Further my post dt. Jun 21, 2013 5:18 AM (http://mathforum.org/kb/message.jspa?messageID=9141612): > > Joe Niederberger posted Jun 20, 2013 8:48 PM > (http://mathforum.org/kb/message.jspa?messageID=914137 > 8): > > GS Chandy says: > > >A couple of years later, we had a math teacher <snip>> > > It was very long ago, and I don't know if my memory <snip> > > Those of us that he did manage to reach soon decided > (more or less on our own) that we should do the 'hard > stuff' of math by doing plenty of problems, etc, etc. > And then we also discovered (to some extent on our > own) plenty of interesting and useful tricks about > how to do stuff with numbers that had earlier been > boring but which now suddenly had become quite > interesting. > <snip> In the above, I specifically note that several of us did, in fact, learn (as noted, to some extent on our own; though with a good bit of help from that teacher, Mr Maiden) - we learned practically all the needed tricks of computation that we needed to handle in real life. (I rarely deal directly with numbers these days, so I do not now recall those tricks much).
I do recall that, many years later (while I was in engineering college, I became known as something of a whiz kid at mental computations AND also at using a slide rule in ways that 'the books' scarcely ever showed. For instance, I read a hint somewhere that the slide rule could be used to help solve quadratics - and I then taught myself how to do that; as well as to do plenty of other quite complex stuff (approximate solutions of differential equations, etc) for various engineering calculations using the slide rule.
Now, I am NOT claiming that I (or any of that group of students who got 'turned on' to computation - and, in my case, to pure math) could ever achieve the 'miraculous' insights and powers of Gauss (or even of much lesser mathematicians).
E.g., recall the two astonishing stories, recounted by Eric Temple Bell in "Men of Mathematics":
i) how Gauss at age 3 was able to discover (through mental computation) an error in his father's computation of the wage bill of a sizable number of workers whom he (the father) supervised; and
ii) how Gauss at age 6 or 7 discovered that a long list of big numbers given to the class to add up were in fact in 'arithmetic progression' (AP); applied the AP formula (which he had worked out on his own, and gave the answer - almost the instant he had been given that problem!].
I do not have access to that book right now, so my retelling of these two minor miracles wrought by Gauss may contain some errors of detail.
Nor, for that matter, do I claim that any of us developed the kind of insights that "Young Archimedes" (Guido? Carlo?? I don't have a copy of that book now) had - as recounted in the beautiful short story of that name by Aldous Huxley. ['Young Archimedes' on his own, age 10 or so, re-discovered the Pythagoras Theorem with no help at all!!!]
I AM claiming that several of us actually learned how to perform 'numerical computations' quite- perhaps very - proficiently (and and even to truly enjoy working with numbers) - DESPITE having been entirely turned off by the 'by-rote math teaching' to which we had earlier been subjected. (It does appear that a quite sizable number of children who may not be 'good at math' in our conventional school system, do in fact possess quite good math skills).
[I need to make the above clarifications view the distortions and falsehoods, about OPMS for instance, that have been made by one of my critics here. If I do not make such clarification, he may well state that I had claimed I was another Gauss!]