I read something recently where a person was talking about her approach to teaching math - that she reassures her class that they are not "bad" at math, but that somewhere along the way, they had a bad teacher, or they missed a day, and the lacking knowledge accumulated so that now they are confused by various things. And I was thinking of how many gaps I have in my own knowledge of math, and how crazy these gaps drive me when they show up.
It's hard to even recognize that something is caused by a gap. A certain topic will show up (infinite series, say, or rules of limits) and my mind will just go "that's too hard" or "I can't do those" without asking why. Are these topics somehow such that I alone cannot learn them? Do I have some tiny genetic flaw that has knocked out the part of my mind that would let me understand what a Taylor series is?
No. I just don't understand something because I have some gaps, and the thing to do, then, if I'm serious about math, is to figure out what the gaps are and fill them in. It's unlikely I'm missing anything that I can't learn, so I need to just get on that, as it comes up. And now that I'm finally more of a badass about reading and understanding math, I'm in a perfect position to do so.
4 comments:
The title of this post made me think of discontinuities.
I think pretty much any math beyond arithmetic is something that you would never be "alone" in not learning, though I agree that it seems unlikely there is a brain developmental disorder or lesion/insult that would have the specific effect of not letting you understand Taylor series.
Your use of the word "insult," which I take to be a technical term, made me smile a lot. In a Sally knows words and stuff! kind of way.
Although I wrote "I alone" I think I may have meant kind of the other thing - that there isn't something about, say, Taylor series that is so different from the math I already know that I am incapable of learning about them. Because you're right, of course - plenty of people don't understand basic things.
Strangely, there does appear to be some evidence for a double dissociation between multiplication and subtraction in dyscalculia - i.e. some people with brain damage can multiply but not subtract and others can subtract but not multiply - which I assume (but have not read the literature) is related to differences in retrieval of mathematical facts vs. making comparisons (since people often the learn the multiplication tables by rote memorization).
And yeah, insult is just another word for injury.
Well, sure, insult and injury must be the same kind of thing or you couldn't add one to the other.
:D
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