Towards Algorithm Comprehension

A central topic in computer science is algorithms that solve specific problems efficiently and elegantly. It is often not obvious why these algorithms solve the problem or why they are more efficient than naive methods. Therefore, these algorithms are usually presented together with a proof or a proof sketch that proves properties of the algorithm. In the context of this paper, we accordingly conceive of algorithms as a description of a process, e. g., in pseudocode, and a chain of reasoning that proves, e. g., in the form of a proof sketch, properties of the process. Algorithms, such as those presented in advanced lectures, textbooks, and technical articles, fall into this category. Thus, comprehending these algorithms is particularly relevant for students who have already passed the introductory stage of study and have foundations in the basics of programming and discrete mathematics. Although algorithms play a central role in research and teaching, they have received little attention in this form in educational research. One possible reason for this is the young age of the research discipline and the fact that programming has been given far greater importance as a prerequisite for software development and as the basis of advanced topics such as algorithms. Therefore, this thesis aims to develop a theory of algorithm comprehension so that future work can draw on it to improve, for example, the teaching of algorithms. To this end, this thesis provides an overview of previous research regarding algorithms and related didactics, particularly theories of program and proof comprehension. Algorithm comprehension is then examined quantitatively and qualitatively for similarities and differences. This work concludes that these theories cannot fully explain algorithm comprehension from these fields or their direct combination. Therefore, we develop a Grounded Theory that can explain comprehension processes by considering algorithm-specific properties. The theory describes three mental components that are developed and interconnected during algorithm comprehension. These represent the comprehension of the process, the chain of reasoning, and the domain in which the algorithm is situated. Furthermore, influencing factors such as the material and algorithm-specific prior knowledge are addressed. According to the theory, algorithm understanding can be described by the development of components containing different levels of abstraction that are strongly linked in themselves and with each other.