I was in Math high school and in Math class. We had 12 of mixed math per week: algebra, geometry, linear algebra, probability and what not. Too bad in college we couldn't pick classes like in USA, so we had to do some of them over again in 1st and 2nd semester. Our math teacher was a very old, smart and animated Jewish guy. He received money from Soros fund for being awesome, and also survived Nazi blockade of Leningrad. In his 80s he still went there EVERY year to walk across frozen lake in memory of that event.
For 4 years he taught us he always asked after explaining the task: so, Joe, what do you think we should do here? And we can go on and on about how we should find a common denominator or perhaps build an additional triangle and... he just smile and say "we need to think". And then he will tell us step by step his thought process. By the end of the 12th grade we all knew answer to that question.
