15 au 17 novembre 2021

*Modifying mathematical situations to foster mathematical reasoning through manipulatives use: Which variables to consider?*

Whether in literature, institutional documentation, or elementary school professionals’ discourse, manipulatives use is often posed as a way to foster mathematical learning and even cited as a necessity ( Ball, 1992; Moyer, 2001, Corriveau & Jeannotte, 2015). However, research results are ambivalent. When some studies report a correlation between success in mathematics and manipulatives uses (e.g. Sherman & Bisanz, 2009), Carbonneau, Marley & Selig (2013) provide a nuanced picture of the situation. In particular, they showed that the latter has little effect on problem-solving and justification skills in mathematics compared to the use of so-called abstract mathematical symbols. Those results suggest that some variables are important to take into account when it comes to the use of manipulatives. For example, the perceptual qualities of manipulatives seem to play on the learning outcome (see Carbonneau & al, 2013).

However, Carbonneau & al (2013) deplore the lack of research that identifies these variables and their contribution. We hypothesize that this identification would provide tools to help teachers develop significant ways of doing mathematics with their students. Furthermore, Puchner, Taylor, O’Donnell, and Fick (2008, p. 323) point out that « […] teachers need support making decisions regarding manipulatives use, including when and how to use manipulatives to help them and their students think about mathematical ideas more closely ». In this workshop, we will explore two tasks and students’ reasoning aiming to utter different variables that can be made to modify a mathematical situation. In the first task, students are invited to determine how to illustrate a fraction when provided with the representation of another fraction (e.g. If something represents 1/12, how could you represent ¼). A limited number of Patterns blocks are provided to solve the task. In the second task, students have to solve an open word problem using some manipulatives, each team using a different one. This exploration will be guided by some elements that emerged from a literature review and some from the MathéRéaliser project that has been taking place since 2013.