Reconciling factorizations made with CAS and with paper-and-pencil: the power of confronting two media.

P.H.M. Drijvers; C. Kieran

Reconciling factorizations made with CAS and with paper-and-pencil: the power of confronting two media.

P.H.M. Drijvers, C. Kieran

Dept of Mathematics

extern

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

Abstract

The study presented in this report is part of a larger project on the co-emergence of technique and theory within a CAS-based task environment for learning algebra, which also includes paper-and-pencil activity. In this paper, an example is presented in which 10th graders in Canada use handheld computer algebra to factor expressions of the form xn – 1. The factorizations made by the computer algebra system are compared with the students’ by-hand factorizations. This confrontation, and the students’ wish to reconcile the two, turned out to be productive for the development of both theoretical understanding and paper-and-pencil and machine techniques. These findings are in line with the anthropological theory of didactics.

Original language	Undefined/Unknown
Title of host publication	Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education
Editors	J. Novotna, H. Moraova, M. Kratka, N. Stehlikova
Place of Publication	Prague
Publisher	Charles University
Pages	473-480
Number of pages	8
Publication status	Published - 2006

Keywords

Mathematics
Landbouwwetenschappen
Natuurwetenschappen
Wiskunde: algemeen

Cite this

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title = "Reconciling factorizations made with CAS and with paper-and-pencil: the power of confronting two media.",

abstract = "The study presented in this report is part of a larger project on the co-emergence of technique and theory within a CAS-based task environment for learning algebra, which also includes paper-and-pencil activity. In this paper, an example is presented in which 10th graders in Canada use handheld computer algebra to factor expressions of the form xn – 1. The factorizations made by the computer algebra system are compared with the students{\textquoteright} by-hand factorizations. This confrontation, and the students{\textquoteright} wish to reconcile the two, turned out to be productive for the development of both theoretical understanding and paper-and-pencil and machine techniques. These findings are in line with the anthropological theory of didactics.",

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author = "P.H.M. Drijvers and C. Kieran",

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pages = "473--480",

editor = "J. Novotna and H. Moraova and M. Kratka and N. Stehlikova",

booktitle = "Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education",

publisher = "Charles University",

address = "Czech Republic",

}

Reconciling factorizations made with CAS and with paper-and-pencil: the power of confronting two media. / Drijvers, P.H.M.; Kieran, C.
Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education. ed. / J. Novotna; H. Moraova; M. Kratka; N. Stehlikova. Prague: Charles University, 2006. p. 473-480.

Research output: Chapter in Book/Report/Conference proceeding › Conference contribution › Academic › peer-review

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T1 - Reconciling factorizations made with CAS and with paper-and-pencil: the power of confronting two media.

AU - Drijvers, P.H.M.

AU - Kieran, C.

PY - 2006

Y1 - 2006

N2 - The study presented in this report is part of a larger project on the co-emergence of technique and theory within a CAS-based task environment for learning algebra, which also includes paper-and-pencil activity. In this paper, an example is presented in which 10th graders in Canada use handheld computer algebra to factor expressions of the form xn – 1. The factorizations made by the computer algebra system are compared with the students’ by-hand factorizations. This confrontation, and the students’ wish to reconcile the two, turned out to be productive for the development of both theoretical understanding and paper-and-pencil and machine techniques. These findings are in line with the anthropological theory of didactics.

AB - The study presented in this report is part of a larger project on the co-emergence of technique and theory within a CAS-based task environment for learning algebra, which also includes paper-and-pencil activity. In this paper, an example is presented in which 10th graders in Canada use handheld computer algebra to factor expressions of the form xn – 1. The factorizations made by the computer algebra system are compared with the students’ by-hand factorizations. This confrontation, and the students’ wish to reconcile the two, turned out to be productive for the development of both theoretical understanding and paper-and-pencil and machine techniques. These findings are in line with the anthropological theory of didactics.

KW - Mathematics

KW - Landbouwwetenschappen

KW - Natuurwetenschappen

KW - Wiskunde: algemeen

M3 - Conference contribution

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BT - Proceedings of the 30th Conference of the International Group for the Psychology of Mathematics Education

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