Modeling, symbolizing, and tool use in statistical data analysis

This chapter looks at symbolizing and mathematical learning from a social constuctivist perspective that is motivated by an interest in instructional design. The central theme is that of a concern for the way students actually use tools and symbols. Point of departure are analyses treat people's activity with symbols as an inegral aspect fo 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 then seen not so much as somthing to be mastered, but qas a consituent part of the mathematical practices in which students come to participate. This view corresponds with the author's 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 thoeretical construct of a classroom mathematical practice is introduced, which involves taken-as-shared ways of symbolizing.<br>Against this background an analysis is presented of the mathematical practices established duing a seventh-grade classroom teaching experiment that focused on statistical data analysis, that is based on RME theory. This analysis is supplemented with a description of the taden-as-shared ways in thish two computer-based analysis tools were used in the classroom, which is cast in terms of the emergence of a chain of signification. The chapter finishes with a reflection on the general notion of modeling. In connection with the notion of participation, a distinction is made between the use fo the term model in mathematical discourse, and an alternative formulation that relates to both semiotics and design theory.