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Achievement Gaps
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What are the Achievement Gaps?

  1. Achievement Gap in Income

States Differ on Achievement Gap Patterns

National data on achievement gap trends among white and non-white students can mask differences in trends among states. A researcher examines differences in state achievement gap patterns.

This reports some of the ideas and findings from the following source:

Lee, J. (1998). State policy correlates of the achievement gap among racial and social groups.Studies in Educational Evaluation, 24,137-152.

To see other reports that originated from this same citation, go to the bibliography.

Formulating state policies to address the achievement gap in schools is a very tricky business, says scholar Jaekyung Lee.

  • One the one hand, if states cannot accommodate student and school differences with regard to discrepancies in achievement, the gap is likely to get worse.
  • On the other hand, if states do try to address these inequities, but do it improperly, they may also make the achievement gap worse.

Lee notes that all states have instituted some kind of education reform over the past decade. How have these reforms made an impact on the achievement gap? Lee says that the results are mixed.

In his study, Lee systematically analyzes how the achievement gap among different racial and social groups varies across different states. He also looks at how standards-raising efforts are related to student outcomes.

Breaking Apart Within-School and Between-School Achievement Gap Patterns

Lee emphasizes the importance of understanding how the achievement gap operates at different levels. He makes a distinction between achievement gaps that occur within schools and achievement gaps that occur between schools. He notes that previous research finds racial and social gaps at both levels.

Lee is concerned in this analysis with two kinds of achievement gaps:

  1. Racial Gap: the difference in academic performance between whites and non-Asian minorities.
  2. Social Gap: the difference in academic performance between wealthier and more economically deprived students.

Drawing on these two distinctions, Lee says that research on mathematics achievement identifies the following gaps.

Racial Gap

Social Gap

Within-School Gap

Differences in math achievement exist between white and minority students at the same school.

Differences in math achievement exist between students of different socioeconomic status (SES) within the same school.

Between-School Gap

When comparing predominantly white and predominantly minority schools, substantial disparity in math achievement is evident.

When comparing high-SES and low-SES schools, a difference in average math achievement also exists.

Lee argues that it is important to make the distinction between within-school and between-school gaps, since different causes may be working at different levels. At the within-school level, student and classroom differences come to bear on the achievement gap. At the between-school level, differences in resources and school structure and curriculum may also help bring about different average levels of student achievement.

Lee does not leave the analysis there. He adds another level of analysis. If we want to understand how state policy might affect differences in student achievement, we must also be able to distinguish state-level effects from within-school and between-school effects.

Different Levels Have Different "Weights" When It Comes to Explaining the Achievement Gap

By comparing different statistical models, Lee seeks to tease out the different "proportion" of the achievement gap that within-school, between-school, and state-level influences might explain. He uses data on 4th and 8th graders from the 1992 National Assessment of Educational Progress (NAEP) Trial State Assessment.

Partitioning the effects on achievement gap between these different levels, Lee finds that student-level and school-level effects explain most of the variation between student math achievement scores. See Figure 1.

Figure 1. Student-, School-, and State-Level Predictors for Math Achievement

How Do State Averages in the Achievement Gap Change with Student Age?

Figure 1 not only demonstrated that most of the influence on student math scores comes from student-level and school-level effects, but also that the makeup of these effects appears to change somewhat as students age. Lee estimates the achievement gap averages for40 states in terms of both race and SES and within-school and between-school effects.

Lee finds that the within-school SES gap grows substantially between 4th and 8th graders (from an average of 33.41 points in 4th grade to 49.15 points in 8th grade). That is, among students at the same school, differences in economic level becomes a stronger predictor of differences in math achievement. In contrast, within- and between-school racial differences remain relatively unchanged between 4th and 8th grade. Lee also notes that the between-school SES gap also drops slightly between 4th and 8th grade. See Figure 2.

Figure 2. Average Math Score Gap between Richer and Poorer Students and Richer and Poorer Schools: 4th Grade and 8th Grade Comparison

What does this mean? Even though the differences in math scores of students at richer and poorer schools are large, these differences do not change much over time. What changes is the differences between richer and poorer students at the same school. Poorer 8th grade students do worse in math (relative to their richer peers at the same school) than poorer 4th grade students.

