Enhancing cognitive flexibility through a training based on multiple categorization: Developing proportional reasoning in primary school

Abstract

Proportional reasoning is a key topic both at school and in everyday life. However, students are often misled by their preconceptions regarding proportions. Our hypothesis is that these limitations can be mitigated by working on alternative ways of categorizing situations that enable more adequate inferences. Multiple categorization triggers flexibility, which enables reinterpreting a problem statement and adopting a more relevant point of view. The present study aims to show the improvements in proportional reasoning after an intervention focusing on such a multiple categorization. Twenty-eight 4th and 5th grade classes participated in the study during one school year. Schools were classified by the SES of their neighborhood. The experimental group received 12 math lessons focusing on flexibly envisioning a situation involving proportional reasoning from different points of view. At the end of the school year, compared to a control group, the experimental group had better results on the posttest when solving proportion word problems and proposed more diverse solving strategies. The analyses also show that the performance gap linked to the school’s SES classification was reduced. This offers promising perspectives regarding multiple categorization as a path to overtake preconceptions and develop cognitive flexibility at school.

Les espaces analogiques

“…Or lorsque l'hybridation est considérée, cela conduit à mettre au centre non pas une asymétrie entre une source d'analogie, pourvoyeuse de connaissance, et une cible qui en serait le récipiendaire, mais deux situations aux entrelacements multiples, dont l'intégration conceptuelle suscite la création de sens. Cette manière de voir s'avère particulièrement féconde dans certains travaux à visée éducative fondés sur le principe du recodage sémantique (Gvozdic & Sander, 2020 ;Rivier & Sander, 2022 ;Scheibling-Sève et al, 2022) qui mettent en évidence que les élèves progressent dans la compréhension de notions scolaires lorsque des séquences pédagogiques sont construites afin de susciter des intégrations conceptuelles, que les élèves n'auraient pas spontanément réalisés et qui leur permettent d'élaborer des hybridations qui les mènent au-delà de leurs compréhensions premières et favorisent l'abstraction et le transfert d'apprentissage. Parmi les champs possibles les plus féconds d'étude des intégrations conceptuelles et mais peut-être parmi encore les moins explorés figurent selon nous celui des apprentissages et de la formation, car s'appuyer sur le phénomène d'intégration conceptuel pour orienter la construction d'espaces mentaux nouveaux est une direction jusque-là encore peu explorée mais qui recèle de forts potentiels pour susciter l'acquisition de nouveaux savoirs.…”

Leveraging cognitive flexibility through flexible categorization training

“…Several studies have indicated that the ability to discard one's initial interpretation of a problem and construct a new, more relevant interpretation, is an essential component of solving counter-intuitive problems (Brissiaud & Sander, 2010;Gros et al, 2020;Ragni et al, 2018). This recoding process sometimes makes it possible to categorize the problem into a different category, associated with different solving strategies (Scheibling-Sève et al, 2022). However, it is worth noting that one's experience and knowledge of the world have a significant influence on their initial interpretation of the problems they encounter (Bassok et al, 1998;Bassok & Olseth, 1995;Coquin-Viennot & Moreau, 2003;Cosmides & Tooby, 1992;Gros et al, 2019;2020, 2024.…”

How do pre-service mathematics teachers resolve proportion tasks? Focus strategy of proportion solving

“…The concept of ratio has been defined differently by Euclid and Euler. In Euclid's book, the ratio is described as a relationship in terms of size between two equal quantities, where the quantities have ratios to each other that, when multiplied, can exceed each other (Grattan-Guinness, 2004;Simson, 1838). On the other hand, Euler in his book "Elements of Algebra" categorizes ratios into arithmetic ratio, which is the difference between two numbers, and geometric ratio, which represents how many times one number is greater than another number.…”

“…Studies have demonstrated that student's capacity to make well-informed financial choices is influenced when they employ additive techniques in proportional scenarios that necessitate comparisons (Scheibling-Sève et al, 2022). Furthermore, proportional reasoning is essential for higher-level math classes, providing access to higher education and employment opportunities (Cox & Root, 2020).…”