The Case of Base Cases: Why are They so Difficult to Recognize? Student Difficulties with Recursion

摘要

Recursion is a central concept in computer science, yet it is a very difficult concept for beginners to learn. In this paper we focus on a specific aspect of comprehending recursion - the conception of the base case as an integral component of a recursive algorithm. We found that students have difficulties in identifying base cases: they handle redundant base cases; ignore boundary values and degenerated cases; avoid out-of-range values; and may even not define any base cases when formulating recursive algorithms. We also found that students have difficulties in evaluating recursive algorithms that deal with imperceptible base cases. We suggest that teachers should make a special effort to discuss different aspects of the base case concept. Emphasis should be put on both declarative and procedural aspects of categorizing and handling base cases as part of recursion formulation.