I've indicated before my love for flea markets and thrift stores. And it's always a good day when I find some math book gem at such a site for a buck or less.
...Today, was a good day!
At a local thrift I stumbled upon a volume I'd not seen before from 1987. It's from Oxford University Press (no slouch of a publisher ;-) so I suspect many of you will be familiar with it: "Discovering Mathematics: The Art of Investigation" by British writer A. Gardiner.** Dover continues to publish it, so it is still readily available today: http://amzn.to/1UIbmn1
I'm not all that far in yet, but my first impression is that it appears very interesting, engaging, and a fun treatment even though in a slightly textbook-ish format... and, perhaps in line with what a lot of current math education reform is attempting to accomplish.
The author's focus is on "mathematical discovery," similar to what others would call "mathematical thinking."
From the back cover:
"The word 'mathematics' usually conjures up a world of more-or-less familiar problems to be solved by more-or-less familiar techniques. This book examines a very different aspect of mathematics, namely how one can begin to explore unfamiliar, fresh ideas and chance observations, how one can pursue them through various stages until the light eventually begins to dawn, and how this whole process invariably throws up other interesting questions one would otherwise never have thought of."
Anyway, take this as a recommendation... if I change my mind as I get further into it, I'll update this post.
Here's an earlier review from MAA:
http://www.maa.org/press/maa-reviews/discovering-mathematics-the-art-of-investigation
** I've seen the author listed variously as "Anthony Gardiner" and "Alan Gardiner;" if someone knows for sure the correct designation I'd appreciate the information.
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