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| Multiple categorizations involves presenting students with mathematical problems that can be solved from different perspectives. Illustration Credit: Calliste Scheibling-Sève |
At school or in everyday life, proportional reasoning is essential for many activities. This type of reasoning allows us to adapt the quantity of ingredients in a recipe or to calculate the distance traveled as a function of speed by relying on ratios and proportions. In school settings, certain intuitive conceptions of proportions can mislead students and hinder their learning. A team from the University of Geneva (UNIGE) shows that multiple categorizations in mathematical problems - the ability to adopt several points of view on the same problem - makes it possible to go past this obstacle. These results open up new perspectives for the learning of mathematics but also for other disciplines. They can be found in the Journal of Numerical Cognition.
Proportional reasoning is a cognitive process that involves ratios and proportions to solve a mathematical problem. This reasoning is regularly practiced and applied in school, but it is also very useful in our daily lives. It allows us to calculate the price of certain products when we shop, to adapt the quantity of ingredients in a recipe, and to convert foreign currencies. It is at play when we understand that a speed of 30mph is equivalent to a distance of 15 miles travelled in 30 minutes. It is also involved in assessing our risk-taking: for example, when we make choices about our health by weighing the effectiveness of a treatment or vaccine against the risks of the disease.
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