Making sense(s) of multiplication

Abstract

This paper examines drawings created by third-grade students during a mathematics lesson using the multi-touch iPad application TouchTimes, which provides a way of engaging directly with multiplication through the user’s fingertips. Using a theoretical perspective that recognises the materiality of mathematical concepts, we study the students’ conceptualisations of multiplication (which are imbricated with their fingers and the application) by analysing the multiple sensory meanings expressed in their drawings. We show how these sensory meanings relate to characteristics of multiplication discussed in the literature—through actions we call multi-plying and unitising. We also discuss additional features of the drawings, such as the inclusion of fingers and hands, the order of multiplier and multiplicand and limited use of colour.