I've been thinking lately that one of the reasons my students have such difficulty with long-term retention of mathematical concepts is due to the small number of times I ask them to thoroughly summarize what they have learned. They do lots of problems, but the language of the problems often does not enter into their brains. As we learned in Orwell's 1984, without language, there is no thought. So I am going to start providing more explicit opportunities for the students to summarize and discuss what we are doing in class.
Comic Strips (Unit 5, Lesson 9: doc / keynote / powerpoint)
Quite a few students are still struggling with graphing lines. They know the general process, but don't pay attention to the details - is the slope positive or negative; if a term is missing, is it the slope or the y-intercept, and how does that change the graph? So, I had all students draw comic strips to summarize the process in these different cases. I like how this went, but I definitely did not provide them with enough time to do all I asked. Here are a few good examples. The first didn't scan that well, but he did an awesome job.
Think-Pair-Share (Unit 5, Lesson 11: doc / keynote / powerpoint)
This is a tool that our humanities classes tend to use a lot. I got some advice from them, and will be trying these periodically during the next couple of units. We did one so far, and it went reasonably well for a first try. Students need a lot of practice both writing down their ideas and sharing them out. Here is the handout I gave (it was used immediately after doing a Do Now problem of the type described).
?
