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Linear algebra instruction is an essential competency that is necessary for success in multiple engineering disciplines. Research in realistic mathematics education and the development of an empirically tested curriculum in inquiry oriented practices for teaching linear algebra helps improve the ability of instructors to teach the content via multiple lenses and modes. While there have been good instructional materials and strategies developed to apply inquiry oriented instruction for linear algebra, students struggle to apply and connect the different modes. Game based learning provides a platform to creatively include multiple modes and strategies via a fun and engaging manner. In this paper, we present we discuss the addition of game-based learning elements into an existing curriculum that teaches undergraduate linear algebra via an inquiry-oriented pedagogy. The aim of this paper is to discuss the game design strategies used in connecting game based learning to inquiry oriented methods. 

Linear algebra instruction is an essential competency that is necessary for success in multiple engineering disciplines. Research in realistic mathematics education and the development of an empirically tested curriculum in inquiry-oriented practices for teaching linear algebra helps improve the ability of instructors to teach the content via multiple lenses and modes. While there have been good instructional materials and strategies developed to apply inquiry-oriented instruction for linear algebra, students struggle to apply and connect the different modes. Game-based learning provides a platform to creatively include multiple modes and strategies in a fun and engaging manner. In this paper, we present we discuss the addition of game-based learning elements into an existing curriculum that teaches undergraduate linear algebra via an inquiry-oriented pedagogy. The aim of this paper is to discuss the game design strategies used in connecting game based learning to inquiry oriented methods. 

We present preliminary results of students’ strategies playing Vector Unknown: Echelon Seas [VUES], a 3D videogame intended to support student reasoning about vectors. Our team designed VUES by drawing on theories from Inquiry-Oriented Instruction (IOI), Game-Based Learning [GBL] and Realistic Mathematics Education [RME]. VUES builds from a prior 2D game by giving players vectors with 1, 2, or 3 components, depending on the level. We use codes from our team’s prior analysis (Mauntel et al, 2020) to analyze strategies in the 3D game. Early results show that students develop similar strategies during 3D gameplay as other students developed while playing the 2D game. However, we have also found new strategies that we did not witness with 2D gameplay, requiring us to extend our coding scheme. Further, early results emphasized the need for design changes to the 3D game to better support players’ progress. 

Los sistemas de ecuaciones lineales (SEL) corresponden a un concepto fundamental del álgebra lineal, pero hay relativamente poca investigación, pero hay relativamente poca investigación acerca de la enseñanza y el aprendizaje de los SEL, particularmente de las concepciones de los estudiantes acerca de sus soluciones. Se ha encontrado que la resolución de sistemas con un número infinito de soluciones o sin solución tiende a ser menos intuitivo para los estudiantes, lo cual indica la necesidad de más investigación en la enseñanza y aprendizaje de este tema. Entrevistamos a dos estudiantes de matemáticas que eran también maestros en formación a través de un experimento de enseñanza por parejas para mirar cómo razonaban acerca de las soluciones de SEL en ℝ3. Presentamos los resultados enfocando en la progresión del razonamiento de los estudiantes sobre las soluciones de los SEL a través del lento de simbolización. Documentamos la progresión de su razonamiento como una acumulación de significados numéricos, algebraicos y gráficos coordinados y las simbolizaciones de sus conjuntos solución.