# Characteristics of divergent mathematical thinking in eighth grade students

- Donna Kotsopoulos,
*Wilfrid Laurier University*
- Joanne Lee,
*Wilfrid Laurier University*
- Annalise Clarkson,
*Wilfrid Laurier University*

## Abstract

This research examined the characteristics of eighth grade
students who exhibited divergent mathematical thinking during problem solving.
Divergent mathematical thinking is defined as creative, efficient, and accurate
engagement in the cognitive processes of reasoning, problem-solving,
communicating, representing, and proof. Using modified talk-aloud protocols,
real-time naturalistic analysis of a group of eighth-grade students’
mathematical problem solving were conducted. In total, 344 video-taped episodes
were analyzed from six students who completed “mathcam video diaries”
of their problem-solving during homework completion. Results suggest that
students who exhibited divergent mathematical thinking tended to engage error
analysis and mathematical analogy more often than those that did not.
Furthermore, those students tended to benefit from productive failure from
ill-defined mathematical problems more so than students who did not exhibit
divergent mathematical thinking. Implications for student learning, classroom
instruction, homework, and for further research will be discussed.

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