Written plans and the challenges of self-regulation in vector calculus

Vector calculus is an important branch of mathematics for many undergraduate science and engineering programmes, used, for example, in fluid dynamics, electromagnetism and control systems. Core to vector calculus are the three theorems of Green’s, Stokes’ and Gauss’. The rich problem-solving potential offered by these theorems makes vector calculus an ideal component within a standard calculus curriculum to bring true problem solving into the classroom. To benefit from this flexibility, we have redesigned our vector calculus curriculum to have problem solving at its core, with “decision making” as the underpinning principle. Research has shown that writing about one’s problem-solving approach deepens understanding of the problem and it has been argued that expository writing engages similar cognitive processes to effective problem solving. Having observed weaknesses in self-regulatory behaviour in vector calculus problem solving, we conducted an experimental-control intervention to determine if writing a plan before attempting to solve problems with multiple solution possibilities would have any effect on problem solving behaviour. Our findings suggest that requiring students to write a plan did not generally reduce reliance on multiple strategies in problem solving and thus did not provide evidence of greater confidence. The only exception was in one programme, where the experimental group employed fewer strategies than the control group. However, planning did not improve the overall quality of problem solving: in one of the problems, students in both groups were equally likely to select an inappropriate strategy. Furthermore, the experimental group was less likely to complete the more challenging of the two problems. We consider the implications for teaching and outline directions for further investigation.