Abstract
I propose that a semiotic perspective of mathematical students' activity with a Computer Algebra System (CAS) highlights both the power of CAS as a tool for learning mathematics and the complexities of the learner's transformation of CAS into an effective tool for mathematical learning (instrumental genesis). Using this viewpoint, I argue that the multiple representations that a CAS affords may facilitate the learning of mathematics. This argument is based on Duval's (2006) cognitive paradox: how can a learner distinguish a represented object from its semiotic representations when there is no access to the mathematical object apart from its semiotic representations? I use a semiotic lens to demonstrate how a pair of first-year mathematical students, who were not computer literate on entry to university, engage in a task involving CAS near the end of their first academic year. I show that these students had difficulties in using the CAS effectively and efficiently; however I also show that these students were ultimately able to benefit from the alternate representations afforded by CAS.
Published Version
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