Mental models of recursion revisited

Abstract

Students struggle to understand recursion and we need to find good ways to teach the concept. We believe that an understanding of the mental models of recursion that students develop will assist us in teaching them more effectively. In 2003 we reported on a study of the mental models our students developed. This paper discusses some changes that we made to our teaching in 2003 after that study. An analysis of the students' mental models in 2003, 2004 and 2005 shows that more students are developing the copies model of recursion which is always a viable model.

First year students' understanding of the flow of control in recursive algorithms

“…The step, return value and algebraic models simply demonstrate various forms of confusion on the part of the student. Sanders et al (2006) corroborated the findings of Götschi et al (2003) as regards the first year students. Subsequent work (unpublished) identified the existence of a risky viable passive mental model of recursion where only the passive flow is shown.…”

“…In addition, the research highlighted the fact that understanding of the process is not related to the demonstrated trace mental model. Previous research has indicated that the supposedly simple tail recursive algorithms should be avoided because these can make students think of recursion as a "loop" (Sanders et al, 2006). This research shows that embedded recursive functions, where there are executable lines of code both before and after the recursive call, should be used as the first examples in teaching the concept.…”

“…Some changes have already been made in the teaching of recursive algorithms to the first years. In particular, the obvious, "more simple", recursive algorithms like factorial are not the first examples covered in class and an attempt has been made to try to introduce recursive algorithms which require understanding of both the active and passive flow (Sanders et al, 2006). In algorithms such as those shown above ( Figures 5 and 6) the solution is built up in the passive flow.…”

“…Continuous efforts have been made to determine whether first year students do, in fact, build viable mental models of recursion by studying how students trace recursive functions, analogous to the work of Kahney (1989) and Dicheva & Close (1996). Traces in specific test and examination questions over a number of years were analyzed (Götschi, Sanders & Galpin, 2003;Sanders, Galpin & Götschi, 2006). The students' mental models were then determined based on their representation of the flow of control in the recursive functions.…”

“…Many first year students do, in fact, develop viable copies mental models of recursion (Götschi et al, 2003;Sanders et al, 2006). These students can use a tracing method (e.g.…”