Student Utilization of Metacognitive Strategies in Solving Dynamic Programming Problems

Dynamic Programming (DP) is commonly regarded as one of the most difficult topics in the upper-level algorithms curriculum. The teaching of metacognitive strategies may prove effective in helping students learn to design DP algorithms. To explore both whether students learn and use these strategies on their own and the effect of guidance about using these strategies, we conducted think-aloud interviews with structured guidance at two points in a college algorithms course: once immediately after students learned the concept and once at the end of the course. We explore 1) what metacognitive strategies are commonly employed by students, 2) how effectively they help students solve problems, and 3) to what extent structured guidance about using metacognitive strategies is effective. We find that these strategies generally help students make progress in solving DP problems, but that they can mislead students as well. We also find that the adoption of these strategies is an individualized process and that structured strategy guidance is often insufficient in allowing students to solve individual DP problems, indicating the need for more extensive strategy instruction.