Localized considerations and patching: Accounting for persistent attributes of an algorithm on a contextualized graph theory task

Students often hold on to algorithms that are inappropriate for the problem at hand, despite being presented with evidence of their inappropriateness during testing. Past research has tended to focus on the rejection and replacement of an algorithm in its entirety, rather than small refinements to an otherwise intact algorithm. In this study, we take a fine-grained view, focusing on the iterative refinement and augmentation of an algorithm, rather than its wholesale replacement. We ask: how do students decide what to change and what to keep when revising their algorithm upon testing? We analyze the collaborative work of three students on a graph theory task which invited the students to develop an algorithm for a contextualized problem. Two terms, localized considerations and patching, are introduced to describe how the group revised and validated their algorithms while retaining one specified attribute of their initial algorithm throughout.