Students’ Semantic-Proof Production in Proving a Mathematical Proposition

Abstract

Proving a proposition is emphasized in undergraduate mathematics learning. There are three strategies in proving or proof-production, i.e.: procedural-proof, syntactic-proof, and semantic-proof production. Students’ difficulties in proving can occur in constructing a proof. In this article, we focused on students’ thinking when proving using semantic-proof production. This research is qualitative research that conducted on students majored in mathematics education in public university in Banten province, Indonesia. Data was obtained through asking students to solve proving-task using think-aloud and then following by interview based task. Results show that characterization of students’ thinking using semantic-proof production can be classified into three categories, i.e.: (1) false-semantic, (2) proof-semantic for clarification of proposition, (3) proof-semantic for remembering concept. Both category (1) and (2) occurred before students proven formally in Representation System Proof (RSP). Nevertheless, category (3) occurred when students have proven the task in RSP then step out from RSP while proving. Based on the results, some suitable learning activities should be designed to support the construction of these mental categories.