The Back and Front of Mathematics

[Chase Mitsuda]

Describe a time when you experienced mathematics from the back, where “passion, curiosity, dead ends, gut feelings, drama, collaboration, and magic” happen?

How might we debunk the myths about the front of mathematics, that it’s “formal, precise, ordered, and abstract”?

Example Punahou Summer Mathematics classes that show learning from the back:

http://www.punahou.edu/news/item/index.aspx?LinkId=4625&ModuleId=40

Resource:

Mathematics Has a Front and a Back
Reuben Hersh
Synthese
Vol. 88, No. 2, New Directions in the Philosophy of Mathematics (Aug., 1991), pp. 127-133

https://www.jstor.org/stable/20116933?seq=1#page_scan_tab_contents

[Julie Wright]

I was also very struck by the distinction between math “in back” and “in front.” It made me realize why I have such an uneasy relationship with Standard for Mathematical Practice 6, “Attend to precision,” in my teaching. I do feel like precision is essential for making math useful: we need to be using the same language, we need to be clear on the meaning of our answers and our work, and often we need to make sure we really have a truthful result. But I feel like the spoilsport at the party when kids are excited about their messy, creative, intuitive work solving a problem and I come along and gripe, “You’re not finished! You forgot to say what units these are.” OK, I don’t put it quite like that, but I feel like that deflating reaction is what comes across. So then I’m tempted to let things like that slide, but that doesn’t work out either because communication between students and between students and me break down, and misunderstandings of the underlying math start creeping in.

Hmm… maybe I’ll leave a followup comment after I read Chapter 5. I feel certain Tracy knows how not to spoil the math party!

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