This is my second year of teaching AP calculus. Last year I felt like my students weren’t getting a full understanding of the conceptual underpinnings of calculus. This year, I’ve been taking a little bit more time with concepts, Implementing more activities that aren’t skills practice, but ask students to dig deeper into the math. I’m trying very hard to get students to talk about the math more. (See my last post.) Also, my students are doing metacognitive journaling every week via a blog. This is another technique I’m using to try to get kids to think deeper about the concepts. In the journaling and in the conversations it seems like I’m seeing good conceptual understanding. However, when I gave the most recent quiz I saw that my students seem to be lacking in applying those concepts to new situations. Let me explain more.
The problems that students practiced over and over, the skills problems, seemed to go pretty well. The problems that ask students to explain concepts directly, also seemed to go pretty well. However, there were some skills type problems that were really asking students to take the concepts and apply them in a slightly different way. My thoughts in writing those problems were that students would have the tools they needed to solve them, they just needed to pull the right tools out of the box and apply them. Either my students didn’t know which tools to use, or they weren’t entirely sure of what the tools they had were used for.
There seems to be a disconnect. My students can practice something over and over and over again and replicate those processes on the test. (Maybe this isn’t surprising.) My students seem to be able to grab on to conceptual underpinnings and explain them. However they struggle to apply the concepts in new situations. I’m still not entirely sure of how to bridge that gap. How do I put students in a position to be successful on those types of problems?