Dual anticipation of start and stop as an intermediate stage in constructing the multiplicative Double Counting scheme¶

Theory · All theories
Evidence · 2 claims (2 for) · 1 study (1 qualitative), q2 · 0 of 1 report an effect size · 2 claims rest on one study

Description¶

The article postulates that constructing the first multiplicative scheme, multiplicative Double Counting (mDC), requires a dual anticipation: anticipating where to shift each count of a composite unit (unit rate, first anticipation) and where to stop the count for the compilation of composite units (second anticipation). The authors state that "It is this dual anticipation that makes operating on harder numbers, for example, when CUs and/or 1s exceed the number of fingers on one hand, a challenging feat to overcome." They present Devin's case as illustrating a possible intermediate stage in SLDs' development of mDC, analogous to start/stop anticipation in additive counting on.

Design Implications¶

Context¶

Requirements¶

• The learner must coordinate more than one simultaneous count, each requiring anticipation of both a starting and a stopping point

Constraints¶

• The account is inferred from a single case study with one fourth grader and is offered as a possible intermediate stage, not a tested general model

Target Learners¶

• fourth graders identified as having learning difficulties in mathematics (SLDs)

Target Learning Objectives¶

• transition from additive to multiplicative reasoning
• coordinating composite units and unit rates in multiplication

Claims¶

• Sld Anticipates Start But Not Stop In Mdc Hard Numbers [+M]
• Mdc Stop Anticipation Remains Prompt Dependent [+M]

Related Theories¶

Examples¶

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Key Sources¶

• Risley, R., Hodkowski, N. M., & Tzur, R. (2016). Devin's construction of a multiplicative double counting scheme: Dual anticipation of start and stop. Proceedings of the 38th annual meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. https://www.pmena.org/proceedings/