With respect to race, Lee finds that there is more difference in math scores between predominantly white and predominantly minority schools than there is between white and minority students at the same school. He also finds that these differences do not change much between 4th and 8th grade.

Figure 3. Average Math Score Gap between White and Minority Students and Predominantly White and Predominantly Minority Schools: 4th Grade and 8th Grade Comparison

How Do Racial and Social Achievement Gaps Relate to Each Other?

Lee then explores how the four different dimensions in his analysis are related to each other. He makes the following conclusions:

  • Among 4th graders in the same school, the greater the socioeconomic differences among students, the stronger the racial differences in achievement. This relationship between socioeconomic differences and race weakens as students move to 8th grade, however.
  • States where there are significant racial differences among 8th graders also tend to show equally strong racial differences within schools.
  • States that have a significant gap between high-SES and low-SES schools also find similar differences between richer and poorer students at the same school.

What Is the Relationship between State Average Achievement and Racial and Social Achievement Gaps?

We see that there is a difference between student math achievement when we take into account race and SES and consider the differences within and between schools. But, how do higher- and lower-performing states compare across these differences? In other words, is there any relationship between state math achievement and the achievement among racial and social groups?

Lee points out two main findings from his analysis comparing higher and lower performing states:

  1. White and minority 4th graders in the same school tend to have more similar math scores in states with higher average math performance. This similarity declines over time. So the math scores of white and minority 8th graders at the same school tend to become less similar.
  2. High-performing states appear fairly similar to lower performing states in terms of the math score gap between the richer and poorer students at the same school. This holds for both 4th graders and 8th graders.

Is the Level of State Activity in Addressing the Achievement Gap Associated with Any Changes in Achievement Gap Patterns?

Looking specifically at states actively involved in reform efforts, Lee makes draws three main conclusions from his analysis:

  1. There is a negative relationship between a state's average achievement and the level of reform activism by the state. Measures of 1984 levels of state activism are negatively correlated to the 1992 state average SAT math scores. Lee interprets this to mean that low-performing states were more active in enacting standards-raising policies in the last decade. However, they were still performing poorly into the early 1990s.
  2. Within-school gaps are mixed in more active reform states. As the level of state activism increases, the level of within-school racial gap increases as children move from grade 4 to grade 8. In contrast, as the level of state activism increases, the level of within-school social gap decreases as students move from grade 4 to grade 8. In other words, as students in active reform states age, the within-school racial gap tends to increase while the within-school social gap decreases.
  3. Between-school gaps may be mixed in more active reform states. Similarly, Lee found that racial gaps between schools also tended to increase in active states as students moved from 4th to 8th grade. However, social gaps between schools also tended to fall from 4th to 8th grade in active reform states.

The Bottom Line

What does all this mean for state policies?

Lee says the achievement gap inactive reform states is likely to be relatively smaller between high-SES and low-SES students as children move from the 4th to the 8th grade.

Lee also says that active reform states are likely to see just the opposite pattern with regard to the racial achievement gap. More-active states are likely to see larger achievement gaps for race as students get older.

In this regard, says Lee, ". . . standards-raising state policies face the challenge to meet the needs of culturally diverse minority students" (p.147).

Research Design:

Research Questions

How are state policies associated with racial and social-achievement gap patterns?

How are within-school and between-school achievement gap patterns related?


Lee draws on data sources from the 1992 National Assessment of Educational Progress Trial State Assessment. He focuses on mathematics achievement for 4th and 8th graders. This provided the following number of subjects:

4th Grade

  • 56,596 students
  • 4,266 schools
  • 40 states
  • 78.7% white students
  • 15.9% black students
  • 4.5% Hispanic students
  • 0.9% Native American students

8th Grade

  • 70,741 students
  • 3,601 schools
  • 40 states
  • 82% white students
  • 12.4% black students
  • 4.7% Hispanic students
  • 0.8% Native American students

State policy measures were constructed from the 1984&–1985 state policy survey data, measuring state responses to 26 separate policies.

Statistical Methods

Lee used hierarchical linear modeling to tease out student-level, school-level, and state-level effects. Student composite score on the total NAEP mathematics assessment was treated as the dependent variable.

To calculate policy and state ranking, Lee calculated the probability of that a given state would enact a certain policy.

Funding Source

Supported by a grant from the American Educational Research Association and the National Center for Education Statistics.


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