PROCEEDINGS OF THE 16TH ANNUAL CONFERENCE ON RESEARCH IN UNDERGRADUATE MATHEMATICS EDUCATION (Vol 2)
2013
Denver, Colorado
Using Metaphors to Support Students’ Ability to Reason about Logic
Page: 2-91
In this paper, we describe an inquiry-oriented method of using metaphors to support students’ development of conventional logical reasoning in advanced mathematics. Our model of instruction was developed to describe commonalities observed in the practice of two inquiry-oriented real analysis instructors. We present the model via a general thought experiment and one representative case study of a students’ metaphorical reasoning. Part of the success of the instructional method relates to its ability to help students reason about, assess, and communicate about the logical structure of mathematical activity. In the case presented, this entailed a students’ shift from using properties to describe examples to using examples to relate various properties. The metaphor thus imbued key example sequences with meta-theoretical significance. We introduce the term “wedge” to describe such examples that distinguish oft-conflated properties. We also present our analytical criteria for empirically verifying the specific influence of the metaphorical aspect of instruction.