# Reasoning by equivalence as elementary formal proof: the potential contribution of an automatic proof checker

@inproceedings{Sangwin2018ReasoningBE, title={Reasoning by equivalence as elementary formal proof: the potential contribution of an automatic proof checker}, author={Chris Sangwin}, year={2018} }

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…

## References

SHOWING 1-10 OF 30 REFERENCES

Specifying Rewrite Strategies for Interactive Exercises

- Computer ScienceMath. Comput. Sci.
- 2010

A language for specifying strategies for solving exercises is introduced, which makes it easier to automatically calculate feedback, for example when a user makes an erroneous step in a calculation.

Mixing Microworld and Cas Features in Building Computer Systems that Help Students Learn Algebra

- Computer ScienceInt. J. Comput. Math. Learn.
- 2004

The design principles for a new kind of computer system based on the microworld paradigm that allows students to make their own calculations, without being obliged to use commands, and to verify the correctness of these calculations.

The interaction of representation and reasoning

- Computer ScienceProceedings of the Royal Society A: Mathematical, Physical and Engineering Sciences
- 2013

This paper will illustrate the automation of representational change by drawing on recent work in the research group, with a special interest in the way that representation and reasoning interact.

Design principles of Mathpert: software to support education in algebra and calculus

- Computer ScienceComputer-Human Interaction in Symbolic Computation
- 1998

This paper lists eight design criteria that must be met if we are to provide successful computer support for education in algebra, trigonometry, and calculus. It also describes Mathpert, a piece of…

The Mathematical Analysis of Logic: Being an Essay Towards a Calculus of Deductive Reasoning

- Philosophy
- 2007

This chapter discusses the role of syllogisms in the education of teachers and their role in the development of classroom pedagogical practices.

An audited elementary algebra

- PhysicsThe Mathematical Gazette
- 2015

Solving equations is one of the core reasons for elementary algebraic manipulation. As Chrystal wrote [1]: There are few parts of algebra more important than the logic of the derivation of equations,…

‘It takes me longer, but I understand better’ – student feedback on structured derivations

- Education
- 2010

In this article, we present the results from a qualitative study on students' initial reactions to the use of structured derivations in mathematics education. Our findings suggest that the approach…