The chart gives the increase (decrease) in average student performance for each reduction (increase) in class size of one student. That is, if K-2 class sizes dropped on average one student per class, the average scores of all K-2 students would increase 3 points. In addition as they reached the 3-7 grade group given no other changes their grades 3 through 7 test scores would go up 1 point and their grades 8 through 12 scores would also go up one point. If you added teachers to the 3-7 grade group such that grades 3-7 class sizes dropped one student, the average scores of those 3-7 students would got up 1.5 points and when they reach the 8-12 grade group, assuming nothing else happened, their 8-12 scores would go up 0.75 points.
The Department of Education is seeking a long-term strategy. To calculate the net effect of a reallocation of teachers, these score changes would have to be “weighted” by the number of students in each grade group. As such a reduction in K-2 class size by 2 would result in an overall increase in scores equal to:
2 * (3 * 250,000 +1 * 425,000 + 1 * 400,000)/ 1,075,000
Of course any increase in teachers in one grade group must result in a decrease in teachers in another grade group. (Hint: total number of teachers remains the same.) If the teaches in the example above came from the 3-7 grade group causing their average class size to go up 1.5 students per class, their scores would change (go down) according to the following:
-1.5 * (1.5 * 425,000 + 0.75 * 400,000)/ 825,000
If no teachers were taken from the 8-12 group, their scores would change as follows:
0 * (0.75 * 400,000)/ 400,000
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