Though it'll be a few days before my MATH 280 students submit their final take-home exams to me, I'm already excited about their responses to the last problem on the exam, a very open-ended one which reads as follows:
Go back over all of the topics we've talked about in our class this semester, and select one about which you'd like to know more. (Please try to make your topic a relatively narrow one..."binomial coefficients" would be a good choice, for instance, whereas "combinatorics" would be a bit broad, and "proofs" would be faaaaaaaar too general.) Would you like to see more examples of a particular topic, or further applications of it? Would you like to know more about where it's used in mathematics, or how it connects with other topics we've considered? Do you have a specific question about it, or are you simply interested in learning more about it in general?
Having chosen a topic which you find sufficiently intriguing, write a few paragraphs about that topic. (As always, please use complete, grammatically correct sentences!) Your discussion should indicate clearly why you find your topic intriguing and what about it you'd like to know more about. If you have specific questions, please feel free to raise them. If you have answers to those questions, even conjectural ones, please feel free to share those as well! My goal here is not to get you to answer questions so much as to ask them.
One of my students caught me in the hall a half hour ago and asked if "LaTeX" would be a valid topic for this question. I only hesitated a moment before responding with alacrity: "that would be awesome!" I'd really like to learn more about how students make use of LaTeX, and if they feel it helps them (a) express themselves mathematically with greater effectiveness, (b) present themselves as authentic creators of mathematics, and (c) engage mathematical ideas at a higher cognitive (or metacognitive) level.
To this last point: I hypothesize that in using LaTeX a student is forced to include an additional reflective/analytical stage in her writing process, at which stage the student more carefully than before or otherwise scrutinizes word choice, notation, and other aspects of her writing. I'd love to study this more carefully...maybe some of my Charleston posse would like to take this on with me as a side task. Any other takers?
5 comments:
Latex forces an understanding of what you are writing about far beyond that of turning in homework assignments, at least from my experience. I think this 'ups the game' of prospective mathematicians, and forces an understanding that supersedes turning in hand-written assignments.
@BBB: ...and this is exactly the kind of behavior we may be able to identify through more careful study! In any case, I think it's an interesting phenomenon to investigate. We'll see what we will see...in any case, even if you're right, the worst that results is very easy-to-read nonsense rather than hard-to-read nonsense.
I'm not sure I agree. I've seen students learn to use LaTeX and then proceed to simply type up their homework. While they may learn the syntax associated with LaTeX, this hardly requires them to think any more than doing homework problems by hand.
Hi Doc - I deleted my comment and re-posted it with my real name. And I agree - easy to read nonsense is preferable to hard to read nonsense.
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