Development of an Instructional Model for Fostering Mathematical Competencies in an AI-Integrated Learning Environment

This study aims to develop an instructional model for effectively fostering mathematical competencies in an AI-integrated learning environment. To achieve this goal, an initial model was proposed based on the instrumental orchestration theory, consisting of three dimensions: tool function, tool role, and competency. A two-round Delphi survey was conducted with 16 mathematics education experts to examine the validity and appropriateness of the model. Based on the survey results, the model was refined into three dimensions: tool type, tool role, and competency. The tool type dimension is defined as teachers’ selection and arrangement of appropriate AI tools in accordance with instructional goals and consists of five categories: recommendation-based, dialogue-based, manipulation-based, assessment-based, and collaboration-based. The tool role dimension refers to the pedagogical roles assigned by teachers to AI tools in support of instructional goals. It comprises five roles: conceptual understanding, exploratory promotion, discussion and collaboration, interest and attitude, and procedural fluency. The competency dimension involves setting the targeted mathematical competencies for students and designing instructional assignments and activities to achieve them, based on the five core competencies outlined in the national mathematics curriculum. This study discusses the educational implications of the proposed model and suggests key considerations and application strategies for its implementation in actual classroom settings.