School diversity and standardized test performances of
black and low-income students in Delaware public schools
John Mackenzie
Associate Professor, Dept. of Food & Resource Economics
215 Townsend Hall
University of Delaware
Newark, DE 19717
Member, Christina School District Board of Education
Charles R. Drew Educational Support Center
600 North Lombard Street
Wilmington, DE 19801
(January 2006)
Abstract
This paper addresses a simple
question: do black and low-income students perform better in racially and
socio-economically diverse public schools than in high-minority and
high-poverty schools? It examines the statistical significance and magnitude
of the effects of racial and socioeconomic diversities in Delaware public
schools on the average scores of 3rd, 5th, 8th
and 10th grade black and low-income public school students on the
2005 Delaware Student Testing Program (DSTP) reading, math and writing tests. Black
and low-income children are shown to perform significantly better in more
diverse schools than in high-minority or high-poverty schools, but these
differences in performance are small relative to the overall performance gaps
of black students vis-à-vis white students and low-income students vis-à-vis
non-low-income students. All the data used in this study are publicly
available from the Delaware Department of Education’s DSTP website (http://www.doe.k12.de.us/aab/).
Historical background
Delaware had a long history of “separate but equal” public school systems for white and black children: whites’ property taxes paid for white schools; blacks’ property taxes paid for black schools. In the Delaware Chancery Court decisions Bulah v. Gebhart and Belton v. Gebhart (1952), Collins Seitz found that Delaware’s white and black schools were not equal, and ordered public schools to admit black children. The state’s appeal was one of five school desegregation cases consolidated into the Brown v. Board of Education case, and denied in the US Supreme Court’s 1954 decision overturning the “separate but equal” doctrine of Plessy v. Ferguson.
Delaware was slow to actually implement desegregation. The US Third Circuit court imposed a desegregation plan on New Castle County in 1978, under which schools in Wilmington would teach grades 4, 5 and 6 for all children in the northern half of the county, while suburban schools would teach grades 1-3 and 7-12. Two years later the Delaware Legislature split northern New Castle County into four districts (Brandywine, Christina, Colonial and Red Clay Consolidated), each serving a portion of Wilmington.
Since that time there has been significant racial diversification of the suburbs, so that the large majority of African-American and low-income children in Wilmington-area public schools now live outside the city limits of Wilmington. The federal court lifted the desegregation order in 1995, declaring that the county had achieved “unitary status.” Of the four public school districts serving Wilmington children, the Christina School District has lagged Brandywine, Colonial and Red Clay in dismantling its desegregation-era feeder patterns to comply with Delaware’s Neighborhood Schools law (2000).
Until the introduction of the DSTP in 1998, and the reauthorization of the federal Elementary and Secondary Education Act (aka No Child Left Behind) in 2000, Delaware education policy was not well focused on the persistent performance gaps of black and low-income children. It was sufficient that black and low-income students attended the same schools as white and non-low-income students, and (presumably) got the same education opportunities. Prior to 2000, there was no formal mandate to eliminate these achievement gaps.
Achievement gaps of black and low-income students
Table 1 (see appendix) summarizes current (2005) statewide DSTP achievement gaps for African-American, American Indian, Asian and Hispanic public school students versus white students, by grade, on the most recent 3rd, 5th, 8th and 10th grade reading, math and writing DSTP tests. Schools’ average reading and math test scores generally range between 400 and 550 on a theoretical scale of 150 to 800; schools’ average writing test scores generally range between 5.5 and 9.0 on a theoretical scale of 1 to 15. Higher grades earn higher average scores on all three tests. The 2005 performance gaps for black vs. white children extracted from this table are:
|
Grade |
Avg. Black/White DSTP Reading Gap |
Avg. Black/White DSTP Math Gap |
Avg. Black/White DSTP Writing Gap |
|
3 |
24.97 |
32.21 |
0.79 |
|
5 |
22.50 |
27.69 |
0.64 |
|
8 |
22.46 |
33.25 |
0.58 |
|
10 |
26.48 |
30.15 |
0.96 |
Table 2 (see appendix) summarizes current (2005) statewide achievement gaps for low-income public school students (eligible for free or reduced-price lunches) versus non-low-income students (not eligible for FRPL), by grade, on the most recent reading, math and writing DSTP tests. The 2005 performance gaps for low-income vs. non-low-income children extracted from this table are:
|
Grade |
Avg. Low-Income DSTP Reading Gap |
Avg. Low-Income DSTP Math Gap |
Avg. Low-Income DSTP Writing Gap |
|
3 |
21.55 |
26.71 |
0.36 |
|
5 |
20.99 |
23.99 |
0.83 |
|
8 |
21.85 |
29.68 |
0.68 |
|
10 |
24.40 |
26.50 |
1.08 |
There is a strong correlation between black and low-income performance gaps that reflects the strong statistical overlap between children of color and children of poverty.
