Learning 3D Matrix Algebra Using Virtual and Physical Manipulatives: Statistical Analysis of Quantitative Data Evaluating the Efficacy of the AR-Classroom | Learning and Collaboration Technologies (2024)

• Authors:
• Heather Burte https://ror.org/05x2bcf33Carnegie Mellon University, 15213, Pittsburgh, PA, USA

  https://ror.org/05x2bcf33Carnegie Mellon University, 15213, Pittsburgh, PA, USA

  http://orcid.org/0000-0002-9623-4375

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• Samantha D. Aguilar https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  http://orcid.org/0000-0002-1010-6082

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• James Stautler https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  http://orcid.org/0009-0007-6192-3174

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• Sadrita Mondal https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  http://orcid.org/0009-0008-0594-6686

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• Chengyuan Qian https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  http://orcid.org/0009-0008-0974-0992

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• Uttamasha Monjoree https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  http://orcid.org/0000-0001-5246-3582

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• Philip Yasskin https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  See Also

  7 Best Virtual Manipulatives for Online Math LearningMath Manipulatives: Virtual Manipulatives on the WebNLVM Algebra ManipulativesHow to Teach Odd and Even Numbers in 4 Easy Steps

  http://orcid.org/0000-0003-3103-8127

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• Jeffrey Liew https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  http://orcid.org/0000-0002-0784-8448

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• Dezhen Song https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA https://ror.org/0258gkt32Mohamed Bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, UAE

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/0258gkt32Mohamed Bin Zayed University of Artificial Intelligence (MBZUAI), Abu Dhabi, UAE

  http://orcid.org/0000-0002-2944-5754

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• Wei Yan https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  https://ror.org/01f5ytq51Texas A&M University, 77843, College Station, TX, USA

  http://orcid.org/0000-0003-1092-2474

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Learning and Collaboration Technologies: 11th International Conference, LCT 2024, Held as Part of the 26th HCI International Conference, HCII 2024, Washington, DC, USA, June 29–July 4, 2024, Proceedings, Part IIIJun 2024Pages 50–64https://doi.org/10.1007/978-3-031-61691-4_4

Abstract

The Augmented reality (AR) allows digital information to be overlayed onto a physical plane that users can manipulate. Using the unique capabilities of AR, the AR-Classroom learning tool aims to teach three-dimensional (3D) geometric rotations and their mathematics using virtual and physical manipulatives. In an efficacy experiment, undergraduates completed pre-test measures of matrix algebra and spatial thinking skills, were assigned to interact with virtual (N = 20) or physical (N = 20) manipulatives in the AR-Classroom, or to complete active control activities (N = 20), and then completed post-test measures of matrix algebra and spatial thinking skills. Using a series of ANCOVAs, pre-test accuracy on matrix algebra and spatial thinking tests significantly predicted matrix algebra post-test accuracy. There were no significant group differences indicating that all three groups showed similar improvement in matrix algebra skills. Further ANCOVAs revealed that the virtual and physical conditions showed marginally significant improvements on matrix algebra questions that were taught by the AR-Classroom, specifically rotations and rotations combined with translations. These initial findings indicate that the AR-Classroom may aid students in improving their mathematical skills. Suggestions for future improvements to the AR-Classroom and efficacy experiments on the AR-Classroom are discussed.

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