# Reasoning by Equivalence: The Potential Contribution of an Automatic Proof Checker

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## Abstract

Reasoning by equivalence, a form of line-by-line algebraic reasoning, is the most important single form of reasoning in school mathematics. In this chapter I define reasoning by equivalence and examine the role of reasoning by equivalence in mathematical proof. I base the discussion on an examination of the extent to which students are currently asked to “prove”, “show” or “justify” in high-stakes national examinations. I then report research into how students go about solving such problems on paper. These results inform the design of an automatic proof checker within the STACK software which assesses students’ responses. I report on the use of this software with students. Finally I discuss the implications of this work for what constitutes mathematical “proof” at school level, and how this might be taught and learned online.

## Keywords

Automatic assessment Proof checker Algebra Mathematics education## References

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