Over time, average DSTP scores have tended to rise for all categories of student, but these achievement gaps have persisted across the seven years that Delaware has administered the DSTP. Because DSTP results are not directly comparable to national norms, e.g., the National Assessment of Education Progress (NAEP), increases in average raw scores over time do not necessarily reflect actual gains in student achievement.
Do black and low-income students perform better in more diverse schools?
The 24 scatter-plots in the appendix show the relationships between the racial and socioeconomic diversities of school and the average scores of black and low-income children, by grade level (3rd, 5th, 8th and 10th) and test (reading, math and writing) on the 2005 DSTP. Each data point represents the reported average test score of a Delaware public school. All Delaware public schools with reported DSTP averages for both black and white children, or for both low-income (LI) and non-low-income (not-LI) children, are included in the dataset. (Average test scores are publicly reported for 15 or more students in a category). The horizontal axes represents schools’ percent black or low-income enrollments; the vertical axes represents schools’ average black or low-income DSTP scores on a particular DSTP test.
Most of these scatter-plots show discernible downward trends, indicating that average DSTP scores tend to be somewhat lower for black students in high-minority schools than for black students in low-minority schools, and average DSTP scores tend to be somewhat lower for low-income students in high-poverty schools than for low-income students in low-poverty schools. This is direct empirical evidence that school diversity is positively correlated with black and low-income student achievement.
To actually quantify the effects of school diversity on black and low-income student achievement, I pooled the school-level data across grades (N >= 200 schools) and calculated the linear regression equations that best fit the average reading, math and writing DSTP scores of the schools to grade level (GRADE) and the percent black (PCT_BLACK) or percent low-income (PCT_LI) enrollments of the schools. The empirical regression equations are:
To illustrate the first of these regression models in words, the likely average reading score of 10th grade black students at a school with 50% black enrollment can be estimated as 410.47 (the constant) plus 11.58 times 10 (the grade level), minus 12.36 times 0.50 (the percent black enrollment), or 410.47 + 115.80 - 6.18 = 520.09.
The PCT_BLACK coefficient estimate in the READ_BLACK equation (-12.36) is statistically significant (i.e., greater than zero) with >95% probability; the estimated PCT_LI coefficient in the READ_LI equation (-10.06) is statistically significant with >85% probability; all other coefficient estimates are statistically significant with >>99% probability. The R-Square measures indicate that the grade-level and percent minority or low-income enrollment variables combined account for over 75% of the total variation in average reading and math scores, and about 35% of the total variation in average writing scores.
These regression models indicate that the effects of school diversity on average black and low-income DSTP scores are statistically significant, but when they are compared to current black/white and LI/not-LI performance gaps, the diversity effects turn out to be relatively small. The coefficients on PCT_BLACK and PCT_LI indicate the magnitude of these diversity effects. Interpreted literally, for example, the PCT_BLACK coefficient in the READ_BLACK equation (-12.36) indicates that the average DSTP reading score of black children in a school with 100% black enrollment (PCT_BLACK=1.0) would be estimated to be 12.36 points lower than the average score of black children in a school with near-zero black enrollment (PCT_BLACK=0.0).
More realistically, we can compare a zero-diversity scenario (100% black or low-income enrollment) against a maximum diversity scenario where each school’s racial and socioeconomic profile matches the aggregate state profile. The percentages of 2005 DSTP test-takers statewide that are black or low-income, by grade, are:
|
Grade |
percent of students taking DSTP who are black |
percent of students taking DSTP who are low-income |
|
3 |
33.1% |
41.7% |
|
5 |
33.9% |
40.7% |
|
8 |
35.1% |
36.8% |
|
10 |
29.3% |
26.5% |
(The declines in percentages of black and low-income students between 8th and 10th grades taking the DSTP mostly reflects the disproportionately large high-school dropout rates for black and low-income students by the spring of the 10th grade year.) So statewide, the maximum possible diversity scenario for all Delaware public schools would be about 35% black enrollment and 42% low-income enrollment.
