Diverging Disparities: Race,Parental Income,and Children’s Math Scores,1960 to 2009

Abstract

In recent decades, the black–white test score disparity has decreased, and the test score disparity between children of high- versus low-income parents has increased. This study focuses on a comparison that has, to date, fallen between the separate literatures on these diverging trends: black and white students whose parents have similarly low, middle, or high incomes (i.e., same income or race within income). To do so, I draw on three nationally representative data sets on 9th or 10th graders, covering 1960 to 2009, that contain information on students’ math test scores. I find that math test score disparities between black and white students with same-income parents are to black students’ disadvantage. Although these disparities have decreased since 1960, in 2009 they remained substantively large, statistically significant, and largest between children of the highest-income parents. Furthermore, family and school characteristics that scholars commonly use to explain test score disparities by race or income account for markedly decreasing shares of race-within-income disparities over time. The study integrates the literatures on test score disparities by race and income with attention to the historical and continued structural influence of race, net of parental income, on students’ educational experiences and test score outcomes.

Keywords

race income achievement gaps inequality intersectionality

Disparities in students’ test score outcomes have been central to research in the sociology of education since at least the Equality of Educational Opportunity report (Coleman et al. 1966). Since the mid-twentieth century, disparities across two key dimensions—race and parental income—have trended in opposite directions. Test score disparities between black and white children have substantially decreased (e.g., Magnuson and Waldfogel 2008; Reardon, Robinson-Cimpian, and Weathers 2014), while disparities between children of high- versus low-income parents have substantially increased (Reardon 2011).

Divergent trends of test score disparities by race and parental income have become a central stylized fact in understanding contemporary educational inequality. In education policy, experimental research has found that voters are presently more concerned about and likely to hypothetically support policies that address income inequality in schooling rather than policies that address racial inequality (Valant and Newark 2016). A 2015 New York Times article on the diverging test score trends summarized the view in the popular media: “[R]acial disparities are still a stain on American society, but they are no longer the main divider. Today the biggest threat to the American dream is class” (Porter 2015).

To date, an important comparison has slipped through the cracks of the literatures on test score disparities by race and parental income and conceptions of educational inequality based on them: namely, disparities between black and white children whose parents have the same income. In this article, I track math test score disparities between black and white students whose parents have similarly low, middle, or high incomes across three nationally representative data sources for 9th or 10th graders: Project Talent (1960), High School and Beyond (1980; HS&B), and the High School Longitudinal Study (2009; HSLS). I also investigate the extent to which outcome disparities between same-income black and white students are accounted for by racial differences, net of parental income, in family and school characteristics, such as mother’s education and school racial composition, and changes in these factors’ explanatory power over time.

Throughout this article, I refer to differences in students’ test scores by race, parental income, and race within income as “test score disparities” as opposed to “achievement gaps.” As multiple scholars have argued, the terminology of achievement gaps can support deficit thinking and obscure the role, in producing unequal test scores, of historical and contemporary systemic inequalities in areas such as neighborhood and school quality, family resources, health, and political power (Chambers 2009; Flores 2007; Gutiérrez 2008; Ladson-Billings 2006, 2007).

Background

Theoretical Framework: An Intersectional Perspective on Race, Parental Income, and 50 Years of Test Score Disparities

Diverging trends of test score disparities by race and parental income offer an ideal case for the application of an intersectional perspective. On this question, an intersectional perspective rejects a race-versus-income dichotomy in favor of analyzing how the two are mutually constitutive, jointly forming social locations across which life chances are distributed (Collins 2000; Crenshaw 1989; Golash-Boza 2016; McCall 2005; for examples in the education literature, see Irizarry 2015a, 2015b; López et al. 2018; Quadlin and Conwell 2020). These intersections occur in a sociohistorically dynamic manner, such that patterns of inequality across social locations defined by race and income can shift over time (Massey and Brodmann 2014).

A related and growing body of literature examines how quantitative social science research methods can leverage theoretical insights from critical theories of race and racism (Stewart and Sewell 2011; Zuberi 2001; Zuberi and Bonilla-Silva 2008), including theories like intersectionality that concern the simultaneous interaction of multiple structural positions in inequality processes. Put in that literature’s terms, this study’s intersectional framework is longitudinal and resourced-focused (see Stewart and Sewell 2011). It is longitudinal in that I track outcome disparities across units of analysis formed by intersections of race and parental income over a 50-year time period.

My approach is resource focused in that, as potential explanations for these disparities, I track race–parental income differences in family and school characteristics that, as I will detail, have been of explanatory interest to the previously separate literatures on test score disparities by race and parental income that this study integrates. Black children often experience different family and school environments than do same-income white children due to systemic racial disparities that persist, net of income, in factors such as wealth (Conley 1999; Killewald and Bryan 2018; Oliver and Shapiro 2006), neighborhoods (Pattillo 2005; Reardon, Fox, and Townsend 2015), and family demographic composition (McLanahan and Percheski 2008). This insight is central to research on the black middle class (Feagin and Sikes 1994; Lacy 2007; Landry and Marsh 2011; Pattillo-McCoy 1999), but it applies, in varying magnitudes, from the lowest to highest rungs of the income distribution. I also estimate counterfactual outcome disparities under the assumption that there were not differences between black and white children with same-income parents in these family and school factors at each time point. This longitudinal and resource-focused intersectional approach allows for the possibility that the magnitude or mechanisms of test score disparities between same-income black and white children changed over this study’s 50-year observation period.

