Another problem solving book

I know there already exist books that teach problem solving and contain lots of word problems. Well, there is a new one on the block, now: Solving Math Problems by John R. Dixon. It contains math problems with extremely detailed solutions for middle school, high school, and (some) for college level.

He's made available a superb collection of samples from his book. Each sample has three completely solved problems. There's a sample file for pattern recognition problems, counting problems, word problems, optimization problems, and fun or "recreation" problems.

Even if you're not planning to buy any math books, I encourage you to check his samples and read them through, just for your own learning (and of your students). It isn't often that one finds such detailed expositions on how to solve word problems.

I'm a firm believer in the "apprentice" principle, when it comes to learning problem solving. In other words, one of the best ways to learn to solve problems is to observe an "expert" doing so. (This is why I've often solved word problems here on my blog.) These example solutions can be very enlightening to parents and teachers who might not had much opportunity to witness the thinking that goes into solving even simple problems. For those who can solve word problems easily, such thinking seems to come easily and becomes automated. But for others, it doesn't, and so reading up well-written detailed solutions can help you.

In fact, it would be even more enlightening to witness and expert problem solver solve a problem from scratch and follow his thinking through the incorrect solution paths, as well. You know, all of us, when solving a problem, might (or will) start working on the problem and go down a path that will eventually be a dead end. Good problem solvers monitor their progress on a "meta" level, and "turn back" from those dead ends when they notice them to be so - and try to take a fresh approach.

All too often, youngsters simply give up when such happens! Wrong solution paths are valuable as well. They're just about inevitable when you tackle a non-routine problem!

The book is offered as a softcover for $19.95 and as a download (ebook) fo $9.95. The author claims it's written for middle and high school math teachers, but I feel he shouldn't market it that way — the book has a lot of value for us parent-teachers as well!