RUME 27
2025
Alexandria, Virginia
Coordinate Representation of Vectors and Matrix Representations of Linear Transformations in a DGS Assisted Linear Algebra Learning Environment: The Case of Polynomial Vector Space
Page: 249
The contributed report highlights the understanding of matrix representations of linear transformations mapping finite-dimensional polynomial vector spaces among university mathematics majors within a dynamic geometry software (DGS)-assisted linear algebra learning environment. Through an analysis of data from in-depth qualitative interviews, framed by the theories of representations in linear algebra (Dorier & Sierpinska, 2001; Hillel, 2000) and the concreteness principle (Harel, 2000), the findings reveal a range of innovative and creative ways in which the students integrated visual and analytical approaches to understand, produce, and interpret matrix representations of linear transformations. The results contribute new insights into the pedagogy of university-level linear algebra, highlighting the growing understanding of the role of visualization in the teaching and learning of the subject. The study also adds to the increasing body of evidence supporting the importance of visualization in linear algebra education.