Comments, Questions on "The Art of Problem Posing"

1. Asking students to pose problems has really changed the way I perceive teaching mathematics. It has opened unlimited possibilites for studentsto show their mathematical abilities. I was teaching English in Korea for a few weeks, and teaching English was, at that time, something new for me. My wife is an English teacher and so I borrowed many of her strategies for teaching English. One of those strategies was to ask students to write a "K W L" for each piece of literature as they read it. The "K" stands for Know and so you would write what you already know. The "W" stands for Wonder, and so you would write what you wonder about, and it could be in a form of a question. The "L" stands for what you learned. After asking the students to come up with questions for the "W" column about what they were reading I realized what a powerful tool this is. I was not asking students, on that column, what they knew or prove that you know something, which would have made them feel obligated to bring up something that would be seen as wrong or right. But by coming up with a question, usually about a story we were reading, the student was implicitly showing me that they understood the story.

2. When you ask a student to pose a problem, how do you evaluate him or her? I would think pass or fail. But it is complicated because the teacher is going to go through each problem posed by the kid, think about it and determine whether the student really understood or only paraphrased a problem from the textbook.

3. Are some observations made on a simple statement as "x^2 + y^2 = z^2" more valuable than others?

4. When one comes up with a question, the nature of the question should reflect the level of undarstanding, but it is difficult to judge that.

5. How do the two meanings of undertanding, relational understanding, play into the "Art of Problem Posing"?

6. Is the author aware of the difference between "relational" and "instrumental" understanding?

7. Why does he think that Problem Posing has not taken off in the curriculum and therefore in the majority of the classrooms in North America?

8. Are we going to find great problems in this book?

9. I appreciate the fact that the authors take their time to explain what the book is about, how to read it and who is it directed to (audience).

10. I am really enjoying reading this book, although at some point it can get too hard to understand.