The much higher correlations between years for the same grade are consistent with the belief that differences in teacher quality make a substantial contribution to the variation in test score gains, but they are also consistent with the importance of a variety of other factors that vary systematically by grade. In an effort to isolate the impact of teachers, we divide schools into three groups on the basis of teacher turnover in each grade and subject: 1) less than 33 percent of teachers are the same in both years; 2) 33-99 percent of teachers are the same in both years; and 3) 100 percent of teachers are the same in both years. If differences in teacher quality are responsible for the correlations, it should be the case that the correlation in school average gains in successive years should be higher for schools in which most or all of the teachers teach in both years, and lower in schools in which there is greater turnover. Notice that we are not saying anything about the direct impact of turnover on achievement, only that persistence of achievement gains across years should decrease as turnover rises.
The top panel of Table 4 presents the correlations across schools in math and reading gains for grades 4, 5 and 6 by teacher turnover. The increase in correlations of achievement gain over time with more common teachers is exactly what would be expected when there is an important role for teacher quality. For 5th grade students, the correlation in school average math gains between successive cohorts is . 18 in schools with less than 33 percent of teaching positions staffed by the same teacher in both years, .34 in schools with between 33 percent and 99 percent staffed by the same teacher and .44 in schools with all of the same teachers in both years. The corresponding correlations for 5th grade reading gains are .09, .21 and .30 for high, medium and zero turnover schools respectively, and a quite similar pattern appears for 4th grade math and reading test score gains. The pattern is not quite as pronounced in 6th grade, though the correlations in high turnover schools are much lower than the rest.
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Table 4. Correlations in School Average Math and Reading Test Score Gains and Between Grade Differences in Average Test Score Gains with Individual Fixed Effects: By Grade* and Teacher Turnover
Fixed Individual Effects and Specification Checks
The higher correlations of achievement gains in schools and grades with less teacher turnover provides additional support for the importance of teacher quality in determining achievement.
However, there may be confounding factors unrelated to teacher quality that could be partly or even fully responsible for generating the observed pattern of correlations. In particular, the variance in the academic preparation and commitment of students may be much higher in schools with higher teacher turnover. If so, it would be imperative to account for school average differences in student characteristics.