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

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

6 Citations (Scopus)
68 Downloads (Pure)

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?”.
Original languageEnglish
Title of host publicationIntelligent 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
EditorsJ Carette, L Dixon, C Sacerdoti Coen, S M Watt
Place of PublicationBerlin
PublisherSpringer
Pages75-89
Number of pages15
ISBN (Electronic)9783642026140
ISBN (Print)9783642026133
DOIs
Publication statusPublished - 2009
Event8th International Conference on Mathematical Knowledge Management (MKM 2009) - Grand Bend, Ontario, Canada
Duration: 10 Jul 200912 Jul 2009

Publication series

NameLecture Notes in Computer Science
PublisherSpringer
Number2
Volume5625
ISSN (Print)0302-9743

Conference

Conference8th International Conference on Mathematical Knowledge Management (MKM 2009)
CountryCanada
CityGrand Bend, Ontario
Period10/07/0912/07/09

Fingerprint

Correctness
Equality
Pedagogy
Algebra
Congruence
Pupil
Mathematics

Cite this

Bradford, R., Davenport, J. H., & Sangwin, C. J. (2009). A comparison of equality in computer algebra and correctness in mathematical pedagogy. In J. Carette, L. Dixon, C. Sacerdoti Coen, & S. M. Watt (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 (pp. 75-89). (Lecture Notes in Computer Science; Vol. 5625, No. 2). Berlin: Springer. https://doi.org/10.1007/978-3-642-02614-0_11

A comparison of equality in computer algebra and correctness in mathematical pedagogy. / Bradford, Russell; Davenport, James H; Sangwin, C J.

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. ed. / J Carette; L Dixon; C Sacerdoti Coen; S M Watt. Berlin : Springer, 2009. p. 75-89 (Lecture Notes in Computer Science; Vol. 5625, No. 2).

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

Bradford, R, Davenport, JH & Sangwin, CJ 2009, A comparison of equality in computer algebra and correctness in mathematical pedagogy. in J Carette, L Dixon, C Sacerdoti Coen & SM Watt (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. Lecture Notes in Computer Science, no. 2, vol. 5625, Springer, Berlin, pp. 75-89, 8th International Conference on Mathematical Knowledge Management (MKM 2009), Grand Bend, Ontario, Canada, 10/07/09. https://doi.org/10.1007/978-3-642-02614-0_11
Bradford R, Davenport JH, Sangwin CJ. A comparison of equality in computer algebra and correctness in mathematical pedagogy. In Carette J, Dixon L, Sacerdoti Coen C, Watt SM, editors, 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. 2009. p. 75-89. (Lecture Notes in Computer Science; 2). https://doi.org/10.1007/978-3-642-02614-0_11
Bradford, Russell ; Davenport, James H ; Sangwin, C J. / A comparison of equality in computer algebra and correctness in mathematical pedagogy. 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. editor / J Carette ; L Dixon ; C Sacerdoti Coen ; S M Watt. Berlin : Springer, 2009. pp. 75-89 (Lecture Notes in Computer Science; 2).
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