How much time should be devoted to trying to actually answer the questions posed?
Is there a distinction between posing problems that test knowledge and posing problems to gain knowledge? Should there be?
If a student asks an insightful question that can only be solved using mathematics well beyond his/her background, should the teacher answer the question without justifying it?
Does problem posing by students tend to lend itself to a less linear style of teaching?
How can classes be kept focused when asking such broad and unrelated questions?
Do students benefit from brainstorming questions with peers or is a more solitary approach generally best?
Do more academically talented students tend to ask questions that are more or less insightful than their peers? Do they think of problem posing as a useless exercise when they already understand the material?
Does it get overwhelming for students to have more questions than answers?
Have any in-depth studies been done on the effectiveness of students using these problem-posing techniques to increase mathematical understanding?
How can we assess how well a student problem-poses? Should we assess it at all?
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