Phenomenological Primitives in Introductory Computer Science Students' Understanding of Recursion

Chao, Jie, Curry School of Education, University of Virginia
Feldon, David F. Feldon, Curry School of Education, University of Virginia
Berch, Daniel, Curry School of Education, University of Virginia
Cohoon, James, Department of Computer Science, University of Virginia
Willingham, Daniel, Department of Psychology, University of Virginia

Recursion is a difficult concept to learn in introductory computer science courses. Students frequently construct maladaptive mental models of recursion that interfere with their performance and subsequent skill development. Common explanations assume that these mental models are not decomposable mental structures. However, such an assumption fails to account for the inconsistent manifestation of these mental models across similar tasks. This study applies the knowledge-in-pieces perspective (diSessa, 1993) to explain students' inconsistent performance on evaluation of recursive function. According to this perspective, phenomenological primitives (p-prims), experientially acquired tacit elemental knowledge structures, play dominant roles in naïve knowledge systems. Various task features may differentially constrain their influence, which renders them productive in some instances and problematic in others. This subtle mechanism gives rise to the inconsistent performance across tasks that target the same concept. Reanalysis of data from previous studies suggests a potential p-prim that plausibly accounts for students' inconsistent performance within and across similar tasks. This p-prim reflects intuitive understandings of agentive causality (i.e. agent takes an action on a patient to generate certain effect) that commonly account for misunderstandings in physics concepts (diSessa, 1993). To evaluate this general hypothesis of a computer-as-agent p-prim, participants completed four tasks representing varying levels of constraint on their reasoning and participated in clinical interviews to report and explain their thought processes. It was expected that more participants would demonstrate the normative mental models of recursion in the high-constraint tasks than in the low-constraint tasks, because the computer-as-agent p-prim would be more likely to interfere with appropriate analysis under lower constraint. Further, participants' interpretations of the recursive functions were expected to demonstrate characteristics associated with p-prim-generated interpretations. Results largely support the hypothesized p-prim. Participants' inconsistent performances were successfully explained by various modes of coordination between the computer-as-agent p-prim and relevant programming schemas. This finding advanced our understanding of students' difficulties in learning recursive programming and pointed to ways to improve instructional practices.

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PHD (Doctor of Philosophy)
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