A comparison of equality in computer algebra and correctness in mathematical pedagogy

Reference:

Bradford, R., Davenport, J. H. and Sangwin, C. J., 2009. A comparison of equality in computer algebra and correctness in mathematical pedagogy. In: Carette, J., Dixon, L., Sacerdoti Coen, C. and Watt, S. M., eds. Intelligent Computer Mathematics: 16th Symposium, Calculemus 2009, 8th International Conference, MKM 2009 Held as Part of CICM 2009, Grand Bend, Canada, July 6-12, 2009. Proceedings. Berlin: Springer, pp. 75-89. (Lecture Notes in Computer Science; 5625/2)

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Official URL:

http://dx.doi.org/10.1007/978-3-642-02614-0_11

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?”.

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