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Cook, S. ; Katz, B. ; MooreRusso, 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 openended 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

Cook, S. ; Katz, B. ; MooreRusso, 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 openended 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

Karunakaran, S. ; Higgins, A. (Ed.)In this report, we characterize seven of twentyfive 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.more » « less

Karunakaran. S. S. ; Higgins, A. (Ed.)We present the results of a classroom teaching experiment for a recently designed unit for the InquiryOriented 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 (InquiryOriented 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

Karunakaran, S. ; & Higgins, A. (Ed.)We present the results of a classroom teaching experiment for a recently designed unit for the InquiryOriented 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 (InquiryOriented 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