At some point during the process of teaching multiplication to our children, we really need to come to terms with this question:
What IS multiplication?
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“What’s my answer? It’s not one that society’s going to like. Because society expects — demands, even — that mathematics be concrete, real-world, absolute, having definitive answers.
I can’t give a definitive answer.
Multiplication manifests itself in different ways. So maybe the word ‘is’ there is just too absolute. And it’s actually at odds with what mathematicians do.
Mathematicians do attend to real-world, practical scenarios — by stepping away from them, looking at a bigger picture.”
—James Tanton, What is Multiplication?
For Further Study
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