Here is how I do problem-solving--
step by step, week by week:
When I was in school (Rubik’s Cubes and parachute pants were all the rage—you do the math), teachers taught us how to solve problems. (Sounds reasonable, right?) They would introduce a problem, show us step by step how to solve it, and then give us 20 others just like it to do on our own. All was good—until, that is, I ran across another kind of problem. I would try to solve that problem the same way, with the same “steps”—usually with disastrous results. I wanted everything to fit into a nice little algorithm, and if it didn’t, I was lost.
I have long since forgotten all of those steps and most of those algorithms. But I am very good at problem solving. I use my own strategies—I draw a picture, I guess and check, I work backwards. It isn’t always pretty, but it works.
That’s pretty much the model Larry Buschman advocates in his book, Share and Compare. As teachers, we do not teach or model solutions to a problem. We present the problem, and then guide the children through probing questions as they solve the problem themselves. There is no right or wrong way to solve the problem. Students are encouraged to try new strategies. Afterwards, students share their solutions in Mathematician’s Chair (and learn from each other).
A typical Share and Compare math lesson includes:
1. A Warm-Up activity: Students learn and practice math conventions.
2. The Problem-of-the-Day: Students solve the problem individually or in groups.
3. Mathematician’s Chair: Students share their solutions and give feedback to others.
4. Compare: Students compare their solutions, examining similarities and differences.
When I was first presented with this model, I was skeptical that kindergartners would be able to solve problems without modeling, or would be able to effectively communicate their solutions in a manner that would be helpful to others. But a year-and-a-half later, I’m coming around. It takes a lot of patience and persistence—on both the students’ and teacher’s part! But if you stick with it, I promise you will be convinced as well.