Both will improve math passing rates but decreasing student:teacher ratio to 30:2 will have higher pass rates than decreasing class size to 20.
Preliminary data: The same 20 teachers have been teaching freshmen math for the past 5 years. Class size has been 28-32 consistently. Pass rates for all teachers for all years are known and have been consistent for all 5 years with an overall mean of 30%, std of 2%.
Plan: Take the 600 freshman, and divide them into three groups. 5 teachers will have 100 students randomly selected. 10 teachers will pair up and have 150 students randomly selected. The remaining 5 teachers will have the usual class size of 30, serving another 150 students. The remaining 200 students will be served by 8 new teachers funded under a grant from DOE for this trial.