Families, Schools, and Test Score Disparities between Black and White Students

The black–white test score disparity remains statistically large and substantively consequential. According to data from the National Assessment of Education Progress-Long Term Trend Assessment (NAEP-LTT), the black–white test score disparity among 13-year-olds in 2012 was 0.80 standard deviations in math and 0.62 standard deviations in reading (Reardon et al. 2014). Many studies explain sizeable portions of the black–white test score disparity via inequalities between black and white children’s school and family characteristics, including parental socioeconomic status (SES) measures of education, occupation, and income (e.g., Condron 2009; Fryer and Levitt 2004, 2006; Hanushek and Rivkin 2009; Phillips, Brooks-Gunn, et al. 1998; Phillips, Crouse, and Ralph 1998; Quinn 2015; Roscigno 1998, 2000; Yeung and Pfeiffer 2009).

Today’s black–white test score disparity is a reminder of the persistence of racial inequality in children’s life chances, but this gap has decreased in recent decades. Black–white disparities in math and reading narrowed from the beginning of the 1970s through the end of the 1980s, widened during the 1990s, and have been narrowing since 1999, resulting in an overall decreasing trend (Magnuson and Waldfogel 2008; Reardon et al. 2014). The black–white math and reading disparities among 13-year-olds reported earlier represent a 43 percent decrease in the reading disparity since 1971 and a 26 decrease in math disparity since 1978 (see Reardon et al. 2014).

Many studies have brought together nationally representative data sets, spanning this time period, to assess the extent to which over-time decreases in the black–white test score disparity can be attributed to changes in black–white inequality in family and school characteristics (Berends, Lucas, and Peñaloza 2008; Berends and Peñaloza 2008; Grissmer, Flangan, and Williamson 1998; Hedges and Nowell 1998, 1999). For example, Berends and colleagues (2008) did so with four data sets covering high school seniors in 1972, 1982, 1992, and 2004. In 1972, black–white inequalities in family SES characteristics (mother’s and father’s education and occupational status) and school characteristics (proportion minority composition, mean socioeconomic composition, proportion in urban schools, proportion in private schools) both disadvantaged black students. Between 1972 and 2004, black–white family SES inequalities decreased, while black–white school inequalities increased. In other words, if black–white inequalities in school characteristics would have remained stable or decreased over this time period, the black–white test score disparity could have closed even more than was observed.

Families, Schools, and Test Score Disparities between Students with High- versus Low-Income Parents

Test score disparities between children of high- versus low-income parents markedly increased over the same period that the black–white test score disparity decreased. Drawing on 12 data sets, Reardon (2011) shows that, between cohorts of students born in 1940 and 2001, math and reading test score disparities between children whose parents were at the 90th versus the 10th percentile of the income distribution (i.e., the 90-10 income test score disparity) increased by 66 percent, from around 0.75 to 1.25 standard deviations. Income test score disparities have been driven by the rising correlation between family income and students’ achievement, especially in the top half of the income distribution, not by income inequality per se (Reardon 2011). Parental education remains a stronger predictor of students’ achievement than family income, but over time, income has gained in explanatory power relative to parental education (Reardon 2011).

Inequalities in family and school characteristics are integral to explaining income test score disparities, as is the case for black–white test score disparity. Inequalities in parental spending on children between high- versus low-income families have increased since the 1970s, and this spending has shifted toward the early childhood years, with high-income parents investing in preparation for K–12 schooling (Kornrich and Furstenberg 2013; Schneider, Hastings, and LaBriola 2018). Relatedly, income disparities in characteristics of children’s family demographic contexts, such as their chances of having married parents, as well as developmental resources, such as children’s books, remain large, although they have decreased slightly since 1998 (Bassok et al. 2016). During their K–12 years, high-income children are also more likely than their low-income peers to benefit from supplemental educational resources that parents provide, such as tutoring and test preparation (Buchmann, Condron, and Roscigno 2010).

High-income children have also experienced increased advantages in school context and composition relative to their lower-income peers. Income segregation between schools and districts increased between 1990 and 2010 (Owens, Reardon, and Jencks 2016). Income test score disparities are larger in metropolitan areas where between-district income segregation is higher because high-income students perform better in those districts, consistent with a school district’s income composition proxying for its level of financial and social resources (Owens 2018). Since 1968, high-income children have also had growing advantages in access to private schools and the advantageous school resources, culture, teachers, and peers that such schools provide (Figlio and Stone 2000; Murnane and Reardon 2018).

To date, racial inequality has played a limited and specific role in the literature on income test score disparities. To answer the question, “How large are these [income achievement] gaps?”Reardon (2011, Figures 5.3 and 5.4) compared over-time changes in the size of the income test score disparities in math and reading to the size of the black–white test score disparities in those subjects. For cohorts born in the 1940s to 1960s, black–white disparity was larger than the income disparity, but the opposite was the case for cohorts born since the 1970s. Among the cohort born in 2000 (i.e., today’s college-age youth), the 90-10 income test score disparity in math was more than twice the size of the black–white disparity in that subject.

