How Do Students' Method of Solving Proofs Change When Working in Groups?

Abstract

This study aimed to describe the shift in students’ mathematical arguments from working on a proof individually to working on it in a group. This descriptive-exploratory study used a qualitative approach. Nine undergraduate students from a private university in Jombang, Indonesia, in the 5th semester were the subjects of the study. They were selected because they had already learned the concepts of math logic, argumentation, the theory of numbers, and analysis. Hence, they were ready to construct arguments in dialogue and non-dialogue forms. A task of argumentation and an interview were used to collect data. The study had several stages. First, the students solved the given argumentation task individually. Second, they had to make small groups of 3 members and discuss the same task. The result found that four of them had a complementary shift in their arguments, while the other five students had a reconstructive shift in their views. The complementary change happened because they reconsidered their initial thoughts, complementing their previous thinking structure. On the other hand, the reconstructive shift occurred due to group discussion (i.e., dialogue), which made them reconstruct or even entirely change their previous thoughts. Furthermore, they initially used inductive reasoning and then shifted their reasoning to a deductive one.
 Keywords: Mathematical Argumentation, Proving, Reconstruct, Complementary shift, Reconstructive shift