TY - GEN

T1 - A comparison of equality in computer algebra and correctness in mathematical pedagogy

AU - Bradford, Russell

AU - Davenport, James H

AU - Sangwin, C J

N1 - Proceedings of the 16th Symposium, Calculemus 2009, 8th International Conference, MKM 2009, Held as Part of CICM 2009, Grand Bend, Canada, July 6-12, 2009
ID number: 5625/2009

PY - 2009

Y1 - 2009

N2 - 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?”.

AB - 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?”.

UR - http://www.scopus.com/inward/record.url?scp=69049087815&partnerID=8YFLogxK

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

U2 - 10.1007/978-3-642-02614-0_11

DO - 10.1007/978-3-642-02614-0_11

M3 - Chapter in a published conference proceeding

SN - 9783642026133

T3 - Lecture Notes in Computer Science

SP - 75

EP - 89

BT - 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

A2 - Carette, J

A2 - Dixon, L

A2 - Sacerdoti Coen, C

A2 - Watt, S M

PB - Springer

CY - Berlin

T2 - 8th International Conference on Mathematical Knowledge Management (MKM 2009)

Y2 - 10 July 2009 through 12 July 2009

ER -