Families, Schools, and Test Score Disparities between Black and White Children with Same-Income Parents

Cross-sectional findings of black–white test score disparities between students from comparable parental income backgrounds provide the best evidence on the disparities the present study investigates from a longitudinal perspective. The little available evidence shows the presence of such disparities and suggests they vary in magnitude across the income distribution. Using data on adolescents and young adults ages 12 to 24 from the Adolescent Health Survey, Massey and Brodmann (2014) found that the black–white disparity in the Peabody Picture Vocabulary Test, to black students’ disadvantage, ranged from approximately 14 points in the bottom parental-income quartile to 11 points in the top parental-income quartile.

Prior research also provides little systematic evidence of race–income inequalities in family and school characteristics and how they may have changed over time. Research on racial differences in family structure within education levels provides relevant, longitudinal background for family characteristics. Black mothers are less likely than same-education white mothers to be part of two-parent households (McLanahan and Percheski 2008). From 1960 to 2000, black–white differences in single motherhood increased within the education levels of less than high school, high school, and college, and the difference was largest among the least educated (McLanahan and Percheski 2008). Two-parent family structure is a facilitator of and proxy for numerous advantages for children (cf. McLanahan and Percheski 2008). If the differences observed within education levels hold, to some extent, within income levels, it would mean black children are less likely than same-income white children to reap these benefits, and these differences could be largest at lower income levels.

In the school domain, black families have less access to socioeconomically advantaged school districts than do same-income white families. In a recent cross-sectional study, Owens (2018) found that in the most economically segregated metropolitan areas, the median income of top-income-quintile white students’ school districts was over $60,000, compared with just over $40,000 for same-income black students’ districts. Therefore, compared with same-income white students, black students’ achievement will likely not benefit equally from school and school district income composition via the mechanisms of financial and social resources. Racial differences on this measure may be larger at higher parental income levels than at lower ones, because black–white differences in school district median income are often larger among high-income than low-income families (Owens 2018).

Data And Methods

Data

I observe student test score outcomes, family income, and family and school characteristics in students’ 9th- or 10th-grade year for respondents in three cohort-based longitudinal studies. Online Appendix A provides relevant information about question text, response categories, and coding for each variable I use. All three studies use a multistage probability sampling design to generate samples of students that are representative of those enrolled in targeted grades in U.S. schools at the time the survey went into the field. For each survey, the analytic sample is black and white students with nonmissing information on the test outcome. I use the appropriate weight and adjust standard errors for the complex sampling design of each survey. I also use an extensive battery of established methods to aid with the reliability and comparability of data sets, as I will detail.

Data for the first time period come from ninth graders from the base year of Project Talent (American Institutes for Research 2013). The study was developed by the American Institutes for Research and funded by the U.S. Office of Education. In 1960, the national probability sample of students in more than 1,000 junior and senior high schools included approximately 100,000 ninth graders. Students completed academic tests as well as questionnaires about themselves and their families. School administrators provided information about sampled schools. I use data on ninth graders so patterns of interest are not conflated with large black–white disparities in high school persistence and completion during this time period (U.S. Census Bureau 1999). For comparability, I use data on students of similar ages in the other two studies.

Data from the second time period come from 10th graders in the base year of HS&B (U.S. Department of Education 2001), sponsored by the National Center for Education Statistics (NCES). In 1980, the national probability sample of students in more than 1,000 high schools included approximately 25,000 10th graders. Students completed tests and provided information about themselves and their families. Parents, school administrators, and teachers also provided information.

Data from the third time period come from ninth graders in the HSLS (Ingels et al. 2011), also sponsored by NCES. HSLS’s base-year data collection took place during the fall of the 2009–2010 school year. The study includes data from more than 20,000 ninth graders in more than 900 schools that offered both 9th and 11th grades. Students completed tests and provided information about themselves and their families. Parents, school administrators, and teachers also provided information. Sample sizes for HSLS are rounded to the nearest 10, per NCES guidelines for restricted-use data.

Variables

Math test outcome

The outcome measure for this study is students’ math test score—the only subject tested in all three surveys. In Project Talent, I use students’ combined scores for the three parts of the math assessment: arithmetic reasoning, introductory mathematics (e.g., algebra), and advanced mathematics (e.g., geometry). In HS&B, I use students’ scores from part 1 of the math assessment.¹ The assessment tested computation, arithmetic reasoning, graph reading, elementary algebra, and geometry (Jones et al. 1986). In HSLS, I use students’ scores for the mathematics assessment in algebraic reasoning.

The three math assessments are theoretically comparable: All are tests of high school students’ mathematics skills, tapping some of the same skill domains, such as algebra. I make two additional adjustments to aid in the tests’ comparability. First, I standardize each math test outcome to have a mean of 0 and a standard deviation of 1 by subtracting the unweighted national mean score from each student’s score and dividing this result by the unweighted national standard deviation.² I report test score disparities in standard deviation units, tracking where students fall in the distribution of students who took the same test, instead of relying on the tests’ differing score metrics. Second, I adjust all math test results for measurement error in the three math test instruments.³

Parental income

The key explanatory variable for this study is parental income. In Project Talent, students reported their family income from 1959, covering parents and anyone else in the household who worked, in five categories. In HS&B, students reported their families’ income in seven categories. In HSLS, parents reported family income from 2008 in 13 categories. Online Appendix A provides the dollar values corresponding to the income categories in each data set. As detailed later, I adapt methods developed by Reardon (2011) to convert these categories to weighted income percentiles that are comparable across the data sets. Along with adjusting math test score disparities for measurement error in the math test instrument, I also adjust for measurement error in income reports, based on whether income was reported by parents or students and, if by students, differentially based on students’ age.⁴

Previous research shows black–white test score disparities conditional on current parental income may be upwardly biased, compared with estimates conditional on permanent parental income (Rothstein and Wozny 2013). Multiple features of this study’s analytic strategy are likely to substantially reduce this bias, although I cannot claim it is completely eliminated. Primarily, the high school students in my analytic sample are old enough that, on average, their parents are at an age where their current income is a reasonable proxy for their permanent income (early 30s to mid-40s; see Haider and Solon 2006; Rothstein and Wozny 2013, Figure A1).

