Alcock_RCME_2009_mathematicians.pdf (255.96 kB)
Download fileMathematicians' perspectives on the teaching and learning of proof
This paper reports on an exploratory study of mathematicians'
views on the teaching and learning that occurs in a course designed to introduce
students to mathematical reasoning and proof. Based on a sequence of
interviews with five mathematicians experienced in teaching the course, I identify four modes of thinking that these professors indicate are used by successful
provers. I term these instantiation, structural thinking, creative thinking and
critical thinking. Through the mathematicians' comments, I explain these
modes and highlight ways in which students sometimes fail to use them effectively. I then discuss teaching strategies described by the participants, relating
these to the four modes of thinking. I argue that teaching aimed at improving
structural thinking tends to dominate, and that courses that introduce
proof, regardless of classroom organization, should address all four modes in a
balanced and integrated way.
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