Title: Easy, medium, and hard: Structuring space in 2D and 3D by way of linear combinations
Understanding linear combinations is at the core of linear algebra and impacts their understanding of basis and linear transformations. This research will focus on how students understand linear combinations after playing a video game created to help students link the algebraic and geometric representations of linear combinations. I found that having students reflect upon the game and create their own 3D version of the game illustrated which elements of 2D understanding could be translated into 3D. Also, students' creation of easy, medium, and hard levels provided insight into how students progressively structure space. more »« less
Developing a rich understanding of linear combinations is key to understanding linear algebra. In this paper, I explore the rich connections students make between the geometric and numeric representations of linear combinations through playing and analyzing a video game. I look at population of students who have never taken linear algebra before and analyze how they structure space using the video game, Vector Unknown, as a realistic starting point. I detail and analyze this activity including the activities that transition them from 2D to 3D space.
Lee, Victor R.; Poole, Frederick; Clarke-Midura, Jody; Recker, Mimi
(, The Interdisciplinarity of the Learning Sciences, 14th International Conference of the Learning Sciences (ICLS) 2020)
Gresalfi, Melissa; Horn, Ilana Seidel
(Ed.)
This paper presents an instructional design using expansive framing to introduce computer programming to upper elementary students. By using a tabletop board game as the context for learning, bridging connections between the learning in the board game and its digital instantiation, and privileging student authorship, we show how two students developed and transferred their understanding of several computational practices, including procedures and conditional logic, from the board game into their design of digital games in Scratch.
Lee, Victor R.; Poole, Frederick; Clarke-Midura, Jody; Recker, Mimi
(, The Interdisciplinarity of the Learning Sciences, 14th International Conference of the Learning Sciences (ICLS) 2020)
Gresalfi, Melissa; Horn, Ilana Seidel
(Ed.)
This paper presents an instructional design using expansive framing to introduce computer programming to upper elementary students. By using a tabletop board game as the context for learning, bridging connections between the learning in the board game and its digital instantiation, and privileging student authorship, we show how two students developed and transferred their understanding of several computational practices, including procedures and conditional logic, from the board game into their design of digital games in Scratch.
Mauntel, M.; Levine, B.; Plaxco, D.; Zandieh, M.
(, Proceedings of the 23rd Annual Conference on Research in Undergraduate Mathematics Education)
Karunakaran, S.; Reed, Z.; Higgins, A.
(Ed.)
We present results of a grounded analysis of individual interviews in which students play Vector Unknown - a video game designed to support students who are taking their first semester of linear algebra. We categorized strategies students employed while playing the game. These strategies range from less-anticipatory button-pushing to more sophisticated strategies based on approximating solutions and choosing vectors based on their direction. We also found that students focus on numeric and geometric aspects of the game interface, which provides additional insight into their strategies. These results have informed revisions to the game and also inform our team's plan for incorporating the game into classroom instruction.
Background. Middle school students’ math anxiety and low engagement have been major issues in math education. In order to reduce their anxiety and support their math learning, game-based learning (GBL) has been implemented. GBL research has underscored the role of social dynamics to facilitate a qualitative understanding of students’ knowledge. Whereas students’ peer interactions have been deemed a social dynamic, the relationships among peer interaction, task efficiency, and learning engagement were not well understood in previous empirical studies. Method. This mixed-method research implemented E-Rebuild, which is a 3D architecture game designed to promote students’ math problem-solving skills. We collected a total of 102 50-minutes gameplay sessions performed by 32 middle school students. Using video-captured and screen-recorded gameplaying sessions, we implemented behavior observations to measure students’ peer interaction efficiency, task efficiency, and learning engagement. We used association analyses, sequential analysis, and thematic analysis to explain how peer interaction promoted students’ task efficiency and learning engagement. Results. Students’ peer interactions were negatively related to task efficiency and learning engagement. There were also different gameplay patterns by students’ learning/task-relevant peer-interaction efficiency (PIE) level. Students in the low PIE group tended to progress through game tasks more efficiently than those in the high PIE group. The results of qualitative thematic analysis suggested that the students in the low PIE group showed more reflections on game-based mathematical problem solving, whereas those with high PIE experienced distractions during gameplay. Discussion. This study confirmed that students’ peer interactions without purposeful and knowledge-constructive collaborations led to their low task efficiency, as well as low learning engagement. The study finding shows further design implications: (1) providing in-game prompts to stimulate students’ math-related discussions and (2) developing collaboration contexts that legitimize students’ interpersonal knowledge exchanges with peers.
Mauntel, M. Easy, medium, and hard: Structuring space in 2D and 3D by way of linear combinations. Retrieved from https://par.nsf.gov/biblio/10346131. Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education .
Mauntel, M. Easy, medium, and hard: Structuring space in 2D and 3D by way of linear combinations. Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education, (). Retrieved from https://par.nsf.gov/biblio/10346131.
Mauntel, M.
"Easy, medium, and hard: Structuring space in 2D and 3D by way of linear combinations". Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education (). Country unknown/Code not available. https://par.nsf.gov/biblio/10346131.
@article{osti_10346131,
place = {Country unknown/Code not available},
title = {Easy, medium, and hard: Structuring space in 2D and 3D by way of linear combinations},
url = {https://par.nsf.gov/biblio/10346131},
abstractNote = {Understanding linear combinations is at the core of linear algebra and impacts their understanding of basis and linear transformations. This research will focus on how students understand linear combinations after playing a video game created to help students link the algebraic and geometric representations of linear combinations. I found that having students reflect upon the game and create their own 3D version of the game illustrated which elements of 2D understanding could be translated into 3D. Also, students' creation of easy, medium, and hard levels provided insight into how students progressively structure space.},
journal = {Proceedings of the Annual Conference on Research in Undergraduate Mathematics Education},
author = {Mauntel, M.},
editor = {Karunakaran, S. and Higgins, A.}
}
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