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1. Student reasoning about the least-squares problem in inquiry-oriented linear algebra.

   Wawro, M. ( January 2023 , 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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2. Student Reasoning About the Least-Squares Problem in Inquiry-Oriented Linear Algebra

   Wawro, M. ; Park, M. ; Zandieh, M. ; Bettersworth, Z. ; Lee, I. ( January 2023 , 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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3. What is a vector to students?

   Lee, I. ( January 2022 , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. S. ; Higgins, A. (Ed.)

   This study presents linear algebra students’ vector conception found in the least-squares solution context through an IOLA (Inquiry-Oriented Linear Algebra) classroom teaching experiment. Students’ reflection writings after the classroom teaching experiment are the data source. Using the previously found student conception of vector in another study as a basic framing, the data have been analyzed to investigate how students used the word vector and what they referred to. A framework is developed as a tool to be useful in a wide range of describing student conception of a vector emphasizing their natural way of thinking of a vector and on their use of the vector. 

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4. What is a vector to students?

   Lee, I. ( January 2022 , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

   Karunakaran, S. ; Higgins, A. (Ed.)

   This study presents linear algebra students’ vector conception found in the least-squares solution context through an IOLA (Inquiry-Oriented Linear Algebra) classroom teaching experiment. Students’ reflection writings after the classroom teaching experiment are the data source. Using the previously found student conception of vector in another study as a basic framing, the data have been analyzed to investigate how students used the word vector and what they referred to. A framework is developed as a tool to be useful in a wide range of describing student conception of a vector emphasizing their natural way of thinking of a vector and on their use of the vector. 

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5. What is a vector to students?

   Lee, I. ( January 2022 , 24th conference on research in undergraduate mathematics education)

   S. S. Karunakaran ; A. Higgins (Ed.)

   This study presents linear algebra students’ vector conception found in the least-squares solution context through an IOLA (Inquiry-Oriented Linear Algebra) classroom teaching experiment. Students’ reflection writings after the classroom teaching experiment are the data source. Using the previously found student conception of vector in another study as a basic framing, the data have been analyzed to investigate how students used the word vector and what they referred to. A framework is developed as a tool to be useful in a wide range of describing student conception of a vector emphasizing their natural way of thinking of a vector and on their use of the vector. 

   more » « less