Linear algebra proofs: ways of understanding and ways of thinking in the formal world

Abstract

Research on teaching and learning of proofs in linear algebra is scarce. To help fill this gap, we interviewed six students taking a second linear algebra course and examined some of their coursework that they handed in. In this paper, we examined students’ ways of understanding and ways of thinking (Harel, 2008) in the formal world (Tall, 2008) of mathematical thinking from their statements as they unpacked a particular linear algebra proof. The results show that students were able to unpack and adjust the proof formally in a second course and reacted positively.