Pedagogical Issues to Keep in Mind During/After Problem-Solving

Pedagogical Issues to Keep in Mind
During and After Problem-Solving

What skills does this problem draw upon? (What content knowledge? What types of mathematical thinking/reasoning? What types of cognitive meta-skills?)
What, if anything, distracted or slowed me (or might hold students back) in trying to solve this problem?
Lessons/strategies I learned (or relearned) as a math solver? As a math teacher?
How can I mentally bookmark and/or cross-reference what I've learned?
Are there alternative solutions?
Generalizations of this problem?
Any relations to other areas of math?

If I use this or a similar problem as a teacher,
- What earlier, background preparation would be helpful?
- What just-before warmup, context, or guidelines would help?
- What should I keep an eye open for during the activity? What might come up? How should I react?
- What followup might help solidify the learning (both individual and group; both short and extended)?

Would it make sense to integrate this problem or one like it into the curriculum I teach in my school and county? Or can I use ideas learned here to enhance what I already teach? (try to be as specific as possible)

You may want to make photocopies of this handout and use one per activity, filling in the problem, and date encountered in math 541, at the top