Problem 2 (60 points)

Researchers were interested in the effects of using multiple representations in the calculus classroom. Three modes of representation were used in three different classrooms (Class 1 = symbolic only, Class 2 = symbolic + numeric, Class 3 = symbolic + numeric + graphical). A calculus preparation pre-test (not included) was administered in the classes and they each performed at the same level.

Data were collected on students conceptual understanding of calculus concepts. The response variable was the final exam score.

Data are stored in mathreps.sav. Run an appropriate analysis in SPSS. Be sure to check assumptions and include output.

Based on the results, what suggestions would you give for instructors of calculus?