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1. 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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2. 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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3. Constructing linear systems with particular kinds of solution sets.

   Smith, J. ; Lee, I. ; Zandieh, M. ; & Andrews-Larson, C. ( January 2022 , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

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

   Systems of equations is a core topic in linear algebra courses. Solving systems with no or infinitely many solutions tends to be less intuitive for students. In this study, we examined two students’ reasoning about the relationship between the structure of a system of linear equations and its solution set, particularly when creating systems with a certain number of equations and unknowns. Using data from a paired teaching experiment, we found that both students favored the notion of parallel planes, both geometrically and numerically, in the case of a system having no solution or infinitely many solutions. We also found that algebraic or numerical approaches were used as the main way of developing systems with a unique solution, especially in systems with more than two equations and two unknowns. In particular, one student gravitated toward geometric approaches and the other toward algebraic and numerical approaches. 

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4. Constructing linear systems with particular kinds of solution sets

   Smith, J. ; Lee, I. ; Zandieh, M. ; Andrews-Larson, C. ( January 2022 , Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education)

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

   Systems of equations is a core topic in linear algebra courses. Solving systems with no or infinitely many solutions tends to be less intuitive for students. In this study, we examined two students’ reasoning about the relationship between the structure of a system of linear equations and its solution set, particularly when creating systems with a certain number of equations and unknowns. Using data from a paired teaching experiment, we found that both students favored the notion of parallel planes, both geometrically and numerically, in the case of a system having no solution or infinitely many solutions. We also found that algebraic or numerical approaches were used as the main way of developing systems with a unique solution, especially in systems with more than two equations and two unknowns. In particular, one student gravitated toward geometric approaches and the other toward algebraic and numerical approaches. 

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5. Constructing linear systems with particular kinds of solution sets

   Smith, J. ( January 2022 , 24th conference on research in undergraduate mathematics education)

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

   Systems of equations is a core topic in linear algebra courses. Solving systems with no or infinitely many solutions tends to be less intuitive for students. In this study, we examined two students’ reasoning about the relationship between the structure of a system of linear equations and its solution set, particularly when creating systems with a certain number of equations and unknowns. Using data from a paired teaching experiment, we found that both students favored the notion of parallel planes, both geometrically and numerically, in the case of a system having no solution or infinitely many solutions. We also found that algebraic or numerical approaches were used as the main way of developing systems with a unique solution, especially in systems with more than two equations and two unknowns. In particular, one student gravitated toward geometric approaches and the other toward algebraic and numerical approaches. 

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