The utility of diagrams in elementary problem solving.

• Diagrams are one type of external representation for solving mathematics problems. • Participants included 1187 grade 6 students. • Task success was linked to effective use of diagrams during problem-solving. • Instruction in effective diagram use may help when solving new or complex problems. This investigation examined the strategies students employ to solve graphic and non-graphic mathematics tasks. The students' strategies were classified in terms of representation, specifically whether or not they used self-decoded diagrams to solve the tasks. The study involved 1187 Grade 6 students (from Singapore and Australia) solving graphic- and non-graphic mathematics tasks typically encountered in national tests. Data from these students provided solution strategies to mathematics problems; the strategies were classified as diagrammatic or analytic solutions. Data analysis was confirmatory in nature, which sought to analyze students' solutions to understand more fully the extent to which task representation relates to task difficulty, understanding and success. There was a strong association between task success and representation for items with moderate level of difficulty—with the employment of diagrammatic solutions more likely to lead to correct solutions. [ABSTRACT FROM AUTHOR]