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A growing emphasis on computational thinking worldwide necessitates student proficiency in creating algorithms. Focusing on the use of counterexamples for developing student-invented algorithms, I reanalyze two pieces of data from previously published research, pertaining to two different cases of students’ algorithmatizing activity. In both cases, after multiple iterations of testing and revising in response to counterexamples, the student(s) had not created a generalized algorithm. Going beyond a dichotomous right or wrong perspective, the analysis provides insights into how educators can build on the small nuanced revisions that students conduct on their algorithms, rather than expecting students to make one gigantic leap from an incorrect to a correct algorithm, and regarding the absence of such a leap as failure.

Explicating how students revise their algorithms in response to counterexamples: building on small nuanced gains