Computer Algebra as an Instrument: Examples of Algebraic Schemes

Abstract

In this chapter, we investigate the relationship between computer algebra use and algebraic thinking from theperspective of the instrumental approach to learning mathematics in a technological environment, which was addressedin the previous chapter.Data comes from a research study on use of computer algebra for developing algebraic insights. Teaching experimentswere carried out in ninth- and tenth-grade classes in which the students used symbolic calculators to solve algebraicproblems, and in particular for solving parameterized equations and substituting expressions.We describe in detail instrumented action schemes for solving parameterized equations and substituting expressions. Weobserve that the approach which students take in their work in the computer algebra environment is closely related totheir mental conceptions. The instrumental approach offers ways of making this connection more explicit and betterunderstanding students’ difficulties. In particular, we note that students found it difficult to integrate the two schemesinto one comprehensive scheme.We argue that a relationship needs to be established and elaborated between the instrumental approach and othertheoretical notions on learning such as the symbolization perspective.