The first regression model above indicates that black children in a school with 35% black enrollment would be predicted to average (1.00 – 0.35) × 12.36 = 8.03 points higher on the reading DSTP than black children in a school with 100% black enrollment. Comparing 100% vs. 35% black enrollment scenarios, we can estimate the maximum DSTP score gains for black children that might be achieved under an ideal diversity scenario:
|
Grade |
Average black/white DSTP reading gaps |
Average black/white DSTP math gaps |
Average black/white DSTP writing gaps |
|
3 |
24.97 |
32.21 |
0.79 |
|
5 |
22.50 |
27.69 |
0.64 |
|
8 |
22.46 |
33.25 |
0.58 |
|
10 |
26.48 |
30.15 |
0.96 |
|
maximum possible test score gain from ideal diversity |
8.03 |
12.21 |
0.61 |
|
maximum gain as % of current gap |
33%
|
40% |
82% |
Similarly, comparing 100% vs. 42% high-poverty enrollment scenarios, we can estimate maximum DSTP score gains for low-income children that might be achieved under an ideal diversity scenario:
|
Grade |
Average LI/notLI DSTP reading gaps |
Average LI/notLI DSTP math gaps |
Average LI/notLI DSTP writing gaps |
|
3 |
21.55 |
26.71 |
0.36 |
|
5 |
20.99 |
23.99 |
0.83 |
|
8 |
21.85 |
29.68 |
0.68 |
|
10 |
24.40 |
26.50 |
1.08 |
|
maximum possible test score gain from ideal diversity |
5.83 |
16.14 |
0.60 |
|
maximum gain as % of current gap |
26%
|
60% |
82% |
Even the ideal diversity scenarios fail to close the achievement gaps between black and white students, or between low-income and not-LI students.
Summary and policy implications
The two principal conclusions from this analysis are:
1. School diversity has a statistically significant (i.e., non-zero) beneficial effect on the average DSTP scores of black and low-income students.
2. The diversity effects are small relative to persistent black and low-income performance gaps.
The direct implication of these findings is that racial and socioeconomic diversification of schools is not a sufficient strategy for eliminating these performance gaps.
The legacy of the 1978 desegregation order is mixed. Wilmington children endured a disproportionate share of the busing, and Wilmington parents had difficulty staying engaged in their children’s suburban schools. The dismantling of Wilmington’s middle schools and high schools effectively disempowered the communities they had served. For over 25 years Delaware has largely relied on school integration (diversity) per se to assure educational equity for minority schoolchildren. An entire generation of children has already passed through desegregated schools in northern Delaware, but the large achievement gaps between black and white students, and between low-income and non-LI students, remain.
More recently, Delaware’s Charter School Law (14 Delaware Code ch. 5) and Neighborhood Schools Law (14 Delaware Code ch. 2[II]) have both led to the re-creation of high-minority, high-poverty schools in Wilmington. Wilmington is politically divided over the relative merits of diverse but distant suburban schools versus high-minority, high-poverty neighborhood schools in the city. But Wilmington now has four charter schools with 100% black enrollment that meet the demands of many city parents for neighborhood schools.
This is not to dismiss the value of diversity, but Delaware’s black and low-income schoolchildren need more than that. The overall dispersions of schools’ average DSTP performances by black and low-income students easily outweigh the diversity effects. Every scatter-plot shows some high-minority schools that are outperforming schools with very low black enrollments, or some high-poverty schools that are outperforming schools with very few poor children. The principal implication of this study is that achieving true equity for all children in public schools will require analyzing the cultures and practices of these high-performing schools and replicating them effectively in all schools. That is an important topic for further research.
