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Learning isn't possible without unlearning whatever temporary construct we used as a crutch, but it doesn't mean using that temporary construct is wrong even if it's not technically correct. More specifically in mathematics, the interplay between formalism and intuition, like a mental danse or gymnastics, is a powerful process in furthering our understanding of mathematical truths: From a formal perspective, mathematical objects can be created in so many ways, some constructions being more intuitive and beautiful than others (axioms, groups, rings, fields). The formalism itself let us see what intuition can't. From an intuitive perspective, it's useful to latch on whatever concept one have to learn the next level of abstraction, while acknowledging that the intuition might not be 100% correct. Like using addition to intuitively understand multiplication, or addition and multiplication to intuitively understand fields. The intuition let us familiarize with otherwise novel ideas. Ironically, this article wants to be very normative about which mathematical intuition is better (which there isn't, I'm sure many don't think of "multiplicand" as something special), while disregarding any cues from any formalism. |
> Ironically, this article wants to be very normative about which mathematical intuition is better…
No, the article is not being normative about “which intuition is better,” this is an incorrect reading of the article.
The article is giving advice about how to teach multiplication. Advice that is apparently based on years of experience teaching multiplication.
It’s not uncommon for people to experience teachers who prescribe specific intuitions about math rather than accommodate different intuitions—but the author is not doing that. What she’s doing here is outlining the various ways in which one particular intuition may fail you.