Promoting the use of diagrams as tools for thinking

A diagram is a visual representation that displays information in a spatial layout. In problem solving, a diagram can serve to unpack the structure of a problem and provide the foundation for problem solution. Hence, students are often recommended to use diagrams in solving mathematical problems. For some students, this recommendation is helpful and they are able to use the diagram as a powerful tool in mathematical thinking and learning. However for other students, this suggestion is singularly unhelpful. Some students are unable or perhaps unwilling to use diagrams on a problem-solving task. Students’ lack of knowledge about the utility of a diagram suggests that they need to be empowered to use the diagram as an effective mathematical tool. This chapter explores the knowledge that students require to become diagram literate and identifies some of the difficulties that students experience in their use of diagrams. As we discuss here, it is essential that students know why a diagram can be useful in problem solving, which diagram is appropriate for a given situation, and how to use a diagram to solve a problem. The chapter concludes with suggestions for developing diagram literacy within the mathematics curriculum.