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  1. Matthew Mauntel
  2. Presenter’s NSFRESOURCECENTERS
  3. Arizona State University ASU, Clayton State University, Florida State University
  1. Ashish Amresh
  2. http://dt.asu.edu
  3. Research Scientist
  4. Presenter’s NSFRESOURCECENTERS
  5. Arizona State University ASU
  1. David Plaxco
  2. Associate Professor
  3. Presenter’s NSFRESOURCECENTERS
  4. Clayton State University
  1. Michelle Zandieh
  2. Assistant Professor
  3. Presenter’s NSFRESOURCECENTERS
  4. Arizona State University ASU

Simulation-Based Inquiry-Oriented Linear Algebra

NSF Awards: 1712524

2020 (see original presentation & discussion)

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.  

You can play the game at https://tinyurl.com/linearbunny with the username:STEMshowcase.

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Original Discussion from the 2020 STEM For All Video Showcase
  • Icon for: Ashish Amresh

    Ashish Amresh

    Co-Presenter
    May 4, 2020 | 01:52 p.m.

    Hi All,

    Just a reminder that  you can play the game at https://tinyurl.com/linearbunny

    with the username: STEMshowcase.

     
    1
    Discussion is closed. Upvoting is no longer available

    David Plaxco
  • Icon for: Matthew Mauntel

    Matthew Mauntel

    Lead Presenter
    May 5, 2020 | 06:46 a.m.

    Welcome to the STEM showcase!  Please feel free to play the game with the link provided by Ashish and ask any questions here!

     
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    Discussion is closed. Upvoting is no longer available

    David Plaxco
  • Icon for: Sara Yeo

    Sara Yeo

    Facilitator
    May 5, 2020 | 04:47 p.m.

    I liked that a capstone course in game design was approached to take on this project! What a great way to encourage cross-campus collaboration among students. Have you evaluated the impact of the game on students' learning of linear algebra? If so, how?

    Looking forward to the discussion, thanks!

     
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    Discussion is closed. Upvoting is no longer available

    David Plaxco
  • Icon for: Matthew Mauntel

    Matthew Mauntel

    Lead Presenter
    May 5, 2020 | 05:16 p.m.

    Sara, thank you for the question!  Currently, we have conducted a set of interviews to evaluate student strategies for playing the game and have a paper under review on the subject.  David Plaxco and Michelle Zandieh have used the game in their linear algebra courses and written some problems for the game. 

    I conducted a few of the interviews and have been helping to analyze them as well.  One thing I will say is that I was amazed that students who hadn't taken linear algebra, were currently in linear algebra, and had already taken linear algebra were able to take something away from playing game in regards to connecting the geometry of linear combinations to vector equations.  

     
    2
    Discussion is closed. Upvoting is no longer available

    Sara Yeo
    David Plaxco
  • Icon for: Sara Yeo

    Sara Yeo

    Facilitator
    May 7, 2020 | 02:33 p.m.

    Thank you for your response, Matthew. Great to hear that students at many levels were able to learn something from the game!

  • Icon for: Nancy Shapiro

    Nancy Shapiro

    Facilitator
    May 5, 2020 | 08:30 p.m.

    Very cool! I, too, would be interested in the answer to Sara's question--have you found that the game enhances student learning?  But I'm also  intrigued by the idea that you brought students from the CS and gaming class into a real-time experiment with lower-division math students.  Is that collaboration between the math researchers, the CS/game faculty and students something that might continue? I understand you are also looking at 3D representations--where do you think you will get the biggest bang for the buck?  in the math classes or in the CS/gaming classes?  Among the math students or the CS students? 

    thanks for sharing such an interesting project!

     

     
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    Discussion is closed. Upvoting is no longer available

    David Plaxco
  • Icon for: David Plaxco

    David Plaxco

    Co-Presenter
    May 5, 2020 | 08:52 p.m.

    Wow. Great questions.

    As Matt said, Michelle and I have had some of our Linear Algebra students play the game as homework during the first few weeks of school to extend their work with the IOLA tasks in class. I’ve taught with IOLA for 10 semesters now and the game definitely gave students a different and useful context to describe the mathematical relationships they saw within a set of vectors and between the set and locations in the plane (this connects to the first two tasks of IOLA). I had students discuss and share their strategies after playing the game at home. The team’s work identifying student strategies was definitely helpful toward anticipating the types of things students would talk about in class. Also, as Matt mentioned, one of the most effective aspects of the game is in getting students to connect geometric and algebraic representations of linear combinations using a real-time, dynamic model. I also very much look forward to working more with the 3D game and I think the math students would benefit from a new type of linear dependence that can be modeled in 3D. 

  • Icon for: Nancy Shapiro

    Nancy Shapiro

    Facilitator
    May 6, 2020 | 09:30 a.m.

    Thanks for explaining some of the "back story."  Good luck with the project!

  • Icon for: Cheryl Bodnar

    Cheryl Bodnar

    Higher Ed Faculty
    May 6, 2020 | 08:40 a.m.

