Students' Semantic-Proof Production in Proving a Mathematical Proposition

Proving a proposition is emphasized in undergraduate mathematics learning.
There are three strategies in proving or proof-production, i.e.: proceduralproof,

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.