From calculation to adaptive mathematical competence: Reconceptualizing mathematical operations for the generative AI era in school mathematics
DOI:
https://doi.org/10.33830/ijdmde.v3i2.15544Keywords:
mathematical operations;, procedural fluency, procedural flexibility, conceptual knowledgeAbstract
Mathematical operations are often treated as routine calculation, yet generative artificial intelligence (AI) challenges this view because procedures can now be executed instantly by digital tools. This structured narrative review reconceptualizes mathematical operation competence for the generative AI era by synthesizing 44 English-language sources published between 1991 and June 2026 on procedural fluency, conceptual knowledge, strategy flexibility, adaptive expertise, mathematical errors, instruction, and AI-mediated learning. The synthesis shows that operation competence is multidimensional, integrating accuracy, efficiency, conceptual understanding, flexibility, metacognitive monitoring, verification, and transfer. Conceptual and procedural knowledge develop iteratively, while effective strategy selection requires knowledge of multiple procedures and sensitivity to problem characteristics. Persistent operational errors arise from interacting conceptual, cognitive, affective, and instructional factors, including misconceptions, working-memory demands, mathematics anxiety, and teaching focused primarily on answer production. Generative AI introduces an additional risk of procedural outsourcing, whereby AI-generated solutions replace students’ independent reasoning, execution, and monitoring. Effective instruction should therefore integrate structural and conceptual understanding, comparison of solution strategies, deliberate and spaced practice, analysis of errors, productive struggle, formative feedback, and systematic verification of AI- and CAS-generated outputs. The review proposes an integrative definition of mathematical operation competence and identifies priorities for construct validation, longitudinal and cross-cultural research, classroom interventions, teacher knowledge, and human-AI interaction, positioning structured AI verification as a central component of future mathematical competence.
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