
Why Does Exploding Dots Work? - dwohnitmok
https://mathenchant.wordpress.com/2018/06/16/why-does-exploding-dots-work/
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romwell
FWIW, the answer to the question in the article (why you always end up with
the same set of coins if you don't use quarters) is "Diamond Lemma"[1]. The
author does mention it in a footnote, but doesn't go into details.

As a mathematician, I love the concept. I love New Math, too, however -- and
yet it was not a success.

Why? I believe that the article is asking the wrong question: will _the kids_
get it?

The question to ask is: will _the teachers_ get it?

Given that the answer is hidden in the footnote (and is usually not taught
unless you're getting a graduate degree), I am pessimistic about that.

I've spent a long time thinking about how we can teach math better (and quite
a bit teaching it, mostly as a TA, but also as an instructor and tutor). I
think the answer is -- we have to raise a new generation of _teachers_ before
even trying to change the curriculum or methods in any way. As it stands, a
college degree in math education (or even _mathematics_ , sadly) does not
prepare someone to be able to do mathematics. And that's the thing that needs
to change _first_.

[1][https://en.m.wikipedia.org/wiki/Newman%27s_lemma#Diamond_lem...](https://en.m.wikipedia.org/wiki/Newman%27s_lemma#Diamond_lemma)

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webkike
I'm confused, isn't exploding dots just binary?

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Jtsummers
Not just binary. It seems to be teaching the place value idea with a graphical
representation. It would work for any base.

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schoen
In fact, it seems that the representation is also used to study polynomials
and other objects.

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foobarbecue
For binary, I like this better:
[https://youtu.be/zELAfmp3fXY](https://youtu.be/zELAfmp3fXY)

