Three Perspectives on Diagrams as Signs Contributing to Learning Mathematics

Abstract

Although researchers have studied the contribution of diagrams to learning mathematics based on various perspectives, the meta-analysis of relevant studies is lacking. The purpose of this study is to advance the discussion of epistemological assumptions underlying various approaches to the relationship between diagrams and mathematics learning. To this end, we reviewed theoretical and empirical studies about the contribution of diagrams in mathematics learning, focusing on how they account for the relationship between diagrams as signs and mathematics. The review has led to a proposed framework that categorizes the perspectives on diagrams as signs in pertinent research into structure-based, context-based, and material-based perspectives. We further identified differences in the epistemological background upon which studies from the three perspectives are based and the way the perspectives describe the relationship between diagrams and mathematics learning. The framework was useful identifying the multidimensionality of mathematics learning related to diagrams as well as the use of theoretical lenses by researchers depending on specific aspects of mathematics learning.

Keywords

• diagram
• diagrammatic reasoning
• sign
• semiotics
• epistemological perspective