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Proportional reasoning is related to flexible use of the scalar and functional relationships that exist in proportional situations. More specifically, in regard to the functional relationship, students’ understanding of the multiplicative comparison that exists between two quantities in a ratio is a key concept. We conducted student interviews with 12 high performing students to examine their conception of the functional relationship. Analyses provided initial evidence that the majority of students did not conceive of the multiplicative comparison when solving problems designed to press the functional relationship, indicating students’ written work that makes use of the functional relationship should not imply understanding of the multiplicative comparison.

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This document was originally published in Proceedings: Thirty-Eighth Annual Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education by the International Group for the Psychology of Mathematics Education. Copyright restrictions may apply.