The anticipation of where to stop the unit-rate count remained inconsistent and prompt-dependent across subsequent episodes with harder numbers¶

Claim · All claims
Evidence · 1 study · qualitative r3 · 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is a peer-reviewed article with a DOI: it rests on a source with no registered publication record (a web page, book or unpublished report).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? Three teaching episodes after the prompted success, Devin still needed prompting to regulate stopping the unit-rate count on a 7T6 task, indicating his construction was at the participatory (prompt-dependent) stage. → 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 · r3

Analysis of an October 23, 2014 episode (task 7T6, chosen because both the compilation of composite units and the unit rates exceeded the five fingers on each hand): Devin again anticipated where to start both counts but shifted to counting five instead of six items per composite unit past the second tower.

"This inconsistency suggests that, in the previous episodes, Devin's construction of the coordinated count was at the participatory (prompt-dependent) stage."

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
• 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 — 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
• In the S0-54 tutoring episode, the learner reaches the correct posterior (1/6) yet the three Stage 2 evidence scopes yield different diagnoses, with full trajectory credit withheld because part of the interpretation remains tutor-owned — related