Orient students' reflection onto their own tracking methods to foster monitoring of goal-directed counting¶

Strategy · All strategies
Evidence · no claims cited

Description¶

This teaching strategy has the teacher-researcher mirror and describe the student's own counting gestures back to him, prompting recognition of errors in the unit-rate count. In the episode, the teacher held her hand over the table, folded fingers down, and asked Devin to tell her what he was doing; the authors assert that "when Nina oriented Devin's reflection on his own tracking methods, she fostered his monitoring of his own goal-directed activity." This enabled Devin to begin monitoring a stop at 6 for each tower.

Design Implications¶

Context¶

Requirements¶

• The student must already have observable tracking methods (e.g., finger gestures for towers and cubes) that the teacher can mirror and discuss

Constraints¶

• The resulting monitoring was prompt-dependent: Devin's anticipation of where to stop remained inconsistent in later episodes without prompting

Target Learners¶

• elementary students with learning difficulties in mathematics

Target Learning Goals¶

• monitoring simultaneous counts of composite units and unit rates
• anticipating where to stop each count in multiplicative double counting

Related Strategies¶

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/