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I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it. Quite often "root learning versus understandin

I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it. Quite often "root learning versus understanding" is the difference between being able to show and demonstrate you know your stuff ("root learning") and not being able to show or demonstrate it, but you think you kinda know it ("understanding").

Jtsummers 12y ago
> I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it. Perhaps I missed something or misread it, but that wasn't my takeaway. Rather, it seemed he was expressing that mechanics doesn't, on its own, directly lead to understanding (measurable by ability to apply the tools to novel, to the student, problems/situations). Given that he also endorsed Khan Academy in this same article it seems he has no problem with it developing mechanical understanding as a complement to the understanding needed by practitioners (scientists, mathematicians, engineers, etc.).
tokenadult 12y ago
You and onlookers may enjoy reading the article, "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education"[1] (1999) by Hung-hsi Wu, for a discussion of what leads to deep understanding of mathematics. Another classic article on the topic is Richard Askey's review[2] of Liping Ma's book Knowing and Teaching Elementary Mathematics, a very good read indeed. [1] http://math.berkeley.edu/~wu/wu1999.pdf http://math.berkeley.edu/~wu/wu1999.pdf [2] http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf
deleted 12y ago
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betaclass 12y ago
'I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it.' I think that's a bit of a straw man. The challenge is that simply getting the right answer, especially in terms of arithmetic (one small piece of math), can mask how well a student understands the underlying concepts and whether s/he can flexibly apply the concepts. Here's a great video on that topic: https://www.youtube.com/watch?v=_ofQ_WnQiZ4 And here's a great video that shows what a participatory classroom with a great teacher can achieve: https://www.youtube.com/watch?v=BlvKWEvKSi8

Jtsummers 12y ago

> I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it. Perhaps I missed something or misread it, but that wasn't my takeaway. Rather, it seemed he was expressing that mechanics doesn't, on its own, directly lead to understanding (measurable by ability to apply the tools to novel, to the student, problems/situations). Given that he also endorsed Khan Academy in this same article it seems he has no problem with it developing mechanical understanding as a complement to the understanding needed by practitioners (scientists, mathematicians, engineers, etc.).

tokenadult 12y ago

You and onlookers may enjoy reading the article, "Basic Skills versus Conceptual Understanding: A Bogus Dichotomy in Mathematics Education"[1] (1999) by Hung-hsi Wu, for a discussion of what leads to deep understanding of mathematics. Another classic article on the topic is Richard Askey's review[2] of Liping Ma's book Knowing and Teaching Elementary Mathematics, a very good read indeed. [1] http://math.berkeley.edu/~wu/wu1999.pdf http://math.berkeley.edu/~wu/wu1999.pdf [2] http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf http://www.aft.org/pdfs/americaneducator/fall1999/amed1.pdf

deleted 12y ago

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betaclass 12y ago

'I don't know any evidence, that teaching the "mechanistics" of math should lower the chance of understanding it.' I think that's a bit of a straw man. The challenge is that simply getting the right answer, especially in terms of arithmetic (one small piece of math), can mask how well a student understands the underlying concepts and whether s/he can flexibly apply the concepts. Here's a great video on that topic: https://www.youtube.com/watch?v=_ofQ_WnQiZ4 And here's a great video that shows what a participatory classroom with a great teacher can achieve: https://www.youtube.com/watch?v=BlvKWEvKSi8