The Effectiveness of Visualization for Learning Expression Evaluation

A controlled study was conducted to evaluate the effectiveness of providing visualization as part of feedback in a problem-solving software tutor on arithmetic expression evaluation. Data was collected over six semesters from multiple institutions. ANOVA analysis of the collected data was conducted in three stages. Statistically significant results include that visualization helped students learn more concepts; visualization did not improve the speed of learning; the benefits of visualization accrued primarily to less-prepared students; and visualization may affect different demographic subgroups differently. Incidental results include that there was no difference among demographic groups (male/female, traditional/underrepresented, Computer Science/non-CS) in the number of concepts learned using the software tutor, although some groups (female, underrepresented) were less-prepared before using the tutor than their counterparts, and some groups learned concepts with fewer practice problems (male, traditionally represented) than their counterparts. Concurrence of the results obtained whether the analysis was conducted based on pre-condition (need) or post-condition (benefit) of using the tutor strengthens the claims made as a result of this study.