Modeling, Symbolizing, and Tool Use in Statistical Data Analysis

Abstract

This chapter looks at symbolizing and mathematical learning from a social constructivist perspective that is motivated by an interest in instructional design. The central theme is that of a concem for the way students actually use tools and symbols. Point of departure are analyses treat people’s activity with symbols as an integral aspect of their mathematical reasoning rather than as external aids to it. As a consequence, the process of learning to use symbols in general, and conventional mathematical symbols in particular, is cast in terms of participation. Symbol use is then seen not so much as something to be mastered, but as a constituent part of the mathematical practices in which students come to participate. This view corresponds with the author’s instructional design perspective, according to which it is essential to account for the mathematical learning not merely of individual students but of the classroom community taken as a unit of analysis in its own right. To account for this collective learning, the theoretical construct of a classroom mathematical practice is introduced, which involves taken-as-shared ways of symbolizing negotiated by the teacher and students.