I have in the past challenged the presumption that certain topics are instances of 'foundational' learning but suggesting that concepts like succession and substitution might be more basic in math than addition and multiplication. This article (12 page PDF) makes that case in a much more convincing form. It attacks "a false assumption: that mathematics is a fixed, linear sequence of skills that must be acquired ... building block by building block." And it argues against the idea "that topics are unitary things." And here's the point: "assumptions about pedagogical priority based on the structure of mathematics can create barriers to children's learning, as can using statistical prevalence to make claims about cognitive necessity." What we call 'foundational' might be statistical or conventional, but it is not indispensable. Related: Jeannine Diddle Uzzi, We should teach math like it's a language.
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