AI-supported Mathematical Modeling Tasks through the Lens of Variation Theory

Abstract

This study evaluates the effectiveness of AI-supported mathematical modeling tasks by examining their alignment with task design criteria through the lens of variation theory. Seven AI-generated tasks related to climate change were analyzed using qualitative content analysis. The tasks were assessed based on their realism, relevance, authenticity, openness, and the utilization of modeling subcompetencies. To enhance the quality of these tasks, three different variations were employed. While the criteria of realism and relevance remained consistent across all versions, authenticity, clarity, and engagement with modeling competencies improved significantly in the third variation, which integrated more contextual and scenario-based prompts. The findings indicate that incorporating structured variations can foster more authentic and open-ended tasks, thereby deepening learners' engagement with mathematical modeling processes. This study demonstrates that task variations structured based on Variation Theory enhance AI systems’ ability to discern critical aspects of mathematical modeling processes. This study highlights the potential of AI as a valuable support tool for educators in designing meaningful, contextually rich tasks and calls for further research on its role in culturally responsive and adaptive pedagogy.

Keywords

• artificial intelligence
• mathematical modeling
• modeling tasks
• variation theory

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