A student with learning difficulties independently anticipated where to start a coordinated count but failed to anticipate where to stop the unit-rate count with harder numbers¶

Claim · All claims
Evidence · 1 study · qualitative r2 · q2
Currency · newest study 2016 · not yet checked against its sources · not reviewed by a person
Evidence quality · No study behind this claim is a peer-reviewed article with a DOI: it rests on a source with no registered publication record (a web page, book or unpublished report). It is kept because 2 design pages cite it; treat it as a lead to check, not an established finding.

Subclaims¶

q2 i? With easy numbers the role of each unit in regulating Devin's counting activity was properly anticipated, but with hard numbers his focus on accrual of both unit types took over these roles, leading to counting five instead of six items per composite unit. → Risley 2016

Evidence¶

Risley 2016¶

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/

q2 · i? · the article prints no effect size for this finding · qualitative · r2

Case-study analysis of a video-recorded teaching episode (task 5T6, October 15, 2014) in which Devin independently initiated counting from the second multiple of 6 but then, as the authors put it, shifted "to counting only five (instead of six) items per composite unit" while tracking six towers, arriving at 34 cubes.

"whereas with "easy" numbers the role of each unit in regulating Devin's activity was properly anticipated, with "hard" numbers his effort to focus on accrual of both types of unit took over these roles."

Discussion¶

Related Claims¶

• Challenges of students with learning difficulties in constructing multiplicative double counting may stem from conceptually born factors beyond memory issues — a broader claim this one bears on
• The anticipation of where to stop the unit-rate count remained inconsistent and prompt-dependent across subsequent episodes with harder numbers — related
• A teacher's prompting that oriented a student's reflection on his own tracking methods fostered monitoring of his goal-directed counting activity — related
• Spontaneous break-apart-make-ten strategy use is associated with stronger multiplicative double-counting reasoning — related