 1992.

Family Background Differences Between Students in Top

and Bottom Schools

The results in tables 1 and 2 show that students in the top and bottom

quarters of a representative sample of American schools differ greatly

in reading and mathematics achievement in first grade. Table 3 shows

they also differ greatly in the educational and economic backgrounds of

their families.

About half the students in the top schools come from households where

the average education exceeds high school, while about one-third of the

students from the bottom schools come from households where the

average education exceeds high school (table 3, line 1). Students in the

top schools also come from households with significantly higher

incomes than students in bottom schools (table 3, line 2).

Table 3.—Family background differences of first-grade students in

top and bottom schools

Bottom Bottom

Top quarter quarter Top quarter quarter

of schools of schools of schools of schools

1. Percent of households

 with average education

 above high school 48 31 53 31

2. Average household

 income in 1991 $46,147 $22,773 $48,423 $21,618

Mathematics

achievement

Reading

achievement

SOURCE: U.S. Department of Education, Prospects: The Congressionally Mandated

Study of Educational Growth and Opportunity, 1991, 1992.

Conclusions

These results show a largely stratified American education system at

the end of the first grade—stratified both in achievement and in

backgrounds of the students attending them. Such achievement and

family differences may be associated with substantial differences

between schools in curricular demands, school climates, and levels of

parental support.

These differences raise important policy questions that deserve further

investigation. Do these large differences in achievement at the end of

first grade reflect differences students bring with them upon entering

school, differences that occur after starting school, or both? Are the top

schools “better” schools than the bottom schools? If this is the case,

these results indicate that first-graders in top-ranked schools are much

more likely to come from better educated and wealthier backgrounds

than first-graders in bottom-ranked schools.

If the top schools have higher achievement than the bottom schools

only because they have more privileged educational and economic

inputs, and not because the top schools are “better” than the bottom

ones, then the wide achievement differences between top and bottom

schools reflect educational and economic differences in students’

backgrounds even before the end of the first grade.