Please Go and Bring for Me (PGBM) game for promoting reflection on units in multiplicative reasoning¶

Element · All elements
Evidence · no claims cited

Description¶

PGBM is a paired game in which a Sender asks a Bringer to build and bring back several same-size towers of cubes, one tower at a time, then answer four questions about towers, cubes per tower, total cubes, and how the total was figured out. The article says "The PGBM game was designed to promote children's reflection on the units used in multiplicative reasoning, by asking them to build towers from a given number of single cubes." In this study the teacher constrained the numbers of cubes per tower and towers, and used a poster with questions and answer-starters to promote full sentences and explicit mention of units.

Design Implications¶

Context¶

Requirements¶

• Play in pairs with Sender and Bringer roles, with the Sender posing tasks one tower at a time and asking four questions about the towers brought

Constraints¶

• In this study the teacher constrained the game to particular numbers of cubes per tower and towers, and disallowed using the same number for both kinds of unit

Target Learners¶

• elementary students (fourth graders) with learning difficulties in mathematics

Target Learning Goals¶

• multiplicative reasoning
• coordinating number of composite units with unit rate

Affordances¶

• Dual Anticipation Start Stop Mdc Intermediate Stage

Claims¶

Related Elements¶

Examples¶

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

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/