Examining the effects of writing on conceptual and procedural knowledge in calculus

It has been claimed that writing to learn mathematics (WTLM) may benefit students' conceptual understanding as well as their procedural ability. To investigate this claim, we collected data from students in two sections of an introductory calculus course. In one of the sections, students used WTLM activities and discussed the activities after completing the writing; in the other section, students used similar activities that did not involve writing but engaged them in thinking about the mathematical ideas and in discussing the activities. The errors from the in-class and final exams of both groups of students were categorized and analyzed for information about the students' conceptual and procedural understanding. We found no significant differences between the WTLM group and the non-writing group, which suggests that the real benefit from writing activities may not be in the actual activity of writing, but rather in the fact that such activities require students to struggle to understand mathematical ideas well enough to communicate their understanding to others.