Other explanatory variables: Race and family and school characteristics

In analyses of all three surveys, I also draw on variables for race and family and school characteristics. I code students as black or white, based on their response to the relevant question in each survey. For family characteristics, I include variables for mother’s education (in years), whether the student lives in a two-parent household, and family size. Students report these characteristics in Talent and HS&B, and parents report them in HSLS (see Online Appendix Tables A1, A2, and A3).⁵ For school characteristics, I include variables for the percentage of economically disadvantaged students in the school, the percentage of black students in the school, and the percentage of white students in the school. In all three surveys, school administrators reported this information (see Online Appendix Tables A1, A2, and A3). I also created a variable for the average math test score of sampled students in the school, to measure the school’s academic context consistently across the three surveys.

Multiple Imputation

Within each survey, some students with nonmissing information on the math test outcome were missing data on explanatory variables, including income (in Talent and HS&B). I imputed missing data with the ice commands in Stata 14.1, using multivariate imputation by chained equations with five iterations (Royston 2005). For each survey, the imputation model included students’ school identifier, their race and parental income percentile, and all other explanatory variables discussed earlier; each model was weighted by the appropriate sampling weight. The models also include the math test outcome variable to preserve its relationships with the explanatory variables; for each survey, results are based on the subset of students who had a nonmissing score for that outcome in the original data (von Hippel 2007). I also imputed race for some students in Project Talent during this procedure (for details, see Online Appendix B).

Analytic Strategy

Statistical Model

Previous studies on test score disparities and family and school resource inequalities between children of high- versus low-income parents (Bassok et al. 2016; Reardon and Portilla 2016) have used the cubic regression method originally developed by Reardon (2011). By regressing a variable for a test score outcome or a given family or school characteristic (e.g., mother’s education) on variables for income percentile, income percentile squared, and income percentile cubed, one can predict values of the variable at specified income percentiles as well as differences in values between income percentiles (e.g., 90th vs. 10th percentile inequality). Here, I adapt this method to assess black–white test score disparities and family and school resource inequalities between children whose parents are at the same income percentile. To do so, I interact an indicator variable for race (black = 1, white = 0) with the three income terms in the cubic regression specification. The main analytic model is shown in Equation 1:

\begin{matrix} {Outcome}_{it} & = β_{0 t} + β_{1 t} (Blac k_{it}) + β_{2 t} (IncPc t_{it}) \\ + β_{3 t} ({IncPct}_{it}^{2}) + β_{4 t} ({IncPct}_{it}^{3}) \\ + β_{5 t} (Blac k_{it} * IncPc t_{it}) \\ + β_{6 t} (Blac k_{it} * {IncPct}_{it}^{2}) \\ + β_{7 t} (Blac k_{it} * {IncPct}_{it}^{3}) + ε_{it}, \end{matrix},

(1)

where, for each time point t (1960, 1980, or 2009), Outcome_i is the standardized math score or a given family or school characteristic for student i; β₀ is an intercept term; β₁ is a main effect for race; β₂ through β₄ are main effects for income percentile, income percentile squared, and income percentile cubed, respectively; β₅ through β₇ are interactions of race with these income terms; and ε_i is an error term. I estimate all disparities net of students’ gender and age, both of which are also interacted with all three income terms. Results focus on the 10th, 50th, and 90th percentiles, following previous research on test score and resource disparities by parental income.

Online Appendix C shows the results of converting the three surveys’ categorical income variables to weighted income percentiles for use in the cubic regression procedure. At all three time points, black families are overrepresented in lower income percentiles and underrepresented at higher income percentiles. Comparisons at the 10th, 50th, and 90th income percentiles based on the pooled (white and black) distribution always correspond to higher percentiles in black families’ own-race income distribution. Often, the 10th percentile is near the median of black families’ distribution, the 50th percentile is well into the right tail, and the 90th percentile indexes a small number of economically elite black families. Readers should keep this in mind when interpreting the results, as all results are predictions based on percentiles of the pooled income distribution. Robust standard errors for these predictions have the desirable property of varying in magnitude to reflect uncertainty based on differential coverage at various points in the income distribution; for example, they are larger for predictions for higher-income black students, reflecting sparser coverage in the right tail of the income distribution.

Plan of Analyses

I first use the model given in Equation 1 to predict black–white disparities in math achievement and family and school characteristics at specified income percentiles. I then assess the extent to which the latter account for the former. I do this by reestimating students’ math scores, this time net of controls for (1) family factors, (2) school factors, and (3) both. I interact these variables with the three terms in the cubic income specification, allowing their effects to vary by income. I then re-predict black–white disparities at the focal income levels as if black students had the same means on family and school factors as same-income white students. The models implicitly assume that these factors’ effects on achievement are equal across races. These counterfactual analyses are descriptive and correlational and as such should not be given a causal interpretation.

