for the learning of mathematics

Colin Foster - Vol. 42 Num. 3 (2022)
 Using coherent representations of number in the school mathematics curriculum


In this article, I argue that the common practice across many school mathematics curricula of using a variety of different representations of number may diminish the coherence of mathematics for students. Instead, I advocate prioritising a single representation of number (the number line) and applying this repeatedly across diverse content areas. I set out how this might work and the possible implications, focusing particularly on multiplication. I highlight limitations of other models of number, including circular ‘pizza’ for fractions and 2-dimensional area models, making the case that fewer, more carefully-chosen representations of number may better support students’ sense making.


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