Differentiating between counterexamples for supporting students’ algorithmic thinking

Abstract

This study examines the use of counterexamples for supporting the development of students’ algorithmic thinking. Working from the premise that some counterexamples are more effective than others for the development of generalized algorithms, the study proposes distinctions between counterexamples in relation to the iterative refinement of student-invented algorithms. Furthermore, the study identifies some factors that may influence differences among counterexamples. Using task-based interviews, data were collected from 23 undergraduate students working in pairs (n = 8) and individually (n = 7) on three algorithmatizing tasks. From a thematic analysis of the data, two illustrative cases are presented to show how and why different counterexamples might bring about particular revisions in students’ algorithms. The two illustrative cases highlight two types of counterexamples—set-of-instructions-changing (SoI-changing) and domain-of-validity-narrowing (DoV-narrowing)—and their influencing factors. Implications of the findings are discussed with respect to existing literature, further research, and teaching.