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  1. ; ; ; ; ( , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S. ; Katz, B. ; Moore-Russo, D. (Ed.)
    The method of Least Square Approximation is an important topic in some linear algebra classes. Despite this, little is known about how students come to understand it, particularly in a Realistic Mathematics Education setting. Here, we report on how students used literal symbols and equations when solving a least squares problem in a travel scenario, as well as their reflections on the least squares equation in an open-ended written question. We found students used unknowns and parameters in a variety of ways. We highlight how their use of dot product equations can be helpful towards supporting their understanding of the least squares equation. 
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    Accepted Manuscript Full Text Available
  2. ; ; ; ; ( , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    Cook, S. ; Katz, B. ; Moore-Russo, D. (Ed.)
    The method of Least Square Approximation is an important topic in some linear algebra classes. Despite this, little is known about how students come to understand it, particularly in a Realistic Mathematics Education setting. Here, we report on how students used literal symbols and equations when solving a least squares problem in a travel scenario, as well as their reflections on the least squares equation in an open-ended written question. We found students used unknowns and parameters in a variety of ways. We highlight how their use of dot product equations can be helpful towards supporting their understanding of the least squares equation. 
    more » « less
    Accepted Manuscript Full Text Available
  3. ; ; ( , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    Karunakaran, S. ; Higgins, A. (Ed.)
    In this report, we characterize seven of twenty-five students’ responses to a single written homework assignment from the Spring 2021 academic semester. The homework was designed to incorporate the Vector Unknown 2D digital game to investigate how students answered questions about span and linear independence after playing various levels of the game. We present our modification of the roles and characteristics framework of Zandieh et al. (2019), our identification of students’ grammatical use of game language and math language, as well as the results of analyzing students’ homework responses using our framework. 
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    Accepted Manuscript Full Text Available
  4. ; ; ; ; ( , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    Karunakaran. S. S. ; Higgins, A. (Ed.)
    We present the results of a classroom teaching experiment for a recently designed unit for the Inquiry-Oriented Linear Algebra (IOLA) curriculum. The new unit addresses orthogonality and least squares using Realistic Mathematics Education design principles with the intent to implement the new unit in an IOI (Inquiry-Oriented Instruction)-style classroom. We present an analysis of students’ written responses to characterize how they thought about the notion of shortest distance, travel vectors, orthogonality, and dot product in the “Meeting Gauss” context. 
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    Accepted Manuscript Full Text Available
  5. ; ; ; ; ( , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)
    Karunakaran, S. ; & Higgins, A. (Ed.)
    We present the results of a classroom teaching experiment for a recently designed unit for the Inquiry-Oriented Linear Algebra (IOLA) curriculum. The new unit addresses orthogonality and least squares using Realistic Mathematics Education design principles with the intent to implement the new unit in an IOI (Inquiry-Oriented Instruction)-style classroom. We present an analysis of students’ written responses to characterize how they thought about the notion of shortest distance, travel vectors, orthogonality, and dot product in the “Meeting Gauss” context. 
    more » « less
    Accepted Manuscript Full Text Available