Abstract

Linear algebra with its rich theoretical nature is a first step towards advanced mathematical thinking for many undergraduate students. In this paper, we consider the teaching approach of an experienced mathematician as he attempts to engage his students with the key ideas embedded in a second-year course in linear algebra. We describe his approach in both lectures and tutorials, and how he employed visualization and an emphasis on language to encourage conceptual thinking. We use Tall's framework of three worlds of mathematical thinking to reflect on the effect of these activities in students' learning. An analysis of students' attitudes to the course and their test and examination results help to answer questions about the value of such an approach, suggesting ways forward in teaching linear algebra. (Contains 5 figures.)

Citation

Hannah, J., Stewart, S. & Thomas, M. (2013). Emphasizing Language and Visualization in Teaching Linear Algebra. International Journal of Mathematical Education in Science and Technology, 44(4), 475-489. Retrieved August 10, 2024 from https://www.learntechlib.org/p/168099/.

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Keywords

• action research
• algebra
• case studies
• Language Skills
• Lecture Method
• Mathematics Instruction
• Mathematics Skills
• Mixed Methods Research
• student attitudes
• teaching methods
• thinking skills
• undergraduate students
• Visualization
• Written Language