Mental models of recursion

Mental models of recursion provide some idea into a student's understanding of recursion. However there has been concern regarding whether viable trace mental models of recursion show students' true understanding of recursion. We have conducted an investigation to further examine the understanding of recursion of students with viable trace mental models. The investigation looked at students' understanding of the termination of a recursive function, their descriptive mental models and their ability to generate a recursive function. This research provides evidence to show that trace methods are essentially mechanical processes that can allow students with little understanding of recursion to correctly evaluate a recursive function but that students do not fully understand recursion and in particular have difficulties with the passive flow. Based on the results of the study, this paper discusses possible changes that can be made to our teaching in order to more eectively teach recursion to first year students.