Q1: I think it takes less time to do problem solving. Also, using problem solving allows them to pull from their own understanding/background is more effective.
Q2: They will force me to seek out help from other teachers. From my experience, I have learned that some students get it better when someone else explains the concept. Often, other people can explain things in way that's easier than myself. Different strokes for different folks
Q3: I would argue that they don't have to discover 'everything' and we as teachers have to be creative enough to pull children close enough to the answer and solutions without giving it to them. Usually, "reinventing wheel" for themselves proves to be better for them in the long run.
Q4: You can ask them to explain how they got to where they are in the problem. You can ask them questions that force them to think more critically about the problem.
Q5: They were asked to build on their prior knowledge and pull from previous mathematical experiences.
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