Timeline for What are the qualities of a good (math) teacher?
Current License: CC BY-SA 2.5
8 events
| when toggle format | what | by | license | comment | |
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| Aug 3, 2013 at 12:01 | comment | added | Sergei Akbarov | I saw math teachers who are unable to build a logical chain carefully, without gaps and/or mistakes. I think, Jose had in mind that a teacher must have enough qualification for doing this in case when he sees that his pupils don't understand the logic of the exposition. Not that every time he must explain each millimeter of the proof. Am I right, Jose? :) | |
| Jul 25, 2010 at 21:14 | comment | added | Richard Dore | I agree (to a point) with Anton. The goal should be for students to reason precisely. More fine, detailed steps should be a means to that end. Demanding justification can add or subtract from this goal. You want justification where being ambiguous or unclear affects the reasoning. But demanding every minute justification may undermine the cause -- students might view such steps as symbol pushing disconnected from the "real" reasoning. | |
| Nov 14, 2009 at 16:42 | comment | added | Jon Awbrey | @Anton : Thanks for the frabjous essay! I'll have to print it out and give it another couple of readings. | |
| Nov 14, 2009 at 16:06 | comment | added | Jon Awbrey | The level of detail that suits the teachable moment at hand is of course a judgment call, but the rule of thumb that reason must be given where reason is due — that, I think, is basically sound. Our teaching seminars in grad school expressly cautioned against impressing students too deeply with the "Bag of Tricks" theory of mathematical prestidigitation. Sure, we all love those tricks, but leading students down the path of thinking that math is "nothing but tricks" is going a bridge too far. | |
| Nov 14, 2009 at 15:34 | comment | added | Anton Geraschenko | For an argument longer than 600 characters, see Paul Lockhart's "A Mathematician's Lament" (maa.org/devlin/LockhartsLament.pdf), which I first came across in this question: mathoverflow.net/questions/5074 | |
| Nov 14, 2009 at 15:30 | comment | added | Anton Geraschenko | I disagree with this. Carefully justifying every step very much sends the message that math is a collection of boring symbolic manipulations. When I do mathematics, I don't justify every step, and I don't think kids should either. Unless it's the crux of the argument, I would never say to a kid "hold it right there; how do you know the sum of two even numbers is even?" The place for careful arguments is when something interesting happens, when your intuition (or something you "proved") says something you know is wrong. Kids should learn the value of being meticulous, not have it forced on them | |
| Nov 14, 2009 at 14:40 | history | made wiki | Post Made Community Wiki by Anton Geraschenko | ||
| Nov 14, 2009 at 13:54 | history | answered | Jose Brox | CC BY-SA 2.5 |