How to teach students to ask Polya-type questions I've recently read "How to Solve It" by Polya.  In that book, the author basically explains the method that I use in my own teaching - asking relevant, prompting questions to get students to reason through a problem.

However, I have a problem with this method (including in my own teaching) - the real challenge should be to get the students to ask those questions themselves.  I'm not doing anything other than asking "the right" questions to get the students to move forward, but they aren't spectacularly difficult questions to come up with on your own.

I fear that all I'm doing is pushing the responsibility back on myself by taking away the really hard part of problem solving: figuring out the path you need to take.

So how do you teach students to ask good questions while problem solving without the need for teacher assistance?  We can limit the question to STEM problem solving if we'd like, but I'm sure this problem exists in non-STEM fields.
Like most things, students need to be actually taught to do it. And "taught" doesn't mean having it explained to them, but rather practicing it via some sort of planned exercise or activity. 

It is an interesting idea, though. 

What I would do is to periodically hold a brainstorming session with students, assuming that the scale is reasonable. Take a problem that they haven't solved and ask for questions about it. Don't answer the questions, but ask for more questions - beyond the horizon questions - outrageous and maybe only potentially useful questions. Spend time on just gathering questions, making something of a game out of it. Note that I've done similar sorts of "gaming" activities with adult doctoral students, so don't assume that this just works with youngsters. 

Talk to them about what sorts of questions are generally useful. What is a smaller problem than this that we know how to solve? What is a related question? Where could we find information about this question? What do these words actually mean, individually and it conjunction? 

After you have a bunch of questions, try to have the students sort them in some way. Which are useful for this idea? Which are useful for extending the idea, or a related idea. 

If you practice this with them they will start to become more comfortable thinking that way, though you can probably expect more classroom interruptions in the normal course of things.