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

Russell Bradford*, James H. Davenport, Christopher J. Sangwin

*Corresponding author for this work

Research output: Chapter in Book/Report/Conference proceedingConference contribution

Abstract / Description of output

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?".

Original languageEnglish
Title of host publicationLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
PublisherSpringerLink
Pages75-89
Number of pages15
Volume5625 LNAI
ISBN (Print)3642026133, 9783642026133
DOIs
Publication statusPublished - 2009
Event16th Symp. on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2009 and 8th Int. Conf. on Mathematical Knowledge Management, MKM 2009. Held as part of the Confs. on Intelligent Computer Mathematics, CICM 2009 - Grand Bend, ON, Canada
Duration: 6 Jul 200912 Jul 2009

Publication series

NameLecture Notes in Computer Science (including subseries Lecture Notes in Artificial Intelligence and Lecture Notes in Bioinformatics)
Volume5625 LNAI
ISSN (Print)03029743
ISSN (Electronic)16113349

Conference

Conference16th Symp. on the Integration of Symbolic Computation and Mechanized Reasoning, Calculemus 2009 and 8th Int. Conf. on Mathematical Knowledge Management, MKM 2009. Held as part of the Confs. on Intelligent Computer Mathematics, CICM 2009
Country/TerritoryCanada
CityGrand Bend, ON
Period6/07/0912/07/09

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