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 ================================== "Computer science is the new mathematics." - Dr. Christos Papadimitriou ==================================
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