The Art of Problem Posing - 10 Questions

1. What qualities should “good” and “bad” questions have and what are the strategies for distinguishing them?
2. In what specific ways and/or how can problem posing for students help them to better understand mathematical concepts? Evidence for this?
3. How does our past experiences and goals limit our thinking?
4. Why is it that students with prior knowledge to a certain mathematical topic have difficulties devising observational questions?
5. How can we pose problems that will engage and keep students focused on the problem presented?
6. How and in what ways do we see things differently when we pose questions?
7. What constitutes a “foolish” or “nonsensical” question?
8. What are ways to avoid imposing “a context on the situation”?
9. What is the strategy for challenging the given?
10. What are/is the most effective way for posing the “general questions” that applies to a very specific mathematical topic.
Yes, one last question.
11. How or in what ways should we ask students questions so that it is not too overwhelming for them to answer?