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Drawing as problem-solving : young children’s mathematical reasoning through the act of drawing

University of British Columbia

This project investigates how young children employ mathematical reasoning through the act of drawing while solving mathematical problems. Included is an examination of how grade 2 children responded when presented with two mathematical problems to solve, the kinds of pictures or representations they drew spontaneously - and the purpose for those drawing - what students were thinking while they drew, and how (or if) the act of drawing or the drawings themselves were helping students to reason through the problems. Considered together, video footage of students using drawing as a problem-solving strategy, children’s completed representational work and student interview data informed the creation of a framework for examining students’ drawing as problem-solving strategies and behaviours. Four categories of student behaviour emerged from this analysis, namely: the use of virtual manipulatives, the application of a system, the use of imagery and an examination of the sophistication of students’ representations. These categories form a framework that provides a lens for understanding children’s mathematical reasoning as expressed through and derived from the act of drawing. Questions regarding problem structure and complexity and their impact on student reasoning through pictures are also addressed. Implications of the study are elaborated, and involve a reconceptualizing of drawing in mathematical problem-solving to include a more performance-based approach, observing thinking in the act of thinking, reasoning while drawing. Recommendations for classroom practice are made regarding how teachers can support children in developing these active and metacognitive skills. Further research directions are suggested in the discussion of the results.

Text

2010-01-20

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http://hdl.handle.net/2429/18727

Mathematics Education

University of British Columbia

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