A statistical analysis of the effect of discrete mathematics on the performance of computer science majors in beginning computing classes

Reviewer: Doris C. Appleby

Sidbury compares the grades earned by students in a second course in computer science, grouped according to mathematics courses completed. These courses were Calculus, Discrete Mathematics, Pre-Calculus, and Quantitative Methods. He concludes that “students who take discrete mathematics do better in their beginning computer science courses than do students who take traditional mathematics.” The study is criticized in [1], on both design and methodological grounds. Design problems involve noncomparable groups (those studying discrete mathematics were all CS majors) and the orientation of the mathematics course material, since students in the discrete course were studying material closely related to the CS work, while others were not. The method is faulty in that analyses were carried out only on group means, even though individual scores were available for mathematics grades and SAT scores. Both criticisms are correct. If the faulty statistical trappings are removed from the study, Sidbury's comments boil down to informal evidence that students who take two courses on closely related material do better than students taking only one course. Studies to compare the worth of two or more strategies in learning the same material are extremely difficult to carry out. Controlling other variables, such as teacher and/or student enthusiasm, is next to impossible, as is truly random grouping (not achieved in Sidbury's study). Opinions such as those reported in this study are more validly presented when not cluttered up with inappropriate statistical analyses. But there's the rub. An opinion paper is often not acceptable to either journal or conference referees. As the computer science curriculum becomes more rigid, those with authority to set policy will probably consider studies evaluating the merits of one strategy over another. I join Konstam and Saphire in hoping that they not be swayed by small, inconclusive studies.