Drawing, modelling and gesture in students' solutions to a Cartesian product problem

Abstract

This paper presents and discusses the visual data generated from a single mathematical task. During one session students worked on a 'Cartesian product' problem which required them to consider the combination of the elements of two independent sets; in this case within the scenario of finding the total number of different t-shirt/trousers pairs which could be made by choosing from a 'suitcase' of these clothing items. No task-specific materials were provided, but paper, coloured pens and multilink cubes were available for students to use if they wished. The majority of the students found this task considerably challenging, but were able to tackle it with varying levels of teacher support. A wide variety of visuo-spatial and/or kinaesthetic representations were produced, including colourful pictorial depictions of the items, physical models both with and without movement into different configurations, and text-based notations. Analysis of this qualitative multimodal data is being completed in stages, this paper focusing on descriptive aspects.