Jake’s conceptual operations in multiplicative tasks: Focus on number choice

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Conference Proceeding

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This case study examined how a teacher’s choice of numbers used in tasks designed to foster students’ construction of a scheme for reasoning in multiplicative situations may afford or constrain their progression. This scheme, multiplicative double counting (mDC) is considered a significant conceptual leap from reasoning additively with units of one (1s) and composite units. A researcherteacher’s work with Jake allowed us to center on his gradual cognitive advance as different numbers chosen for the unit rate in problems (e.g., 5 cubes-per-tower) were used in the context of the Please Go and Bring for Me platform task. Our findings show that a child’s use of an evolving scheme may initially depend on the numbers used in the task. We discuss the key recognitions that (a) a new way of operating does not evolve in a “once-and-for-all” way for all numbers and (b) the support our study provides for Pirie and Kieren’s core notion of folding-back.

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