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  1. (, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    S. S. Karunakaran, & A. (Ed.)
    In this paper, we introduce an RME-based (Freudenthal, 1991) task sequence intended to support the guided reinvention of the linear algebra topic of vector spaces. We also share the results of a paired teaching experiment (Steffe & Thompson, 2000) with two students. The results show how students can leverage their work in the problem context to develop more general notions of Null Space. This work informs further revisions to the task statements for using these materials in a whole-class setting. 
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    Accepted Manuscript Full Text Available
  2. (, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    S. S. Karunakaran, & A. (Ed.)
    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. 
    more » « less
    Accepted Manuscript Full Text Available
  3. (, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    S. S. Karunakaran, & A. (Ed.)
    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. 
    more » « less
    Accepted Manuscript Full Text Available
  4. (, Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    S. S. Karunakaran, & A. (Ed.)
    In this paper, we introduce an RME-based (Freudenthal, 1991) task sequence intended to support the guided reinvention of the linear algebra topic of vector spaces. We also share the results of a paired teaching experiment (Steffe & Thompson, 2000) with two students. The results show how students can leverage their work in the problem context to develop more general notions of Null Space. This work informs further revisions to the task statements for using these materials in a whole-class setting. 
    more » « less
    Accepted Manuscript Full Text Available