AI-Assisted Didactic Engineering in Practice: A Case Study of Digital Transposition in Mathematics Education

Integrating generative artificial intelligence (GenAI) into instructional design raises questions about how mathematical knowledge is transposed into digital forms. Grounded in the Anthropological Theory of the Didactic (ATD) and the Theory of Didactic Situations (TDS), this qualitative single-case study examines one high school mathematics teacher’s AI-assisted didactic engineering. The unit of analysis was the teacher’s iterative design and classroom implementation process. Data comprised prompt logs, GenAI-generated drafts, successive teacher-revised artifacts, and classroom implementation records capturing students’ interactions with the materials and their mathematical responses. Using ATD and TDS as analytic lenses, the study traced changes across artifact versions and examined classroom records for evidence of meaningful student action and reasoning in response to feedback from the digital milieu. The analysis identified three progressively complex dimensions of digital didactic transposition. First, textbook materials and style constraints guided GenAI in producing infographics. Second, the teacher prompted GenAI to produce geometric illustrations for modeling problems and subsequently revised them. Third, through a six-step iterative cycle, the teacher developed and implemented a Grade 10 lesson on sets featuring dynamic number lines and interactive Venn diagrams. Initial GenAI outputs required revision to correct geometric imprecision, align representations with intended mathematical meanings, and ensure that interactive features supported purposeful mathematical activity. Classroom records indicated that the revised features elicited meaningful student action and mathematical reasoning. Through targeted prompting, verification, implementation, and redesign, the teacher transformed GenAI outputs into a coherent and usable lesson. Teacher agency therefore regulated the transposition process, turning GenAI’s generative capacity into a pedagogically productive resource while preserving the epistemological integrity of mathematical praxeologies.