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I am a big fan of Love & Logic for discipline. I was fortunate enough to learn about it way back when I was student teaching. I used in it my classroom and I use in now as a parent. One of the central themes of Love & Logic is that we, as adults, need to have a "silent smile" when kids mess up. As uncomfortable as it is to watch your child make a bad choice...the beauty of that bad choice is that it becomes an opportunity to learn something. The same could be said of problem solving...we have to give children the opportunity to struggle, make choices, make bad choices, and learn from those mistakes. It is in those mistakes that learning...real learning...can occur.
There's another tenet of Love & Logic where I see a huge connection to problem solving...it has to be real. With Love & Logic, kids have opportunities to make decisions in the real world & then they have to live with the natural consequences (good or bad) of their decisions. I love the examples that Mr. Meyer gave about how to take a textbook problem & make it real. That's what math is about - real life!! When you're trying to figure out something mathematically there's nothing there to break the problem down into steps for you...there isn't a "math expert" standing right beside you to help you solve the problem (usually!). Regardless of the grade we teach, we could all take a word problem from the textbook and tweak it just a bit so that is becomes real...meaningful...to the students.
Ask fewer & shorter questions...and be less helpful. It's the most helpful thing you can do!
