Saturday, October 3, 2009

10 Questions to the authors of 'The Art of Problem Posing'

1) I would like to know why the authors feel that after we solve a problem we don’t understand the significance of what we have done.  Could they provide an example of this?

 2) I would like to ask the authors how or what ideas they changed in their book for the third edition?  It would be interesting to see how their approach to problem posing has changed over the years.

 3) The Secular Talmund is something I have never heard of and I would be interested in finding out how they came to know this idea and have a little more information on what it is about.

 4) I found the fist chapter interesting from the point of view of the first question asked.  You could see the difference between the more simple to more complicated and relational thinking, making it more clear how we can begin to improve on problem posing.

 5) I would like to know why, when asking a question about isosceles triangles, those with ‘weak’ skills or knowledge come up with more robust questions?

 6) I was unclear about the discussion on ‘challenging’ the given’.  Why would you not accept something like a geoboard as is?  How would you change it?

 7) I liked how the authors used observations to create or pose new problems.  This seems like a useful tool, make observations about what you are looking at and only then begin to pose problems.

 8) Does the author find that by posing a problem that requires an approximate answer, the problem solver becomes more creative?

 9) I thought it was interesting that the authors suggested inquiring about the history of some of the problems.  This seems like a great way to become more familiar with the concepts and be able to have a better knowledge base for posing problems.

 10) I would like to ask the authors for more examples of internal vs. external exploration.  I was a little unclear how to go begin exploring this way in terms of mathematics concepts.

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