    This is a very interesting game.  I think that the use of a game in this context provides a very visual approach to understanding linear algebra.  Great job!

     
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    Discussion is closed. Upvoting is no longer available

    David Plaxco
  • Icon for: Ashish Amresh

    Ashish Amresh

    Co-Presenter
    May 6, 2020 | 09:40 a.m.

    Addressing Nancy's question on "biggest bang for the buck": The CS capstone teams comprise of about 5 students that work on creating the game prototypes for a semester. They are intimately involved in the game and experience that the creative process provides is extremely rewarding and surely helps them get a close look at the game production process. It also provides the students an ability to draw out requirements from a third party client helping them prepare for industry jobs when they graduate. So on an individual basis, the CS capstone student is getting a "lot" compared to a student who plays the game in a linear algebra classroom. However from a project perspective a large number of linear algebra students over many semesters are going to find that having the game helps them make better connections with the concepts being taught and so the impact this will have will be long term and the number of students that will benefit will also be considerably more. 

  • Icon for: Nancy Shapiro

    Nancy Shapiro

    Facilitator
    May 6, 2020 | 09:58 a.m.

    This makes great sense--bang for the buck is different in different contexts.

    thanks!

  • Icon for: Ivory Toldson

    Ivory Toldson

    Facilitator
    May 6, 2020 | 04:23 p.m.

    Thank you for sharing! Including a link for us to play is a nice touch as well. I can always appreciate games that allow the players to exercise decision making problem solving abilities. You have done well to collaborate between senior programming students, game designers, and mathematics educators to create such an innovative solution. Very well done.

    What features or aspects are you looking forward to most regarding the 3D game?

     

  • Icon for: Ashish Amresh

    Ashish Amresh

    Co-Presenter
    May 7, 2020 | 12:30 a.m.

    Hi Ivory,

    We are just at the initial stages of the 3D version of the game with the current Capstone team completing the final features and bugs. We are specifically interested to see if adding another dimension to the mix improves the spatial as well and algebraic reasoning skills for the students.

     
    1
    Discussion is closed. Upvoting is no longer available

    Ivory Toldson
  • Icon for: Monica VanDieren

    Monica VanDieren

    Higher Ed Faculty
    May 7, 2020 | 01:42 p.m.

    Thanks for sharing this project!  I had forgotten about it since I first learned about it.  Now with the move online and redesign of all of our math courses, I'll be sure to share this with my colleagues and incorporate the game into my unit on vectors in Multivariable Calculus this summer.

  • Icon for: Ashish Amresh

    Ashish Amresh

    Co-Presenter
    May 7, 2020 | 03:28 p.m.

    Hi Monica,

    Great to hear about your interest. We are also creating tailored activity units that instructors can use in their classroom. Matt could reach out to you with this information if you are interested.

  • Icon for: Monica VanDieren

    Monica VanDieren

    Higher Ed Faculty
    May 7, 2020 | 03:31 p.m.

    I'm definitely interested!  looking forward to seeing the material!  thanks

  • Icon for: Matthew Mauntel

    Matthew Mauntel

    Lead Presenter
    May 8, 2020 | 10:18 a.m.

    Monica,  we are still working on refining some of the materials.  I have saved your information from your profile and will email the materials to you as soon as they are finished.  

  • Icon for: Monica VanDieren

    Monica VanDieren

    Higher Ed Faculty
    May 8, 2020 | 10:20 a.m.

    wonderful! thanks again!

  • Icon for: Saira Mortier

    Saira Mortier

    Research Program Coordinator
    May 7, 2020 | 10:34 p.m.

    What an awesome resource. Our research lab has put out a number of video games to help with math education so this is a topic near and dear to our hearts! Keep up the awesome work.

  • Icon for: Edith Graf

    Edith Graf

    Researcher
    May 9, 2020 | 02:33 p.m.

     I think it is great that you included students in the design process for the game. The game would seem to facilitate translating among alternate representations of linear combinations, it would be interesting to assess this.

  • Icon for: Gregory Lawson

    Gregory Lawson

    Noyce Scholar
    May 10, 2020 | 07:11 p.m.

    What an awesome way to help students understand a concept! I wish that I would have had something like this when I was taking Linear Algebra.

    Will that link to the game be working for the foreseeable future? 

  • Icon for: Ashish Amresh

    Ashish Amresh

    Co-Presenter
    May 11, 2020 | 11:04 a.m.

    Dear Gregory,

    Yes the game will be available at this link for another two years, newer updates to the game will also be pushed to this link.

     

  • Icon for: Viviana Vazquez

    Viviana Vazquez

    May 12, 2020 | 07:51 p.m.

    I feel this will be a great tool to use for students who are having a bit of trouble with units on vectors, as well as helpful to students who are a bit more visual and hands-on learners. I know having something like this would have definitely helped me understand concepts when I was taking algebra. Thank you so much for this valuable resource!

  • Further posting is closed as the event has ended.

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