GS Chandy
Posts:
7,761
From:
Hyderabad, Mumbai/Bangalore, India
Registered:
9/29/05


Re: Square root of six
Posted:
Aug 27, 2012 10:23 AM



If I were actually doing any teaching of math students, I'd simply try to find out:
i) Do they 'get' it (the 'it' refers, of course, to Newton's method for square roots; Duveen's development; or whatever).
I do (to some extent; not entirely) accept Robert Hansen's [RH's] critique of Peter Duveen's reasons for doing this.
ii) But the heart of the matter is simply this: DO THE STUDENTS FIND THE MATH INTERESTING?
If yes, excellent  you're in very good shape! Proceed!
If not, the teacher needs to find out out just *HOW* to make it interesting.
Skills and fluency in using specific methods and tools will follow automatically  IF [and that's a very big "IF", indeed!] students find it (i.e., math) basically interesting.
I'd guess a teacher should seek to ensure that at least 60% of his/her students find the math interesting. (To expect 100% students to find it interesting is probably too ambitious. But that could lead to another useful 'Mission': how to make math interesting to the 'other 40%'? This one would probably require some 'special handling'  and would be MUCH more complex).
If at least 60% of students DO NOT find the math class interesting, some 'foundational work' is needed  on "how to make the class interesting".
That work may involve redeveloping available methods further (as Duveen has done);
Or:
It may involve something else entirely: like, for instance, *demonstrating* that math CAN be interesting, fascinating, etc, etc.
[As stated, I'm NOT a math teacher  but I did solve the underlying problem for my 13year old granddaughter Mimi, who had come to me with the complaint "Oh, math is SO UTTERLY boring!"
[To demonstrate to her that her idea about math was seriously mistaken, I showed her how to construct a "Yoshimoto Cube"  see, for instance, http://gizmodo.com/5121432/yoshimotocubeblowsmymindthenfriesmybrain; http://www.boingboing.net/2009/01/19/funwiththeyoshimo.html; http://www.momastore.org/museum/moma/ProductDisplay_Yoshimoto%20Cube_10451_10001_45657_1_26698_26698_45658. (The MOMA store sells a very snazzy Yoshimoto cube for above $ 50, which I felt was way 'beyond budget', so I figured out how to make one using thin cardboard, slightly thicker than what is here called 'KG Board'... there are, of course, any number of things apart from the Yoshimoto Cube. I recall, during my early school career, being highly turned on when I was shown the properties of the Mobius curve/strip, using simple KG Board).
[Well, I convinced Mimi that all the 'boring' stuff of math could lead to a whole lot of fascinating things like this. She really got turned on by that, took the cube we'd constructed to school, managed to turn on a few of her student peers  then later she started a 'math club'. She's 16 now, will be appearing in a couple of months' time for her IOS exams (the first level of high school in the Indian Open School system).
[I had at that time developed a few models that helped to show me just how to proceed in the case, specifically wrt the Mission: "To demonstrate to Mimi that math need not be boring at all". These models helped in great measure to guide me, and later Mimi as well. If I recall rightly, I had attached some of those models to some messages at Mathteach, to illustrate my point. (I also recall that RH  of course  got the horse by the wrong end (by the tail instead of by the reins, and misunderstood entirely [as he continues doing to this very day]).
However, my then 13year old granddaughter Mimi did not misunderstand; she later made some small models for herself that, continuingly developed, very successfully guided her through the rest of her school career  in math and in many other things.
Most importantly (as far as I was concerned), she NEVER EVER found math boring again! (Which was the real point of the whole exercise)].
Information about the tools that enable us to model, in exactly the kind of detail that's needed for any specific issue is available in the attachments herewith.
GSC ("Still Shoveling Away!")
Message was edited by: GS Chandy