Results

Black–White Math Test Score Disparities between Students with Same-Income Parents, 1960 to 2009

Table 1 presents estimates of black–white test score disparities between students with parents at the 10th, 50th, and 90th percentiles of the income distribution in 1960, 1980, and 2009. Figure 1 provides additional context for these estimates by presenting test score predictions for black and white students at each income decile at all three time points. Over this 50-year period, changes in within-race test score stratification by parental income have provided the backdrop for black–white test score disparities between students with same-income parents. From 1960 to 2009, this measure increased within both racial groups. During this time, black students’ average position in the national achievement distribution improved, consistent with the shrinking average black–white test score disparity. Among white students, children from high-income families more or less maintained their position at the top of the achievement distribution, whereas white children from lower-income families fell behind.

Table 1.

Black–White Math Test Score Disparities, by Year and Parental Income Percentile.

	1960		1980		2009		1960 to 2009
Parental income percentile	B	SE	B	SE	B	SE	B	SE
10th	−1.47	(.05)***	−.89	(.04)***	−.39	(.07)***	1.07	(.09)***
50th	−1.50	(.06)***	−1.16	(.05)***	−.49	(.08)***	1.01	(.10)***
90th	−1.64	(.16)***	−1.43	(.12)***	−.58	(.14)***	1.06	(.22)***
N	99,019		24,551		10,970		134,540

Note: Robust standard errors are in parentheses. Numbers of observations for 2009 (High School Longitudinal Study) rounded to nearest 10, per National Center for Education Statistics guidelines.

p < .05. **p < .01. ***p < .001.

Figure 1.

Math test score (standard deviations), by year, parental income percentile, and race.

1960

In 1960, the test-score disparity between black and white children with same-income parents was –1.47 standard deviations at the 10th parental income percentile, –1.50 standard deviations at the 50th income percentile, and –1.64 standard deviations at the 90th income percentile (p < .001 for all disparities at all percentiles). These three disparities are not significantly different from each other.

1980

These disparities all decreased between 1960 and 1980. Decreases were largest at the 10th income percentile, where the disparity fell to –0.89 standard deviations, and successively smaller at the 50th and 90th income percentiles, where remaining disparities were –1.16 standard deviations and –1.43 standard deviations, respectively. These patterns resulted in black–white math test score disparities at the 50th and 90th income percentiles being significantly larger than at the 10th percentile (p < .001 for both comparisons), which was not the case in 1960. The disparity at the 90th percentile was also significantly larger than at the 50th percentile (p < .05), which was also not the case in 1960. In 1980, black children whose parents had incomes at the national median, making them relatively well-off for their racial group, were farther behind same-income white children than were low-income black children relative to their same-income white peers. Predictions for the most economically elite black students are measured with less precision due to their small numbers, but they indicate that these children were even farther behind their same-income white peers.

2009

Disparities at all three focal income levels continued to decrease between 1980 and 2009. In contrast to the changes between 1960 and 1980, however, between 1980 and 2009, decreases in disparities were larger at higher income levels (0.50 standard deviations at the 10th percentile, 0.67 standard deviations at the 50th percentile, and 0.84 standard deviations at the 90th percentile). These patterns closed the significant differences between these disparities at the three percentiles observed in 1980, returning them to being statistically indistinguishable from each other, as observed in 1960. Table 1 shows that, between 1960 and 2009, math test score disparities between black and white children with same-income parents decreased by a comparable amount: between 1 and 1.10 of a standard deviation. Despite patterns of within-race test score differentiation by parental income that have come to look more like those among white students over the 50-year period, in 2009, at any given income level, black students still faced a consistent math test score disparity relative to their same-income white counterparts, ranging from –0.39 standard deviations at the 10th income percentile to –0.58 standard deviations at the 90th income percentile.

Black–White Differences in Family and School Characteristics between Students with Same-Income Parents, 1960 to 2009

Table 2 shows black and white students’ means on family and school characteristics at the 10th, 50th, and 90th parental income percentiles in 1960, 1980, and 2009. Taken together, these descriptive results indicate that at a given income level, black children have often not had the same access as white children to the family and school factors that previous research shows are partially responsible for decreasing black–white test score disparities and increasing income test score disparities.

Table 2.

Means of Family and School Characteristics, by Year and Parental Income Percentile.

