Teaching Reform of Linear Algebra Enabled by Artificial Intelligence
Journal: Journal of Higher Education Research DOI: 10.32629/jher.v7i1.4953
Abstract
Linear algebra is a highly abstract and theoretical course, and students often encounter difficulties in conceptual understanding and in connecting theory with applications. With the rapid development of generative artificial intelligence (GenAI), new possibilities have emerged for instructional support, learning feedback, and educational assessment. Based on theories of active learning and inquiry-based instruction, this paper proposes an AI-enhanced instructional model for linear algebra organized around a closed loop of concept construction, inquiry-based learning, and formative feedback. The paper discusses the application of this model to core topics in linear algebra and analyzes the role of GenAI as a cognitive scaffold under teacher guidance. The study argues that, when appropriately regulated, GenAI can effectively support students’ conceptual understanding and transferable knowledge in linear algebra.
Keywords
linear algebra; generative artificial intelligence; inquiry-based learning; active learning; teaching reform
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[2]Pepin, B., Buchholtz, N., & Salinas-Hernández, U. A scoping survey of ChatGPT in mathematics education. Digital Experiences in Mathematics Education. 2025; 11, 9–41.
[3]Turmuzi, M., Azmi, S., & Kertiyani, N. M. I. ChatGPT in school mathematics education: A systematic review of opportunities, challenges, and pedagogical implications. Teaching and Teacher Education. 2026; 170, 105286.
[4]Wawro, M., Andrews-Larson, C., Zandieh, M., & Plaxco, D. Inquiry-oriented linear algebra: Connecting design-based research and instructional change research in curriculum design. In Practice-Oriented Research in Tertiary Mathematics Education. New York, 2023: Springer.
[5]Fredriksen, H., Rebenda, J., Rensaa, R. J., & Pettersen, P. Inquiry-based linear algebra teaching and learning in a flipped classroom framework: A case study. PRIMUS.2024; 1-21.
[6]Stewart, S., Troup, J. Linear Algebra Education: A Scoping Review. ZDM Mathematics Education. 2025; 57, 815–827.
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