Is Algorithm Comprehension Different from Program Comprehension?

Abstract

At the beginning of their undergraduate studies, computer science students are exposed to introductory programming, discrete mathematics, and algorithms. A large body of literature has studied how such students comprehend programs. Much less attention has been paid to understanding how students comprehend algorithms, i.e., representations of problem-solving processes accompanied by proofs of their properties. To investigate whether algorithm comprehension is under-researched or whether we can simply transfer results from program comprehension (and, possibly, proof comprehension) to the domain of algorithms, we conducted a larger study following a Grounded-Theory approach. For this study, we worked with twelve participants with varying degrees of prior knowledge regarding algorithms, from technically no prior knowledge to advanced graduate students pursuing a doctoral degree in algorithms-related fields. In this paper, we report on the analysis and interpretation of interview data focused on exploring potential differences between program comprehension and algorithm comprehension. Our analyses and interpretations revealed both similarities and differences between program comprehension and algorithm comprehension: Unsurprisingly, we found that aspects known from program comprehension, e.g., using top-down approaches or utilizing prior knowledge of programming plans, can be found in algorithm comprehension as well. However, some of these aspects manifest themselves in notably different details or are influenced by, e.g., the wording of a proof. Most interesting, we found that novice and advanced students alike benefit from switching between reading the representation of the program-solving process and the accompanying proofs. We present qualitative results illustrating both similarities and differences between program comprehension and algorithm comprehensions and offer first explanations for these.