A Comparison of Equality in Computer Algebra and Correctness in Mathematical Pedagogy

Authors:
Russell Bradford;James H. Davenport;Christopher J. Sangwin
Affiliations:
Department of Computer Science, University of Bath, Bath, United Kingdom BA2 7AY;Department of Computer Science, University of Bath, Bath, United Kingdom BA2 7AY;Maths Stats & OR Network, School of Mathematics, Birmingham, United Kingdom B15 2TT
Venue:
Calculemus '09/MKM '09 Proceedings of the 16th Symposium, 8th International Conference. Held as Part of CICM '09 on Intelligent Computer Mathematics
Year:
2009

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Abstract

How do we recognize when an answer is "right"? This is a question that has bedevilled the use of computer systems in mathematics (as opposed to arithmetic) ever since their introduction. A computer system can certainly say that some answers are definitely wrong, in the sense that they are provably not an answer to the question posed. However, an answer can be mathematically right without being pedagogically right. Here we explore the differences and show that, despite the apparent distinction, it is possible to make many of the differences amenable to formal treatment, by asking "under which congruence is the pupil's answer equal to the teacher's?".