|  Fephisto | Sep 25, 2007 5:10pm | So, I became a TA....today, and taught my first class. I sucked horribly, and noticed that all the teachers I tried to avoid becoming, I had become.
Any advice for teaching? |
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Sponsor |  Morosoph | Sep 25, 2007 5:25pm | Teach a small group or individuals first, I'd suggest; it's much easier to get on their wavelength and push their boundaries.
Once one understands small-group interactions, a class can be considered as a complex maze of them (assuming that your method isn't chalk and talk). Teaching well is hard.
I've only taught small groups (eg. a philosophy group, when it's my turn to present) and individuals (including maths). People tell me that I'm good at it. I did teach a class a couple of times, since my school used to have one day in the year when the six-formers would take over from the teachers; I made sure that everyone was suitably challenged :o) |
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Sponsor | | disconcision | Sep 25, 2007 5:55pm | | 1: What kind of material are you covering? |
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| | Fephisto | Sep 26, 2007 5:39am | | I'm covering Trigonometry. My class is of about 30 people, and, double unfortunately, I immediately went to 'chalk and talk' method. In my defense though, it's the method I've been seeing in every math class I've been in. |
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Sponsor | | disconcision | Sep 26, 2007 7:35am | "I'm covering Trigonometry."
Please don't even entertain the idea of using a single 'kite problem'. :)
I remember my school introduction to trig: How far is the kite from the ground? How long is the string of the kite? What's the ground distance between you and the kite?
I'm just saying that 'applied examples' aren't defacto 'applied' unless the application is something anyone would ever do, ever.
I've got no experience in teaching, other then a couple months TAing Calc. Pre-secondary math and physics education were very frustrating for me; trig seemed like a lot of memorization to me; complex exponentiation makes it completely straightforward by connected the (relatively unusually) defined trig functions. Suddenly they were connected to the 'rest of math' as I'd been taught.
Of course, the prerequisites for the above approach pretty much eliminates its usefulness.
Like I said, I TA'd a little... 30 people is harsh. Younger kids should get smaller class sizes, not larger ones. I'm assuming you're teaching children and not adults for their 'high-school equivalency' or whatever?
Anyway, regardless of audience, I would suggest introducing some animated content to your class, or (better yet if you can get the resources), physical demonstrations. In particular I'm talking about using simple harmonic motion. It's a great intuitive way for conveying that sine/cosine curves are just 'different way of looking at a circle'.
'Practical' trigonometry is all about getting your hands dirty, anyway. I like the idea of approaching it through (something along the lines of) tinker-toy or mechano models involving pivot points. That way you have triangles the students can both look at and touch.
I mean, a simple example would be showing the validity of side-angle-side and other conditions for ensuring congruence. Just give out some straight-edge mechano pieces + pivots to small groups and let them figure out what things needs to be constrained. Then groups can present their findings to the class or somesuch.
Oh yeah, and try to come up with something funny and embarrassing to reinforce SOHCAHTOA. If you remember SOHCAHTOA, how to measure angles and distances, and how to use a (scientific) calculator, then you're pretty much set insofar as 'trades trig' is concerned. Some people put entirely too much effort into showing how to obtain exact values for certain angles. Useful? Yes. But it's often more complicated then is really beneficial for the majority. Who will use calculators.
"Once one understands small-group interactions, a class can be considered as a complex maze of them"
I really like this perspective. I really like the idea of turning these small groups into 'working groups', trying to figure out part of the curricula themselves based on hints you give in a short introductory chalk-talk. |
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Sponsor | | Morosoph | Sep 30, 2007 7:23am | | Sock-it-to-ya? |
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| | Fephisto | Sep 30, 2007 10:37am | This is a college class, and there is a main lecture. So, it's not like I'm 'teaching' the material, I'm just reviewing it for them.
Either way, I'll try something more active next time and see how it goes. (btw, they're currently going over trig. identities) |
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Sponsor | | disconcision | Sep 30, 2007 5:03pm | I've always thought of trig identities as being really self-indulgent. What is the pedagogical justification for the?
I always found them to be enjoyable; I interpreted them as 'mazes', in that one can start at the both the beginning and the end, and from each 'position' apply a certain set of allowable transformations (i.e. directions available for you to turn), coming together (or failing to) in 'the center'.
I suppose in that sense it's a good introduction to proofs, but I'm not convinced it's the best. And if it's the kind of thing you'd enjoy then I doubt it would actually be useful for you.
Is the reason just that people don't like to deal with imaginary numbers? I found most of (local, curricular) high school math was spend badly tiptoeing around them in situations where they'd make practically everything simpler.
I mean, in terms of pragmatics trig identities can be entirely summed up by e^ix = cis(x) plus definitions. Trig identities hide (transform) the fact that it's 'just algebraic manipulation' in a way that makes the subject seem more meaningful then it legitimately is. |
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Sponsor | | Morosoph | Sep 30, 2007 5:23pm | The ? is to ask "will this do?"
I agree that so many identities are a lot easier if you allow complex numbers. Awkward geometric proofs can now be substituted with algebra. Brilliant!
As for introducing proofs, group theory would be good, IMO, but apparently they try introducing it at around 14, but it was a failure. Whether this was because the pupils couldn't grasp it for being too abstract, or else the teachers couldn't teach it because it was too different, I do not know. |
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Sponsor | | disconcision | Sep 30, 2007 5:58pm | 9: Yeah, I'm currently trying to educate myself on the 'new math'. It seems so well-intentioned. I think it's a problem of using 'conceptual metaphors' (in the George Lakoff sense) that are inadequately present in everyday 'conversational' reality (see my "1 != .999.." thread). So it's everybody's 'fault', really.
I'm still open to different interpretations. Some of the 'New Math' canonical literature seems a bit... I can't deny there may be some inherent intuitive disconnect (i.e. mental structures that have to be in place first, at least for the majority of students).
I dunno, maybe most people just don't deal that well with abstraction. It makes me really sad, because when I got into basic group/set stuff through International Baccalaureate when I was 14-ish, it was one of those things that immediately 'expanded my mind'; I was able to conceptualize so many previously acquired ideas in a simpler fashion. Not just 'math'.
Reminds me of when I finally got my hands on a basic calc text and became super-pissed at my high-school physics teacher for drilling rote formulas (e.g. dynamics) that are trivially derivable from basic principles. It's the same with the imaginaries. So annoying, so many years wasted. At least I learned complete mistrust for 'teachers'. :) |
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