Abstract
Inspired by the entering of computer algebra systems (CAS) in the Danish upper secondary school mathematics program, this article addresses, from a theoretical stance, what may happen when traditional procedures are outsourced to CAS. Looking at the commands “solve” and “desolve,” it is asked what happens when such CAS procedures are objectified in the students’ minds, and what the nature might be of the resulting “objects.” The theoretical analyses draw on a selection of classical mathematics education frameworks on conceptualization and are related to the research literature on technology in mathematics education. The article suggests the following characteristics as elements of negative effects: loss of distinctive features of concept formation, a consequential reclassification of mathematical objects, instability of CAS solutions as objects, and prevailing a posteriori reasoning on students’ behalf when relying solely on CAS in their mathematical work.
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Notes
Personal communication with “maths counsellors” in Danish upper secondary school (Jankvist & Niss, 2015).
With reference to Schoenfeld, “The word problem is used here in this relative sense, as a task that is difficult for the individual who is trying to solve it.” (1985, p. 74). We do not distinguish sharply between problem, exercise, and task. Rather we focus on the relation between student’s CAS-based work and their mathematical conceptualization.
Personal communications with “maths counsellors.”
Inspired by the phenomenon of the experimenter’s regress (Collins & Pinch, 1993, p. 97).
Inspired by R.E.M.’s song “It’s the end of the world as we know it (and I feel fine)” (1987).
For example, Buchberger’s (2002) so-called “purists.”
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We thank reviewers and editor for their valuable comments. This article was partly written in the frame of project 8018-00062B under Independent Research Fund Denmark.
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Jankvist, U.T., Misfeldt, M. & Aguilar, M.S. What happens when CAS procedures are objectified?—the case of “solve” and “desolve”. Educ Stud Math 101, 67–81 (2019). https://doi.org/10.1007/s10649-019-09888-5
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DOI: https://doi.org/10.1007/s10649-019-09888-5