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International Group for the Psychology of Mathematics Education (PME-NA) 2024
Arielle Orsini
Arielle Orsini from the Mathematics Teaching and Learning Lab at Concordia University presented a poster at the PME-NA conference in November on a conceptual replication of manipulative use on students’ perceptions of the objects and their math learning.
Previous studies showed that when students used manipulatives as math tools in a math task context, they perceived the objects as math tools and there was a positive impact on their math learning. In comparison, when children used manipulatives as toys in a play session, they perceived them at toys but there was no effect on their math learning. These studies, however, confounded manipulative use (math tool vs. toy) and context (task vs. play). In her study, Arielle addressed this confound by having Grade 1 students use manipulatives as either math tools or toys only in a play context intervention.
She found that students’ perceptions of the object’s function matched how they were used in the intervention, which was consistent with previous research. It also demonstrates that children can develop a math tool perception of manipulatives in a play context. That said, when children played with the manipulatives, the effect of using them as math tools or toys on learning was no longer present as shown in previous research. This suggests that perhaps context (task vs. play) outweighs how manipulatives are used (math tools vs. toys).

Bianca Dirker
As a master’s student within the Mathematics Teaching and Learning Lab, Bianca Dirker had the opportunity to travel to Cleveland, Ohio at the beginning of November to present preliminary findings on research conducted at Concordia University.
In her research, she analyzed third- and fourth-grade math textbooks by looking at whether pictorial illustrations used in multiplication problems conveyed the structure of multiplication. She coded multiplication exercises as either having a decorative image in the margin of the workbook page or not, which is an illustration that was not related to the targeted concept but intended to capture student interest instead. She then coded multiplication tasks, which are sub questions to the multiplication exercises as either being representational of showing the structure of multiplication, irrelevant, or organizational providing a framework for solving the problem.
Bianca found that over half of the exercises included a decorative image in the margin but only 14% of all tasks contained illustrations showing the structure of multiplication.
Considering the results of this analysis, her goal for the future is to gain a better understanding of how multiplication is conveyed in teaching and look further into different types of illustrations impact children’s understanding of the structure of multiplication in elementary schools.

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