	1960		1980		2009
Parental income percentile and variable	White	Black	White	Black	White	Black
10th income percentile
Mother’s education (years)	11.27	10.76***	11.70	11.56	12.42	12.56
Two-parent household	.84	.60***	.77	.55***	.56	.38***
Family size	4.03	5.40***	3.04	4.25***	2.17	2.32
Percentage of economically disadvantaged students in school (original metric)^a	11.20	27.19***	14.06	36.26***	40.74	58.76***
Black–white ratio of economically disadvantaged students in school		2.43		2.58		1.44
Percentage of black students in school	3.57	86.31***	7.71	53.65***	10.73	45.56***
Percentage of white students in school	88.64	9.72***	85.80	39.95***	76.68	34.59***
Average math achievement score of sampled students in school (standard deviations)	.03	−.89***	−.01	−.50***	−.15	−.34***
50th income percentile
Mother’s education (years)	11.74	11.39**	12.35	12.12	13.81	14.08
Two-parent household	.85	.61***	.88	.62***	.89	.73***
Family size	3.92	5.31***	2.77	3.95***	2.17	2.30
Percentage of economically disadvantaged students in school (original metric)^a	10.41	25.65***	11.70	30.31***	30.78	46.28*
Black–white ratio of economically disadvantaged students in school		2.46		2.59		1.50
Percentage of black students in school	3.70	86.83***	7.26	50.07***	10.23	34.61***
Percentage of white students in school	88.63	9.41***	87.23	43.54***	76.00	41.16***
Average math achievement score of sampled students in school (standard deviations)	.06	−.86***	.07	−.44***	.00	−.18**
90th income percentile
Mother’s education (years)	13.00	12.71	13.81	13.78	15.63	16.21
Two-parent household	.93	.66***	.96	.81**	.96	.99
Family size	3.65	5.14***	2.62	4.29**	2.16	2.21
Percentage of economically disadvantaged students in school (original metric)^a	6.18	21.42***	7.83	27.65***	19.20	32.81
Black–white ratio of economically disadvantaged students in school		3.47		3.53		1.71
Percentage of black students in school	3.04	87.30***	6.30	47.93***	8.89	30.36*
Percentage of white students in school	89.33	8.68***	88.46	44.48***	72.68	48.46***
Average math achievement score of sampled students in school (standard deviations)	.20	−.77***	.26	−.28***	.28	.10*
N	91,579	7,440	20,876	3,675	9,390	1,580

Note: Numbers of observations for 2009 (High School Longitudinal Study) rounded to nearest 10, per National Center for Education Statistics guidelines.

Metric for percentage of disadvantaged students in school varies across surveys: percentage of students in school with household incomes less than $3,000 (1960); students classified as disadvantaged based on state, federal, or other guidelines (1980); students who receive free or reduced-price lunch (2009). These figures should be compared within, but not across, time periods. Ratios are provided to facilitate comparisons across time periods.

p < .05. **p < .01. ***p < .001.

Family characteristics

I use three variables to measure black–white differences in family characteristics between same-income students: maternal education, two-parent family structure, and family size. In 1960, at all income levels, black students’ mothers had completed less schooling than white students’ mothers (significantly so at the 10th and 50th income percentiles). By 1980, black–white differences at the 10th and 50th percentiles were no longer significant, and by 2009, black students’ point estimates were higher than white students’ at each income level.

In 1960, black children at all income levels were significantly less likely to grow up in two-parent households than were same-income white children, with differences ranging from 24 percentage points at the 10th income percentile to 27 percentage points at the 90th percentile. Between 1960 and 2009, 10th-income-percentile households of both races experienced decreases on this measure, 50th and 90th percentile white families’ rates stayed relatively flat, and 50th and 90th percentile black families’ rates increased. As a result, by 2009, black–white differences in the likelihood of living in a two-parent household was much larger at the 10th income percentile (0.56 for white children vs. 0.38 for black children, p < .001) than at the 50th (0.89 for white children vs. 0.73 for black children, p < .001) and 90th (0.96 for white children vs. 0.99 for black children, ns) percentiles.

Over this period, black and white families of all income levels experienced large decreases in average family size. These decreases were larger for black families, resulting in relative parity of family size by 2009, at an average of slightly more than two children for all race–income groups. Trends on this measure signal decreasing racial disparities over time in exposure to the possibility that family resources will be spread across larger numbers of children.

School characteristics

I measure school context and composition with variables for school economic and racial composition as well as a variable for the average math achievement score of sampled students in the school. Predictably, at all three time points, black students attended schools with significantly higher percentages of black students than did same-income white students. These differences decreased over time, as white students’ schools enrolled slightly larger shares of black students, and black students’ schools enrolled much smaller shares. For example, among children of median-income parents, in 1960, black students attended schools where, on average, 86.83 percent of their classmates were black, compared with approximately 3.70 percent for white students (p < .001 for difference). By 2009, the same figures were 34.61 and 10.23 percent, respectively (p < .001 for difference).

Table 2 also shows the percentage of white classmates in students’ schools. The percentage of white classmates in white children’s schools decreased slightly over time (between 12 and 15 percentage points, depending on income level), whereas the percentage of white classmates for black children increased, particularly from 1960 to 1980 (by over 30 percentage points at each income level). Between 1980 and 2009, 10th- and 50th-income-percentile black children’s shares of black and white classmates decreased, signaling increased shares of Latinx and other nonwhite students. At the 90th income percentile, black children’s share of black classmates also fell (from 47.93 percent in 1980 to 30.36 percent in 2009), but their share of white classmates continued to increase (44.48 percent in 1980 to 48.46 in 2009).

The metric for percentage of economically disadvantaged students in schools varied across the surveys (see Online Appendix Tables A1, A2, and A3). Table 2 presents this characteristic in the original metric as well as in ratio terms, to facilitate comparisons over time. At each income level and time point, black students were predicted to attend schools with significantly higher percentages of economically disadvantaged students than were same-income white students. Between 1960 and 2009, these differences became smaller at all income levels. In 1960, 10th-income-percentile black students’ schools enrolled 2.43 times the percentage of economically disadvantaged students as same-income white students’ schools, and this inequality decreased to 1.44 times by 2009. Trends were similar at the 50th income percentile. At the 90th income percentile, economically elite black students’ schools enrolled 3.47 times the percentage of economically disadvantaged students as same-income white students’ schools, and this inequality decreased to only 1.71 times by 2009.

