This was a great week in the pilot because for the first time, every lesson had the right mix of instruction vs. small group work. We had challenging problems that drew their interest, enough theory to explain how to complete the problems that arose, and time to solidify skills with additional problems. The biggest challenge of this whole project is determining its structure and order. There isn't any course like it anywhere or any book to model off of so we just have to try, fail, correct, and try again. Some days that's tough because solutions are so obvious in the classroom whereas they're not so apparent on the page.
One really fun thing students encountered this week was the difference in finding a measurement in real life compared to finding it on paper. Students are often put off by traditional math approaches that try to keep everything on paper. They want to experience the situation at hand, not just talk about it. But when we did that (find measurements physically), they could see there are all kinds of additional issues that come up. Solving them makes for good discussion and an interesting class period. They could also see the advantages of paper: it's often more accurate and it can be faster. That's not to say that finding a real life measurement isn't valuable. It is. But it's worthwhile to talk about the advantages and disadvantages of each approach as well as when each is the most useful or appropriate. Like calculators and computers, the less we are completely dependent on one means of solving a problem, the more skillful we become as mathematical problem solvers.
We also realized that we are flipping the classroom in our own way. MyMathLab is used throughout the course but for skills only. We don't have 10 skill examples written out on paper in any lesson, like a traditional text would. We do a few key skill examples, which Heather refers to as naked problems: problems stripped of all context. But practicing more of those can be done outside of class in MyMathLab own their own time. If they need 10 minutes or 2 hours, they can get that. What the classroom provides is a completely different experience, one that is built on talking about and doing mathematics, not skills. There is a movement nationally to put students in a computer lab and have them complete skill problem after skill problem, all the while calling that mathematics. Certainly skills matter but they are not enough. Being able to recognize when to do a skill in a context is one of the key uses of mathematics. I constantly tell my students, no one is going to come to you in real life and say:
Simplify: 3 - 2(x - 1) + 8.
It's not happening outside of a math class or math test. But will they be faced with complex problems where having mathematical skills could serve useful? Yes. That's why I like this course so much. They are talking, arguing, and explaining mathematics to each other, not skills. We had problems yesterday that were pretty meaty and within them they had to simplify an expression like the one I listed above. What was interesting to see was that virtually no one had trouble with the algebra; that was the easy part. The hard part was solving the original problem at hand that required generalizing a situation into an expression. But they figured it out and it was pretty satisfying for them and us.
Next week wraps up another unit and we test. I'm not as nervous as the first time around. They are getting the goal of the course and how it operates. But I still keep my fingers crossed that they'll do well.
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