4b
MATHEMATICS CONT’D
Pieces of the Puzzle
In grade eight math, three of the four jurisdictions made statistically significant gains on the composite measure. Boston improved on the composite measure and in all content areas, and Atlanta improved on the composite measure and in four of five areas (all except geometry). Cleveland showed a significant gain only in algebra, but not in the composite score. Average scores in Charlotte did not change significantly in any of the five content areas between 2003 and 2007, but did show a significant gain on the composite measure. The effect sizes in Boston were two to three times larger than the LC or the national public sample. At both grades in Atlanta and Boston, effect sizes on the composite measure and individual subscales were generally greater than those of either the LC or the national public school sample. Percentile Measures by Subscale In the next analyses, we made indirect, normative comparisons between subscales (within a district) by looking at the percentile (on the national public school sample) to which a given district’s subscale average corresponds. Again, the purpose was to estimate district strengths and weaknesses in math. Tables 4b.4 through 4b.7 (for Atlanta, Boston, Charlotte, and Cleveland, respectively) show the percentiles to which each district’s averages correspond in composite scores and subscales by year in grades four and eight. The tables also show changes (gain or loss) in percentile points between 2003 and 2007, although statistical tests of significance were not performed because of the indirect way percentiles measure performance. Atlanta As shown in table 4b.4, the average performance of Atlanta on the composite math measure and all math subscales at grade four was below the national public school median in 2003, 2005, and 2007. In grade four math, the average student in Atlanta was at the 28th percentile in 2007, but the effect size analysis indicated that the gain over the study period was significant. Fourth graders in 2007 scored at the 30th percentile in number, the 24th percentile in measurement, the 32nd percentile in geometry, and the 29th percentile in both data and algebra. The overall fourth-grade math performance in the district was tightly clustered by subscale around the 30th percentile, except for measurement—the lowest of the five subscales. The effect size analysis indicates that gains between 2003 and 2007 were seen in all subscales, except measurement. Table 4b.4 Atlanta’s average NAEP mathematics percentiles and changes in percentiles, by subscale and grade, 2003-2007 (National Public School median=50) Grade 4
Percentile of the mean scale score Composite
2003 26
2005 27
Shift in percentile
Grade 8
Percentile of the mean scale score
2007
2003–2007
2003
2005
2007
28
2
19
18
25
Number
29
30
30
1
21
19
25
Geometry
24
27
32
7*
18
18
24
29
4*
Measurement Data
Algebra
23 27 26
25 31 30
24 29
1
3*
15 22 22
16 18 23
Shift in percentile
2003–2007 6 4
26
11
27
5
26
6 4
* Difference is due to rounding. Source: U.S. Department of Education, Institute of Education Sciences, National Center for Education Statistics, National Assessment of Educational Progress (NAEP), 2003, 2005, and 2007 Mathematics Assessments.
89 Council of the Great City Schools and the American Institutes for Research
108
PIECES OF THE PUZZLE: FACTORS IN THE IMPROVEMENT OF URBAN SCHOOL DISTRICTS ON THE NATIONAL ASSESSMENT OF EDUCATIONAL PROGRESS