The variable for average math test score of sampled students in a school reveals that, at each income level and time point, black students attend schools that fare significantly worse on this measure than do same-income white students. In 1960, the average math test score in black students’ schools was approximately one standard deviation below that of same-income white students’ schools. At this time, the average math test score in the most economically elite black students’ schools (–0.77 standard deviations for black students at the 90th income percentile) was approximately three-quarters of a standard deviation below that of the least economically advantaged white students’ schools (0.03 standard deviations at the 10th income percentile). This school-level disparity decreased over time, but it remains significant at each income level.

Accounting for Black–White Math Test Score Disparities between Students with Same-Income Parents, 1960 to 2009

Figure 2 shows results of a counterfactual exercise that re-predicts black–white test score disparities between children with same-income parents if black children had the same (1) family, (2) school, and (3) family and school characteristics as same-income white children, and these factors’ effects on math test scores were equal across races. Online Appendix D shows the linear regression coefficients used for the calculations. To reiterate, these counterfactuals are descriptive and correlational and, as such, should not be given a causal interpretation. Also, recall from Figure 1 that math test score disparities between black and white students with same-income parents are appreciably smaller in 2009 than in earlier years. This fact may be substantively important, a point to which I will return.

Figure 2.

Percentage of black–white math test score disparities between same-income students explained by regression adjustment procedure, by year and parental income percentile.

Over time, these family and school factors account for markedly declining shares of black–white test score disparities between students with same-income parents. In 1960, the counterfactual exercise accounts for at least 80 percent of the disparities across income percentiles—driven by school factors’ explanatory power—with the largest percentage explained (95 percent) at the 90th income percentile. By 1980, these factors account for 44 percent of the disparity at the 10th income percentile, 42 percent at the 50th percentile, and 35 percent at the 90th percentile, showing declines in explanatory power and a reversal of the pattern observed in 1960, when the factors accounted for a larger percentage of the disparity at the highest income level. This trend continues from 1980 to 2009, when these family and school characteristics account for less than 18 percent of the math test score disparity between same-income black and white children at the 10th income percentile, 14 percent at the 50th percentile, and 11 percent at the 90th percentile.

The year 2009 is also the first time when adjusting for family characteristics in addition to school characteristics results in larger disadvantages for black students (i.e., the percentage of disparity explained decreases from the family to the family-plus-school models in Figure 2). By this time period, adjusting for family characteristics controls away black students’ advantages relative to same-income white students on factors that are positively correlated with achievement, such as maternal education (see Table 2 and Online Appendix D). In summary, although black–white math test score disparities between high schoolers with same-income parents decreased substantially since 1960, differences between these students in family and school characteristics known to facilitate achievement also decreased. These factors’ ability to account for the disparities also decreased, leaving large percentages to be explained in 2009.

What are we to make of the simultaneous decline in both within-income math test score disparities and the potential contribution of family and school factors to those disparities? At least two interpretations are worth noting. On one hand, at least within income levels, black and white students’ family and school environments, as measured by these variables, may now provide more equitable opportunities for academic success than they have in the past. This makes these factors less likely to contribute to continued reductions in outcome disparities, even if outcome disparities continue to decrease over time. On the other hand, these outcome disparities may be difficult to change, as the legacy of discrimination and structural racism, present at all periods, may mean further reductions in these disparities will only come about when racial inequality is reduced in factors spanning well beyond a single generation of students’ family and school environments.

Discussion and Conclusion

In this study, I documented black–white math test score disparities between 9th and 10th graders whose parents have the same incomes, across three nationally representative data sources spanning 1960 to 2009. Doing so integrates the literatures on diverging trends of test score disparities, since the mid-twentieth century, by race (which have been decreasing) and by income (which have been increasing). These diverging trends present an ideal case for application of an intersectional theoretical framework. The study joins recent work in the education literature that applies an intersectional viewpoint (Irizarry 2015a, 2015b; López et al. 2018; Quadlin and Conwell 2020), and it contributes to this growing research stream by analyzing intersectional—in this case, Race × Income—educational inequalities in historical perspective.

This study has three main findings. First, black–white test score disparities between children with same-income parents are to black children’s disadvantage and decreased over this period, by about one standard deviation at each of the three focal income levels. Despite this closure, in 2009, remaining disparities were substantively large, statistically significant, and largest at higher income levels. Second, black–white differences, net of income, in family and school factors that scholars commonly use to explain test score disparities generally decreased over time, but some remain large and significant, such as differences in measures of school racial and socioeconomic composition. Third, due in part to these decreases, family and school factors account for markedly decreasing shares of shrinking test score disparities between same-income students over time.

Future research should investigate what other mechanisms are responsible for test score disparities and resource differences between same-income black and white students. Data on wealth were not available in the data sets I used here, but black–white differences in wealth, net of income (Darity et al. 2018), are one possible explanation. Wealth has direct effects on children’s educational outcomes, net of income (Orr 2003; Pfeffer 2018). Parents can also leverage wealth to facilitate developmentally advantageous environments for their children, potentially leading to indirect effects of wealth on children’s school experiences and outcomes. For example, families may utilize a wealth transfer to garner access to homes in neighborhoods with more economically advantaged school districts that are better able to boost children’s intellectual growth. This proposed mechanism is consistent with observed black–white differences between same-income families in neighborhood (Sharkey 2014) and school district (Owens 2018) economic composition. Along with being conduits of wealth effects (see Pfeffer 2018), neighborhoods themselves may help produce black–white differences between same-income students and families, because neighborhood disadvantage influences children’s cognitive development (Sharkey and Elwert 2011).

