wcarey

17 ms·

121.
by wcarey 6y ago
The idea that "when you extend that" is something human beings can do is an absolute revelation to young mathematicians. The idea that our notations are, at least in some sense, choices that we make that come with tradeoffs is a h
122.
by wcarey 6y ago
As you say, the artistic use of cross-object synthesis and analogy definitely distinguishes the advanced students from the mechanical. Advanced students develop a sort of dialect that harmonizes the mathematical objects they encounter in a
123.
by wcarey 6y ago
I also didn't encounter it until I was relatively older. Our school has been pushing to introduce more rigorous language and definition in our 7-12th math program. For some students, it really seems to help. For others, it's reall
124.
by wcarey 6y ago
I mean, the general case is certainly trouble for kids. But 15% and 20% look very similar to 15x and 20x. That the two (sometimes!) operate using different rules causes confusion for many students. The implicitness of the fractions conceals
125.
by wcarey 6y ago
Is that commonly done?
126.
by wcarey 6y ago
Absolutely terrifying. How did he communicate with other peer mathematicians?
127.
by wcarey 6y ago
Indeed. And if they're cartesian vectors, you're good. But if that second number is an angle measured in radians, you use yet a different set of rules for the addition. The conversation with 16 year olds when you explain that thei
128.
by wcarey 6y ago
How would you explain that successfully to fourth graders? (Or, for that matter, seventh graders?)
129.
by wcarey 6y ago
> I have a lot to say about notation in math, but this isn't the forum. There are a lot of crimes committed, agreed, but some of the things people pick out are only bad because they don't know the context where they redeem them
130.
by wcarey 6y ago
What isn't really true?
131.
by wcarey 6y ago
Perhaps an argument for arithmetic followed by geometry using Nicomachus and Euclid. We sit on that until 9th grade, but I wonder how young you could go with it?
132.
by wcarey 6y ago
And + is overloaded in a bunch of ways students encounter in high school, and much time is spent talking about when you're allowed to add and when you're not and which rules apply when. Examples: 1 + 2 - fine. 1/2 + 1/2
133.
by wcarey 6y ago
And so it is. edit: I suppose, what I'm trying to get at, perhaps too glibly, is that audience matters terribly much in mathematical writing. In the same way that Latin students don't start with Tacitus or Sallust, famous for th
134.
by wcarey 6y ago
Thanks! I hadn't seen the retraction. That's really interesting.
135.
by wcarey 6y ago
Right. Of course, if you write x(3), other mathematicians should frown at you because you're making bad notational choices. It's a bit like explaining to students that the real way to know which 3rd declension nouns are i-stems in
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by wcarey 6y ago
The more I've taught math, the more convinced I am that getting people to "think about what they mean", and to think about what mathematical words mean is 90% of the project. I remember reading long ago (I'd love to fi
137.
by wcarey 6y ago
This is a lovely (edit: having been in similar shoes, also terrifying-in-the-moment) example of a broader problem in teaching mathematics: the language we use to describe mathematical reasoning is a natural language, like English or Latin,
138.
by wcarey 6y ago
An interesting take for sure. I too read it as a coming of age story - also strangely comforting - but see the part after the plot proper begins as an allegorical coming of age story as well, recapitulating (and I think I can say this wit
139.
by wcarey 6y ago
How far into Anathem did you make it? Anathem has a glacial beginning - the introduction is perhaps 200 pages long. But once you've survived that and the plot starts, it's quite compelling and pays off the glacial introduction. Th
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by wcarey 6y ago
Right - do you draw the distinction between the cases you propose philosophically then? I'm on board with an a priori commitment to the idea that we are not actively deceived in our observations of nature, but I think without the sam
141.
by wcarey 6y ago
How would you distinguish using science-qua-epistemic-method between a world where all claims of causal regularity were false and a world in which scientist were actively deceived?
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by wcarey 6y ago
The do have several articles of the sort you're interested in: https://www.nytimes.com/2020/04/16/business/economy/coronavi... https://www.nytimes.com/2020/04/13/
143.
by wcarey 7y ago
C++ is the language with which I’m most comfortable, having used it professionally for the better part of a decade. I’ve gone back and forth on using it in HS. It’s abstractions are so opaque if you don’t already have a well developed model
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by wcarey 7y ago
Thanks! Definitely an interesting tool. Two of my students are fascinated by the idea of undefined behavior right now (having run into it in practice; the idea that off-by-one errors sometimes crash their program and sometimes behave "
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by wcarey 7y ago
I haven’t - is there a good tool chain you’d recommend me checking out? What’s the enduring idea in ada?
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by wcarey 7y ago
Thanks!
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by wcarey 7y ago
I've been doing the same! It certainly helps for strings. Pointer block diagrams (like K&R use) seem to help too. Mostly what melts their brains is the idea that an identifier can be "in two places at once" - for example,
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by wcarey 7y ago
It's a three year rotation: Python, C (Unix), C (Arduino). My goal with the class is to teach ideas that will stand the test of time. C (and Unix) certainly fit that bill. Happily, the tooling is the easiest part. Every student has a r
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by wcarey 7y ago
I'm teaching C to high schoolers as their first language, which is quite the adventure. Do you have any good advice or resources on how to introduce the way C treats the function stack and heap allocated memory? Most of my students str
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by wcarey 7y ago
Fascinatingly, a verdict means “a speaking of the truth”. Courts at least, consider the aim of the jury to speak the truth. So whether John did punch Jack would be an element of the truth of the matter being adjudicated.

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