Over the past two weeks, we have been examining relationships between teacher salary and and student outcomes. We first discussed the proposed increase to Arkansas’ minimum teacher salary, including identifying which districts currently pay the minimum salary scale. We found little relationship between districts’ starting teacher salaries and either student academic achievement or academic growth. Last week, we explored the relationship between teacher salaries and average class size, and this week we wanted to close the loop by examining how class size is related to student academic growth here in Arkansas. You can play with these data on our interactive viz.
Small classes are popular with parents and teachers alike. In a smaller class, we imagine that each student would get more personalized attention from the teacher, leading to greater academic gains. In Arkansas (and elsewhere around the world), however, small classes don’t seem to lead to consistently positive outcomes for students.
Check out the figures below to see the relationship between school average class size and school average academic growth. Because we already know that average class size in Arkansas varies between school levels (elementary has the largest classes, while high schools have the smallest) we broke the visuals out by school level.
In Arkansas elementary schools, average class sizes ranged from 10 to 25 students, and there was a weak correlation between class size and academic growth (r=0.2). Further analysis, however, revealed that students in schools with larger average class sizes actually demonstrated greater academic growth than their peers in smaller classes! Differences were statistically significant for each of the past two years (the only years for which ESSA growth data are available).
Figure 1. Average class size and average content growth score, by Elementary level schools, 2017-18
In Arkansas middle schools, average class sizes ranged from 5 to 25 students, and there was essentially no relationship between average class size and student growth. Average class size was not a statistically significant predictor of student growth, and results were consistent over the past two years.
Figure 2. Average class size and average content growth score, by Middle level schools, 2017-18
In Arkansas high schools, average class sizes ranged from 5 to 20 students, and there was essentially no relationship between average class size and student growth. Average class size was not a statistically significant predictor of student growth, and results were consistent over the past two years.
Figure 3. Average class size and average content growth score, by High school level schools, 2017-18
Then we got to wondering, what if a school had decreased (or increased) class size- how would that relate to changes in academic growth? Our theory would be that if a school reduced the average class size from one year to the next, the average growth of students in the school would increase.
So we calculated the change in school average class size from 2016-17 to 2017-18, and the change in school growth score in that same time, plotted the results, and ran some regressions!
Figure 4 shows the change in average class size and student academic growth score from 2017 to 2018 for elementary schools. The green square indicates the quadrant where we would imagine schools show up- reduced class sizes and increased growth. There are some schools there, but there are also some schools in the red square– indicating reduced class size and decreased growth. You will notice that the majority of schools, however, show up on the left side of the chart, indicating that they increased average class size from one year to the next.
Figure 4. Change in average class size and average content growth score, by Elementary school level schools, 2016-17 to 2017-18
Just eye-balling these elementary schools, you can see that some of these schools experienced an increase in student academic growth, while others demonstrated declines in academic growth from one year to the next. Further analysis, however, revealed that increasing average class size by one student would result in a reduction of less than 1 point in the change in growth score (holding all other district characteristics constant)!
Figures 5 and 6 show the change in average class size and student academic growth score from 2017 to 2018 for middle and high schools, respectively. Like the elementary schools, the majority of these schools increased average class sizes, and statistical analysis showed that increasing average class size by one student would result in a reduction of less than half a point in the change in growth score (holding all other district characteristics constant)!
Figure 5. Change in average class size and average content growth score, by Middle level schools, 2016-17 to 2017-18
Figure 6. Change in average class size and average content growth score, by High school level schools, 2016-17 to 2017-18
So, what we have learned about average class size is that in Arkansas schools there is not a direct relationship between smaller classes and increased academic achievement. When class sizes are increased, the negative impact on year to year changes in growth is statistically significant but practically insignificant at all levels because of the extremely small size of the change.
Of course, this is not a causal analysis, and there are many variables that we are not controlling for. One of the major issues is that we are using school-level class sizes and growth scores. If the data were available, analyzing at a classroom level might be better- but would also lead to super small sample sizes which raises other concerns. On the plus side- we do know that academic growth isn’t correlated with the typical confounding variables like %FRL and school size.
After the research done in our past three blogs, we now know that larger class sizes are associated with increased teacher salaries, and don’t seem to be meaningfully impacting student growth, so school districts should carefully consider staffing patterns.
So what IS associated with increased student achievement? You know what we think- high quality instruction all day, every day.
Regression Details
Elementary:
2016-17: School average class size significantly predicted school-level academic growth even after controlling for school % FRL, b = .25, t(518) = 4.75, p < .001. Average class size explained a significant proportion of variance in depression scores, R2 = .12, F(2, 518) = 63.24, ( p < .001).
2017-18: School average class size significantly predicted school-level academic growth even after controlling for school % FRL, b = .22, t(518) = 3.77, p < .001. Average class size explained a significant proportion of variance in depression scores, R2 = .09, F(2, 518) = 27.83, ( p < .001).
Change: Change in School average class size from 2016-17 to 2017-18 significantly predicted the change in school-level academic growth even after controlling for school % FRL, b = -.30, t(518) = -4.15, p < .001. Average class size explained a significant proportion of variance in depression scores, R2 = .03, F(2, 518) = 8.63, ( p < .001).
Middle:
2016-17: School average class size did not significantly predict school-level academic growth.
2017-18: School average class size did not significantly predict school-level academic growth.
Change: Change in School average class size from 2016-17 to 2017-18 significantly predicted the change in school-level academic growth even after controlling for school % FRL, b = -.18, t(196) = -2.40, p < .05. Average class size explained a significant proportion of variance in depression scores, R2 = .03, F(2, 196) = 3.52, ( p < .05).
High:
2016-17: School average class size did not significantly predict school-level academic growth.
2017-18: School average class size did not significantly predict school-level academic growth.
Change: Change in School average class size from 2016-17 to 2017-18 significantly predicted the change in school-level academic growth even after controlling for school % FRL, b = -.19, t(292) = -2.29, p < .05. Average class size explained a significant proportion of variance in depression scores, R2 = .02, F(2, 292) = 3.242, ( p < .05).