Mathematicians' perspectives on the teaching and learning of proof
Lara Alcock
2134/8946
https://repository.lboro.ac.uk/articles/chapter/Mathematicians_perspectives_on_the_teaching_and_learning_of_proof/9372596
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.
2011-10-14 13:53:50
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