Sociologists have shown how race is embedded in the functioning of organizations, including schools (Diamond 2018; Ray 2019). Consistent with this, future research should consider the role of within-school inequalities in producing black–white test score disparities between same-income students. In racially integrated schools, black students may be exposed to, and white students may benefit from, multiple forms of discriminatory treatment and opportunity hoarding, including racialized tracking and negative teacher and school administrator reactions to black parents’ attempts to become involved in their children’s schooling (Ispa-Landa and Conwell 2015; Lareau and Horvat 1999; Lewis-McCoy 2014; Lewis and Diamond 2015; Tyson 2011). These factors may play a particularly substantial role in black–white test score disparities among higher-income students, which, as demonstrated earlier, are larger than those among lower-income students. This is because higher-income black students are more likely than their low- and middle-income counterparts to attend schools that are racially integrated, an arrangement that can motivate white families to use racialized school organizational systems to maintain advantages (Lewis and Diamond 2015; Tyson 2011).

Previous research indicates that opportunities to learn, such as course taking, are particularly important to the hierarchical curricular structure of math learning (e.g., Kelly 2009), meaning these patterns may be particularly relevant to test score disparities on the outcome considered here. Data limitations—primarily the fact that the surveys did not measure students’ math course taking in a consistent fashion over time—prevented a systematic analysis of this possibility across the three data sets. However, supplemental analyses for the most recent data set, the HSLS, using a retrospective survey question on ninth graders’ eighth-grade math course taking (see Online Appendix E), show race–income differences in this type of opportunity to learn (e.g., exposure to Algebra I prior to high school entry), to black students’ disadvantage and white students’ advantage. Future research should seek to link racially unequal course-taking patterns and other forms of opportunity hoarding to outcome disparities at the intersection of race and parental income.

This study’s findings and their implications should be considered in light of at least two limitations. First, results are confined to math achievement, the only subject tested in all three data sets used here. Math achievement has implications for students’ success in science, technology, engineering, and mathematics education and related domains (Riegle-Crumb and King 2010), but patterns of race–income inequality in children’s test score outcomes may differ in reading, where average black–white test score disparities are smaller. Second, this study used data only on 9th and 10th graders. Both black–white and income test score disparities are large by the time children begin kindergarten, and as children age, the black–white disparity continues to grow, while the income test score disparity remains stable (Reardon 2011; Reardon et al. 2014). Therefore, the repeated historical cross-sections presented here may miss noteworthy changes in black–white disparities between same-income students as they age.

Recent discussions of test score disparities focus on children of high- versus low-income parents, due to their increasing trend. This increase has occurred while income returns to educational attainment and cognitive skills have also increased (Lemieux 2006). Currently, “the children of the rich do better in school, and those who do better in school are more likely to become rich” (Reardon 2011:111). Findings presented here demonstrate that over this same time period, the influence of race on children’s math test scores was structural in nature, that is, over and above key factors—in this case, parental income—believed to govern the distribution of the outcome (for a classical discussion, see Duncan 1967). These patterns should be borne in mind when crafting future theory, research, and policy concerning disparities in children’s test score outcomes and schooling’s role in the intergenerational transmission of economic (dis)advantage.

Supplemental Material

ONLINE_APPENDICES_FINAL – Supplemental material for Diverging Disparities: Race, Parental Income, and Children’s Math Scores, 1960 to 2009

Supplemental material, ONLINE_APPENDICES_FINAL for Diverging Disparities: Race, Parental Income, and Children’s Math Scores, 1960 to 2009 by Jordan A. Conwell in Sociology of Education

Footnotes

Acknowledgements

For constructive feedback throughout the course of this project, I thank Eric Grodsky, Simone Ispa-Landa, Rourke O’Brien, Jayanti Owens, Brian Powell, Natasha Quadlin, Jim Rosenbaum, Quincy Stewart, and audiences at the 2017 Midwest Sociology of Education Conference, the 2018 American Sociological Association Annual Meeting, and the University of California–Davis Center for Research on Poverty. In the 2016–2017 academic year, work on this project was supported by a National Academy of Education/Spencer Dissertation Fellowship.

Research Ethics

The research reported in this manuscript is based on a combination of publicly available, deidentified secondary data sources (Project Talent, High School and Beyond) and a data source made available via a restricted-use agreement with the National Center for Education Statistics (NCES). The institutional review board at the author’s institution approved the study. Parts of the manuscript reporting on the restricted-use data have been reported in accordance with NCES guidelines.

ORCID iD

Jordan A. Conwell

Supplemental Material

Supplemental material is available in the online version of the journal.

Notes

Author Biography

Jordan A. Conwell is an assistant professor in the Departments of Sociology and Educational Policy Studies at the University of Wisconsin-Madison. His research focuses on trends and consequences of racial, social class, and gender inequality in education, with a particular interest in the multigenerational roles of families and finances in these educational processes, as inputs for children and as outputs for adults.

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