How can critical thinking be promoted in education?

KThompson's answer concludes that critical thinking is awkward for the established curriculum, because unorthodox views would not be acceptable.

However, I am a firm believer that education is better if discovered instead of assimilated by force.

So how can we get the best of both worlds?

Critical thinking can be used to lead to an acceptable, established viewpoint by positing an "incorrect" position and asking students "what's wrong with that?"

For example "It is a well-known fact that slavery is good for mankind's progress. Comments anyone?"

Or "Poverty in the world could be eradicated by giving the poor $50,000 each. Comments?"

Or "Everyone is happier living in a dictatorship."

But how can critical thinking be used when facts must be learned - for example geometry. I don't know how you can critically think your way to Pythagoras. But - the motivation to apply oneself to such learning could be encouraged by asking students to consider, for example "Why would someone want to build a bridge across a river?" And then, having established some reasons, "OK, so how would you go about building the bridge; what would you need to know?" And, as ideas emerge, pick up on them and ask for example "So what will be heaviest thing your bridge will take? How will you know that your design will cope?"

And then eventually "Well, we don't have to work all these things out ourselves, because some very clever people in the past figured out this stuff - wanna see?" And then, as the explanation unfolds, ask "what do you think of that? What might follow from that?"

So for me the idea is that if students think their own way through a topic, much more will "stick".