So, this post is inspired by my most recent trip, my daughter, and by Christopher Danielson. We just returned from a trip to Pittsburgh to see my beloved Mets defeat the hometown Pirates. While on the road my impatient daughter is often asking how much farther we have to travel. Since I don’t imagine that she understands answers such as “28 more miles honey” (she will turn 4 on Thursday) I often answer by saying things like “only 20 more minutes, about the sam time as an episode of PowerPuff Girls”. So, when we were at the pool at a hotel on our trip we were playing a jumping game where she stood on the steps of the pool and jumped to my arms. One time I was too close for her tastes so she told me to back up. When I asked her how far away I should be, she said “Five minutes away.” I asked her, “Don’t you mean five feet away?” But she stood firm in her answer, she wanted me five minutes away from her. Christopher routinely writes about his children’s developing understandings of mathematics and, while I teach in the high school, it has made me more conscious of trying to get at what my students think that they understand about developing situations in the classroom. As a dad, these thoughts intrude as well. I am now debating my use of time as a marker for her, although I am certain that it is a more tangible way to answer her questions about how far away we are from our destination.
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.
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!