- Matthew Mauntel
- Graduate Student
- Presenter’s NSFRESOURCECENTERS
- Arizona State University, Clayton State University, Florida State University
- Ashish Amresh
- http://dt.asu.edu
- Research Scientist
- Presenter’s NSFRESOURCECENTERS
- Arizona State University
- Jeremy Bernier
- Graduate Assistant
- Presenter’s NSFRESOURCECENTERS
- Arizona State University
- Zachary Bettersworth
- Education
- Presenter’s NSFRESOURCECENTERS
- Arizona State University
- David Plaxco
- http://www.davidplaxco.com
- Assistant Professor
- Presenter’s NSFRESOURCECENTERS
- Clayton State University
- Michelle Zandieh
- Professor
- Presenter’s NSFRESOURCECENTERS
- Arizona State University
Vector Unknown: A Game about Linear Combinations
NSF Awards: 1712524
2021 (see original presentation & discussion)
Grades 9-12, Undergraduate
This presentation presents the result of a game created for linear algebra called Vector Unknown, a collaboration between senior programming students, game designers, and mathematics educators. The game is inspired by the Inquiry Oriented Linear Algebra (http://iola.math.vt.edu/index.php) curriculum and specifically the Magic Carpet Ride Task.
The object of the game is to use vectors to move a rabbit from the origin of a gridded plane to a basket in that plane. The player moves the rabbit by pulling one or two vectors from a box on the left of the screen into a vector equation at the top. Adjusting the scalars in front of the vectors in the vector equation generates a geometric representation of the linear combination. When the player has made selections and presses GO, the rabbit moves along each vector in the predicted path until it reaches the sum of the rabbit’s location and the outcome of the vector equation. The mathematical notation for the move is recorded in a log. On higher levels, the predictive path is removed and/or players must collect keys placed around the field before reaching the basket.
Additionally, a new game that focuses on linear combinations of vectors in 3D is being developed this year.
You can play the game at https://tinyurl.com/linearbunny with the username:STEMshowcase.
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Ashish Amresh
Research Scientist
You can play the game at https://tinyurl.com/linearbunny with the username: STEMshowcase.
If you are interested in trying out the 3D game then let us know and we can send you the details
Brian Gane
Fun game, thought it would be easy after the tutorial but I was mistaken! Really fun way to build sensemaking around linear combinations and practice coordinating between the geometric representations and equations. Have you tried measuring students' learning through playing the game? There seem to be many features of the game (e.g., predictive path ON/OFF, etc.) you could manipulate to study and use it as a powerful learning experience.
Jeremy Bernier
Graduate Assistant
In addition to the project Zachary mentioned, Dr. Zandieh and I are working on another project along the same vein as you are asking about. We collected interview data with participants playing the game and solving a similar, pen-and-paper problem in various orders to compare the learning that goes on in those environments. This will also hopefully be shared at the 2022 SIGMAA-RUME conference!
Brian Gane
Interesting. Did you manipulate the order of the pen-and-paper problems in an intentional way to test learning outcomes, or was it more of a way to randomize/minimize order effects?
Jeremy Bernier
Graduate Assistant
So, the ordering is that some of the participants played the game first and did the pen-and-paper task second, and others did the reverse. The goal is to compare the two tasks with each other and see how ordering them differently can effect success on each task.
Brian Gane
Ah I see, thanks for the details. I look forward to hearing about the results!
Zachary Bettersworth
Education
Glad you enjoyed it! So, Dr. Zandieh, Kaki Simmons, and I have been developing written homework assignments to leverage the game in the classroom alongside the Inquiry-Oriented Linear Algebra curriculum. We have collected the homework and intend to continue analyzing it as a data source over the summer. Hopefully, we'll have something fun to share at the SIGMAA-RUME conference this year.
Brian Gane
Sounds like a good approach to foster learning, I look forward to seeing the results in the future!
Laura Larkin
Albert Einstein Distinguished Educator Fellow
Hi Ashish and Zachary-
Like Brian, I thought it would be easy to master but my vector spatial perception needs some practice although I admit to not watching the tutorial! I can see using this in my IB Analysis and Approaches class. What courses were you targeting for this game? Have you noticed if students are willing to persist? I'll be interested in your analysis and student feedback.
Matt Mauntel
Graduate Student
Laura, we have looked at student play and documented their strategies for playing the game. The game is targeted for a linear algebra course, but we presented the game at a showcase at IT/SEC that was open to players of all ages. We had several middle/high school students who played the game and enjoyed it and several middle/high school teachers who commented that they wanted to use it at that level to help students with plotting points (they game was not specifically designed for this use).
Most students I have observed during playtesting are willing to persist until they get an answer. We did create several difficulties which were initially not present in the game based on student feedback and observation..
Laura Larkin
Albert Einstein Distinguished Educator Fellow
Matthew- Thanks for the reply. Vector equations are part of our high school IB curriculum and currently we use paper/pencil. This game (and the 3-D version) is very engaging. I would use this as a check for understanding and some peer practice. Have you considered making it a 2-person game? Would someone (teacher/other student) be able to place the target?
Matt Mauntel
Graduate Student
That is a great question. There was some discussion about making both games a 2-player, but at the moment we are focused on polishing the 3D game. I had students design a 3D version of the 2D game for part of my dissertation and used a GeoGebra that I created (Here is the link). I think it could be for the purpose you propose.
Zach Mbasu
Fun game to teach and learn linear algebra! Linear Algebra is the first abstract mathematics subject for most of new college students in Kenya. Hence most of the students face difficulties to deal with various novel mathematical concepts at that level. I can see how instructors can demonstrate concepts to students through the game and students can therefore experience visualized results, which help enormously in understanding complicated new linear Algebra concepts. Excellent project improving learning environment for teaching linear algebra.
Bridina Lemmer
Technical Assistance Consultant
I'll be honest, I struggled with linear algebra in high school and I suspect my bunny will wander all around the garden before he get's to his basket! If I'm understanding correctly, some students have been using the game for homework- have you seen any difference in their levels of engagement in those classes or their understanding of these concepts?
David Plaxco
Assistant Professor
Yes! We have been implementing some in-class and homework assignments that ask students to reflect on their gameplay and encourage them to articulate the strategies they use. I have not yet analyzed any data from these implementations, but as an instructor who used some of the assignments in my own class, I can say that I definitely had some students who incorporated the Bunny environment into later discussions as we explored linear in/dependence, span, and basis!
David Barnes
Associate Executive Director, NCTM
Vector Unknown: A Game about Linear Combinations
Very intriguing! Just watching the video made me think how nice it would have been to have some of those visuals (Oh, that’s what a scalar does!) when I was taking Linear Algebra. I am not familiar with the IOLA curriculum, but I am wondering if students had any opportunity to consider how they would use matrices (and what kind would be needed) to move something in 3-space? Or how would they make sense of matric multiplication in these domains. Does the game set them up to move beyond just the manipulation of numbers within the frame of a matrix to think of matrices as objects in their own right?
Matt Mauntel
Graduate Student
David, Thank you for the question. We currently do not have a level that is focused on matrix multiplication in 3-space or manipulating numbers in a matrix frame. Outside of the game, we are working on some modules for the IOLA curriculum that helps students visualize linear transformations in 3-space using GeoGebra. We are still a little bit away from incorporating this lesson into a game environment. Thank you for the suggestions, I think developing a game that grounds matrix multiplication in 3-space is an excellent idea.
David Barnes
Associate Executive Director, NCTM
Thanks Matthew. The framework is very powerful and what you offer to support sense making seems like it really could engage students. Thanks for sharing a wonderful project!
Further posting is closed as the event has ended.