We math teachers love to talk about problem solving as a desirable curricular goal. However, I find that many of us don’t really agree as to what constitutes a problem. Not an original thought here, but in my mind I make distinctions between exercises and problems. I see it this way – an exercise is any challenge in front of you where the path to a solution is clear. It might be a technique you’ve been practicing, a new skill that has just been introduced, a specific formula to be applied. You might not get the answer correct, but it’s not because you don’t know WHAT to do. A problem is a challenge where the path to a solution is unclear. It might involve tying together multiple strands, creating (discovering?) a new technique that has yet to be presented, it may involve reaching across curricular boundaries to call on skills from other courses. So, if I am interested in teaching problem-solving, I need to have my cherubs on board and agree with me about what a problem is. I was happy to see the following link (http://fcit.usf.edu/math/resource/fcat/strat.htm) in Fawn Nguyen’s most recent post. Proud to see my old home state has a fairly cogent presentation of problem-solving. Of course, the father of talking about teaching problem-solving is still Georg Polya (http://teacher.scholastic.com/lessonrepro/lessonplans/steppro.htm) A MAJOR goal of mine next year is to reach consensus with my students about this job of ours.
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Getting Started
I’ve been reluctant to dip my toes into the math teacher blogging world for fear that I have little or nothing of note to add. However, I am going to overcome that fear even if my postings end up being read by few (and being of advantage to even fewer) as I try to discipline myself to organize my thoughts and the important thoughts and links I regularly read. Wish me luck!