Art of Problem Posing: Entry #1

There were several aspects of this first reading that I found interesting:

1) I was pleased to see the description of problem posing as a method of inquiry, as it relates to some of the work being done in my other mathematics education course.

2) I have some reservations about how to directly apply this philosophy to math teaching in general.

3) I think that inquiry via problem solving is a useful tool for teaching, but I believe it would need to be supplemented with some conventional (ie: lecture based) methods.

4) I enjoyed how the author describes the significance of a problem as being proportional to its ingenuity and playfulness.

5) By promoting this idea of playfulness, I think it would be much easier to promote a sense of curiosity about mathematics.

6) Also, encouraging students to play around with problems and modify them could go a long way toward combating math phobia.

7) I was also very pleased to see the emphasis placed on shifting contexts and perspectives.

8) This idea of shifting perspectives was also brought up in our other math ed. class as a way of fostering a deeper understanding of a concept.

9) I am curious about the idea of internal vs. external thinking with regard to problem posing, and I hope to see this idea expanded upon in the later sections of the book.

10) I was also interested to read about how lay persons often have an easier time of creating interesting problems than those with more formal math training. It would seem to coincide with Ken Robinson's idea about formal education having a destructive influence on creativity.