10 Questions/Comments on “The Art of Problem Posing”:

1. Do you think it is a good idea to teach students problem posing skills at all? 2. If yes to question 1, at what stage of teaching do you think we can encourage students to pose questions? 3. Which one do you think it is better for students: limit and guide students the kinds of questions they pose, or let students ask any questions they come up with? 4. For x^2+ y^2=z^2, you have actually come up with many questions I did not expect, do you think it is a good idea to raise so many questions to ask the students? 5. Do you feel that too much broad questions will distract students instead of keeping them focused? 6. Which types of questions do you think teachers should focus on to present to students? 7. At the beginning stage of learning of a topic, I would let students focus more on internal exploration instead of external exploration, do you agree with my idea? 8. I feel approximation instead of exact answer is a very important technique which most high school students lack. What types of questions are you going to use to introduce approximation ideas to students? 9. Comment: Historical questions are actually good group projects for students. I feel students should explore the history of math and math stories by themselves. 10. Comment: You have offered some very effective problem posing techniques. I am especially impressed with the idea of “challenging the given”.