2021 Research in Undergraduate Mathematics Education Reports
2021
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Two Students’ Conceptions of Solutions to a System of Linear Equations
Page: 308
Systems of linear equations (SLE) comprise a fundamental concept in linear algebra, but there is little research regarding the teaching and learning of SLE, especially students' conceptions of solutions. In this study, we examine students’ understanding of solutions to SLE in the context of an experientially real task sequence. We interviewed two undergraduate mathematics majors, who were also preservice teachers, to see how they thought about solutions to SLE in ℝ3, especially linear systems with multiple solutions. We found participants used their knowledge of SLE in ℝ2 to think about systems in higher dimensions, sometimes ran into algebraic complications, and initially did not find the third dimension intuitive to think about geometrically. Our findings highlight students’ ways of reasoning with infinite solution sets, such as moving toward the notion of parametrization.