Appendix: Tables and Charts
|
Table 1: Delaware 2005 DSTP (Reading, Math & Writing) -- Statewide Race/Ethnicity Gaps vs. White |
||||||||||
|
Grade |
Race |
Read_N |
Read_AVG |
Read_GAP |
Math_N |
Math_AVG |
Math_GAP |
Writ_N |
Writ_AVG |
Writ_GAP |
|
3 |
_All |
7654 |
445.71 |
9.4 |
8534 |
441.22 |
12.06 |
8473 |
6.92 |
0.28 |
|
3 |
Am Indian |
39 |
442.18 |
12.93 |
40 |
447 |
6.28 |
40 |
6.98 |
0.22 |
|
3 |
Black |
2470 |
430.14 |
24.97 |
2812 |
421.07 |
32.21 |
2808 |
6.41 |
0.79 |
|
3 |
Asian Am |
227 |
466.71 |
-11.6 |
233 |
475.68 |
-22.4 |
231 |
7.97 |
-0.77 |
|
3 |
Hispanic |
627 |
435.3 |
19.81 |
745 |
430.09 |
23.19 |
696 |
6.74 |
0.46 |
|
3 |
White |
4291 |
455.11 |
0 |
4704 |
453.28 |
0 |
4698 |
7.2 |
0 |
|
5 |
_All |
8017 |
485.33 |
8.46 |
8910 |
476.14 |
10.19 |
8920 |
7.26 |
0.24 |
|
5 |
Am Indian |
19 |
495.05 |
-1.26 |
23 |
486.39 |
-0.06 |
23 |
7.87 |
-0.37 |
|
5 |
Black |
2627 |
471.29 |
22.5 |
3031 |
458.64 |
27.69 |
3028 |
6.86 |
0.64 |
|
5 |
Asian Am |
240 |
504 |
-10.21 |
246 |
507.62 |
-21.29 |
246 |
8.21 |
-0.71 |
|
5 |
Hispanic |
586 |
474.68 |
19.11 |
675 |
468.44 |
17.89 |
679 |
6.97 |
0.53 |
|
5 |
White |
4545 |
493.79 |
0 |
4935 |
486.33 |
0 |
4944 |
7.5 |
0 |
|
8 |
_All |
9466 |
524.79 |
9.08 |
10029 |
498.58 |
12.79 |
10059 |
7.84 |
0.23 |
|
8 |
Am Indian |
29 |
528.03 |
5.84 |
32 |
487.91 |
23.46 |
32 |
7.47 |
0.6 |
|
8 |
Black |
3280 |
511.41 |
22.46 |
3528 |
478.12 |
33.25 |
3526 |
7.49 |
0.58 |
|
8 |
Asian Am |
234 |
542.48 |
-8.61 |
240 |
541.94 |
-30.57 |
235 |
8.6 |
-0.53 |
|
8 |
Hispanic |
656 |
512.29 |
21.58 |
690 |
485.89 |
25.48 |
710 |
7.48 |
0.59 |
|
8 |
White |
5267 |
533.87 |
0 |
5539 |
511.37 |
0 |
5556 |
8.07 |
0 |
|
10 |
_All |
7560 |
518.83 |
8.45 |
7768 |
530.65 |
9.03 |
7806 |
8.3 |
0.3 |
|
10 |
Am Indian |
35 |
516 |
11.28 |
35 |
528.77 |
10.91 |
35 |
8.46 |
0.14 |
|
10 |
Black |
2188 |
500.8 |
26.48 |
2265 |
509.53 |
30.15 |
2284 |
7.64 |
0.96 |
|
10 |
Asian Am |
217 |
541.57 |
-14.29 |
220 |
575.19 |
-35.51 |
216 |
9.55 |
-0.95 |
|
10 |
Hispanic |
378 |
504.4 |
22.88 |
391 |
516.08 |
23.6 |
393 |
7.68 |
0.92 |
|
10 |
White |
4742 |
527.28 |
0 |
4857 |
539.68 |
0 |
4878 |
8.6 |
0 |
|
Table 2: Delaware 2005 DSTP (Reading, Math & Writing) -- Statewide Low-Income Gaps vs. Not Low-Income |
||||||||||
|
Grade |
SES |
Read_N |
Read_AVG |
Read_GAP |
Math_N |
Math_AVG |
Math_GAP |
Writ_N |
Writ_AVG |
Writ_GAP |
|
3 |
_All |
7654 |
445.71 |
8.5 |
8534 |
441.22 |
11.19 |
8473 |
6.92 |
0.36 |
|
3 |
LI |
3020 |
432.66 |
21.55 |
3574 |
425.7 |
26.71 |
3531 |
6.42 |
0.86 |
|
3 |
||||||||||