Top 10 Questions/Comments for the Author

In no particular order of importance, here are my 10 questions/comments for the authors:

1. It is very true in math (and even sometimes in the sciences) that given the layout of information, certain questions or problems are assumed (following the x² + y² = z²).
2. Is it our job as future math educators to challenge students' preconceptions and ask them the "unexpected" question?
3. I think the list of possible patterns generated by the class studying the Pythagorean triples shows a higher level of thinking, trying to detect patterns.
4. Something that makes humans unique is our ability to detect patterns in data.
5. A study of the history behind questions and topics can give us background information on the topic and can frame a certain mindset for approaching the question.
6. In discussing the significance of questions and problems, I am reminded of the relational understanding versus instrumental understanding debate. Too often are people lost in plug-and-chug questions that they forget why they were doing them in the first place and lose sight of the meaning.
7. How often do you notice people stuck in internal exploration and don't explore externally?
8. Is it possible to switch gears in children to go from doing questions and accepting everything to learning to challenge the question?
9. "Merely looking for something to challenge will not guarantee that we will find it" (p 18). I find this quote to be very powerful and one of the reasons for doing research in science. If we do research into new areas, we are not sure of the results but that really is the reason for doing research.
10. Why did you choose x² + y² = z² as your first question?

Reference
Brown, S.I.; Walter, M.I. (2005). The Art of Problem Posing, Third Edition, Chapters 1-3, New York, NY, Routledge Taylor & Francis Group.