I had a copy of John Van de Walle's book on my desk the other day when a student asks, "Mr. Cox, what are you reading?"
"Oh, this book on how to teach math. It's pretty interesting."
"Oh, yeah? What's so interesting about it?"
"Well, I like this chapter on Teaching Through Problem Solving. It mentions three different ways problem solving can be taught: Teaching for problem solving, Teaching about problem solving and Teaching through problem solving."
"What's the difference?"
"Well, teaching for problem solving is when students will learn a certain set of skills and then later be asked to solve a problem using those skills. Teaching about problem solving is when students learn about particular strategies for solving problems. And teaching through problem solving is when students are given the problem first and then they figure out how they want to solve it. It's kind of the opposite of teaching for problem solving."
"Hmm. So teaching for problem solving means the teacher shows us how to do stuff first?"
"Yeah, pretty much."
"They don't think we can think for ourselves? That's kind of offensive."