Semiotic Representations of Multiplication and Division in Elementary School Textbooks

Abstract In this report, we present a proposal to explore the meanings related to multiplication and division that are built in Elementary School mathematics textbooks. We carried out a multimodal analysis of the tasks focused on multiplication and division in two textbooks widely distributed in Spain. This analysis allows us to develop a characterisation of the introduction of multiplicative thinking in textbooks based on the potential meanings of multiplication and division derived from the use and coexistence of the different types of symbolic, graphic, and verbal representations that are presented and demanded in the tasks. The results point to a dominance of symbolic representations and a low use of verbal representations in the multiplication and division tasks of the two textbooks analysed.

摘要 本报告提出一项研究方案，旨在探究小学数学教材中所承载的乘除法相关内涵。本研究针对西班牙广泛使用的两套小学数学教材中的乘除法主题习题开展了多模态分析。该分析基于教材习题中呈现与要求的各类符号、图像及言语表征的使用与共存情况，推导出乘除法的潜在内涵，以此对教材中乘法思维的引入方式进行系统性刻画。分析结果显示，在所研究的两套教材的乘除法习题中，符号表征占据主导地位，而言语表征的使用占比极低。