Dynamic programming - Structure, difficulties and teaching

In this paper we describe action research on our third year Algorithms, Data structures and Complexity course, in which students have considered dynamic programming hard in comparison to the other topics. Attempting to amend this, we wanted to know which difficulties the students encountered, where they gained their knowledge, and which tasks they were most certain that they could perform after the course. Such work resides in the didactics of the subject taught, but the general methods of attacking perceived difficulties in a course can be tried on any course. We identified subtasks that could be taught separately, and adapted the lectures to Pattern Oriented Instruction in order to help students cope with the cognitive complexity of solving problems using dynamic programming. For this, we prepared new clicker questions, visualisations and a lab assignment. We also constructed self-efficacy items on the course goals for dynamic programming, and administered them before and after the teaching and learning activities. Among the self-efficacy items, determining the evaluation order and solving a problem with dynamic programming with no hints had the lowest score after the course. As for the activities, arguing correctness of a solution was something many students claimed that they did not learn anywhere. Students considered the lab exercise most useful, but they also learned a lot from the other activities.