John wrote: <<I like to start the year by giving my students an interesting math problem as they walk in the door (yes on the first day and on every other day as well) and encourage them to try to solve it. I encourage them to co-operate. Somehow I can't get past the notion that I need all the time I can get to have them doing math problems. I was hired to teach math. Perhaps it is different in places other than High School>>>
I teach at the community college level but I teach developmental (remedial) math from basic math through intermediate algebra. I think since our subject is soooo content driven we all feel this pressure to work problems or have the students work problems. That does not preclude having them work together in pairs or groups of 3 or more. After all isn't the process of math one of exploration, discussion, debate, defending ones approach, holding our ideas up to scrutiny by peers then sharing conclusions when new ideas are verified. We shouldn't presume that our students cannot also function in this manner while they are also working out more routine problems. Your idea of giving them a special problem at the beginning of each class and encourageing them to cooperate on its solution sounds like a great way to have them explore math in a controlled yet social setting. What kind of reaction do you get from the students?? Do they actually work together on the solutions??? Do the come back to class to face the next days problem??