What happens when CAS procedures are objectified?—the case of “solve” and “desolve”

TY - JOUR

T1 - What happens when CAS procedures are objectified?—the case of “solve” and “desolve”

AU - Jankvist, Uffe Thomas

AU - Misfeldt, Morten

AU - Aguilar, Mario Sánchez

PY - 2019/5/1

Y1 - 2019/5/1

N2 - 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 Bsolve^ and Bdesolve,^ it is asked what happens when such CAS procedures are objectified in the students’ minds, and what the nature might be of the resulting Bobjects.^ 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, insta-bility of CAS solutions as objects, and prevailing a posteriori reasoning on students’ behalf when relying solely on CAS in their mathematical work.

AB - 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 Bsolve^ and Bdesolve,^ it is asked what happens when such CAS procedures are objectified in the students’ minds, and what the nature might be of the resulting Bobjects.^ 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, insta-bility of CAS solutions as objects, and prevailing a posteriori reasoning on students’ behalf when relying solely on CAS in their mathematical work.

KW - APOS

KW - CAS

KW - Conceptualization

KW - Desolve

KW - Pseudo-objects

KW - Solve

U2 - 10.1007/s10649-019-09888-5

DO - 10.1007/s10649-019-09888-5

M3 - Journal article

SN - 0013-1954

VL - 101

SP - 67

EP - 81

JO - Educational Studies in Mathematics

JF - Educational Studies in Mathematics

IS - 1

ER -