[Edu-sig] "dot notation" (in favor of sharing it)

[michel paul]

Hey Kirby,

I've enjoyed the discussion, and of course I completely agree that dot
notation deserves attention in current math education. However, getting
that discussion going? Wow, from what I've seen ... it would be nearly
impossible. It would pretty much just get ignored.

Yesterday I was involved in a math education group at my school where an
example suggested for introducing 'function' was 'toast'. Basically, you
put bread into the toaster, and <magic/technology happens> out comes toast!
So 'toasting' is a function. Seems to make sense, right?

Well, sure, so long as you're allowing for mutation!  A slice of bread is
an object, and, like most objects, it can change its state. Makes total
sense.

However, is that really what they're thinking about? in traditional
mathematics, the kind they think they want to teach in school, variables
aren't supposed to change their values once assigned. That's a huge deal. The
discussion went on from the toaster to use an example like f(x) = x + 2,
let's say. You put in x, and out comes y. OK ... however, x is still x. x
did not become y. If you say x=5 then a little while later say x=7, well,
it sounds like you're running for office! So the analogy actually breaks
down. A math teacher would not want their students to develop the
misunderstanding that x turned into y. If you actually want to say that,
that's OK, we have developed ways to express that.

So it seems to me there are unrecognized conflicts in schoolish
mathematical thinking, and I believe discussion of dot notation and other
aspects of computational thinking could help shed light on them, could make
the unconscious conscious.

-- Michel

==================================
"What I cannot create, I do not understand."

- Richard Feynman
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"Computer science is the new mathematics."

- Dr. Christos Papadimitriou
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