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Should we continue to teach standard written algorithms for the arithmetical operations? The example of subtraction Jean-Paul FISCHER*, Bruno VILETTE (a) , Sophie JOFFREDO-LEBRUN (b) , Mireille MORELLATO (c) , Céline LE NORMAND (d) , Calliste SCHEIBLING-SEVE (e) & Jean-François RICHARD (f)

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.

This study develops and evaluates an intervention aimed at improving flexibility in arithmetic word problems. 9 classes (4th-5th Grades) were divided between experimental, active and passive control groups, and followed this protocol: pre-test, 5 learning sessions for experimental and active control groups, post-test. During learning sessions, both groups learned to solve arithmetic word problems with two strategies — expansion and factorization — by comparing them. But comparing strategies was based on a semantic analysis and choice in point of view for the experimental group whereas comparing strategies was based on identifying keywords and calculations. The experimental condition was expected to promote flexibility in strategy for new transfer problems. At posttest, the active control group and the experimental group got similar scores for learning problems, higher than the passive control group. But for transfer problems, the experimental group was more flexible than the two other groups. Educational entailments of our finding are discussed.

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