Distributions of Average Proficiency Scores

Each age and racial/ethnic group--except 17-year-old Hispanics--has experienced a narrowing in the gap between the highest and lowest achieving students in mathematics . (See figure 1-2.)

The most striking change occurs for black students. Blacks have large increases in average proficiency overall; this increase is especially noticeable among those students below the 50th percentile. Average scores for 13-year-old black students at the 5th percentile increased by 32 points since 1978, while scores at the 95th percentile showed no noticeable improvement (after accounting for standard error). For black students at ages 9 and 17, the differences in gains between the 5th and 95th percentiles were approximately 11 points each.

Scores for white students of all ages at the 5th percentile also grew more rapidly than scores for those at the 95th percentile. The most noteworthy example of this is for 13-year-olds, whose scores for the 5th percentile increased by 16 points, compared to a 7-point decrease for students at the 95th percentile.

The scores for Hispanic students varied little at age 17, with more striking gains for the 9- and 13-year-old age groups. The difference in gains between the 5th and 95th percentile for Hispanic 9-year-olds was 15 points; it was 19 points for 13-year-olds.

In science, as in mathematics, the most striking changes were for 13-year-old students. (See figure 1-3.) For black and Hispanic students, the gains for students at the 5th and 25th percentiles were the largest (26 and 21 points, respectively, for blacks; and 27 and 20 points, respectively, for Hispanics), compared to no gains at the 95th percentile and smaller gains (14 and 16 points, respectively) at the 75th percentile. (Click here for footnote 5.) White students made large gains at the 5th (18 points) and 25th percentiles (12 points)-particularly when taking into consideration that there was only a 4-point gain at the 75th percentile and no real movement at the 95th percentile. The differences in the gains for top and bottom students at age 9 were also noteworthy, but the 17-year-old white and Hispanic students experienced no real change at any level in the distribution. Black 17-year-olds did not exhibit this trend: Their scores improved only at the 50th and 75th percentiles. (Click here for footnote 6.)

Footnote 5:

Although there appears to be an 8-point gain for blacks and a 12-point gain for Hispanics at the 95th percentile, the standard errors are sufficiently large to prevent reporting these as real gains.

Footnote 6:

Although there appear to be large gains at the 5th, 25th, and 95th percentiles, the standard errors are sufficiently large to prevent reporting these as real gains.

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