One of the hardest things to convey in math is the sudden realization you get from seeing all the parts of the picture come together. It is however, one of the most satisfying moments, and one when you realize what math is truly supposed to be about.
Martin Gardner even wrote two books on various types of these experiences, which he calls an aha! solution, now combined into one volume, aha!: a two volume collection. To start getting an aidea of just how satisfying such an experience can be, take a look through it online for free here.
Joe Hurd, in his 5-minute Visual Mathematics lecture, gives some more examples of this:
There are many more excellent examples of this type of thinking at BetterExplained, one of my favorite sites. I've also written my own posts on visualizing Pi, math, and scale. Thanks to StumbleUpon, I've managed to find many great great sites about visualization.
James Tanton brings home the importance of seeing mathematics in pictures in his presentation, Five Principles of Math Genius Thinking:
Part 1
Part 2
I'd love to hear any aha!-type experiences you'd care to share in the comments!
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How to Think Like a Math Genius
Published on Thursday, October 07, 2010 in books, fun, innumeracy, Martin Gardner, math, psychology, videos
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3 Response to How to Think Like a Math Genius
more posts like this please
Thanks for sharing my videos! I am delighted that what I have to say is in line with what people like to hear and consider.
See page 10 of: http://digital.ipcprintservices.com/publication/?i=24870
for examples of visual things kids have done!
Cheers,
JT
Glad I stumbled across this. I wish schools would teach this way. I remember a teacher that finally explained to me why x^0 = 1. I was so grateful. I can't stand memorizing formulas without understanding them. It's like using a word without understanding its definition.
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