# Is the graphic calculator a useful mediating tool for students in the early stages of forming a concept of a variable?

Gage, Jennifer Anne (2005). Is the graphic calculator a useful mediating tool for students in the early stages of forming a concept of a variable? PhD thesis The Open University.

## Abstract

The graphic calculator offers an environment in which children can start to understand basic algebra. It acts as both a mediating physical tool and psychological sign in the sense Vygotsky described, shaping the higher mental processes of the students. The combination of a graphic calculator and two students is theorised as a zone of proximal development, a term used by Vygotsky to indicate the potential students have to achieve more when supported than they could do alone. The graphic calculator also acts as a focus for reflective discussion, providing students with language to enable them to articulate their ideas, and a locus for trying out those ideas. The immediate feedback provided enables students to challenge misconceptions they already hold, so enabling them to develop conceptions that are more appropriate.

The graphic calculator forms a learning environment by providing a model for a variable that is concrete and easily understood by even quite young children. The stores of the calculator are labelled with alphabetic letters, and so can be thought of as boxes into which numbers can be put. These stores can then be operated on in the same way as an algebraic variable. Although this model is not sufficient to explain a variable as a number that can change continuously, it is quite adequate to help children understand the concept of a 3 variable up to the stage of a generalised number.

Three case studies and a survey, using the graphic calculator model of a variable and teaching materials designed to exploit its affordances, are discussed in this thesis. Instances were found of students making cognitive gains as a result. Statistical evidence indicating that the students improved both their understanding of the nature of variables, and their skills in working with simple algebraic expressions is also given.

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