Undergraduate students' understanding of the contraposition equivalence rule in symbolic and verbal contexts

Stylianides, A. J., Stylianides, G. J., & Philippou, G. N.

ABSTRACT.
Literature suggests that the type of context wherein a task is placed relates to students’ performance and solution strategies. In the particular domain of logical thinking, there is the belief that students have less difficulty reasoning in verbal than in logically equivalent symbolic tasks. Thus far, this belief has remained relatively unexplored in the domain of teaching and learning of mathematics, and has not been examined with respect to students’ major field of study. In this study, we examined the performance of 95 senior undergraduate mathematics and education majors in symbolic and verbal tasks about the contraposition equivalence rule. The selection of two different groups of participants allowed for the examination of the hypothesis that students’ major may influence the relation between their performance in tasks about contraposition and the context (symbolic/verbal) wherein this is placed. The selection of contraposition equivalence rule also addressed a gap in the body of research on undergraduate students’ understanding of proof by contraposition. The analysis was based on written responses of all participants to specially developed tasks and on semi-structured interviews with 11 subjects. The findings showed different variations in the performance of each of the two groups in the two contexts. While education majors performed significantly better in the verbal than in the symbolic tasks, mathematics majors’ performance showed only modest variations. The results call for both major- and context- specific considerations of students’ understanding of logical principles, and reveal the complexity of the system of factors that influence students’ logical thinking.