Mathematical conceptual analysis of two linear algebra-based learning games

Authors

  • Hilda Sari Laonga Universitas Tadulako Author
  • Ade Lia Rahmaningrum Universitas Islam Negeri Siber Syekh Nurjati Cirebon Author
  • Tasya Agustin Hermawati Universitas Islam Negeri Siber Syekh Nurjati Cirebon Author
  • Fatimah Azzahra Universitas Islam Negeri Siber Syekh Nurjati Cirebon Author
  • Habib Giynastiar Universitas Islam Negeri Siber Syekh Nurjati Cirebon Author

DOI:

https://doi.org/10.66256/permata.v2i1.27

Keywords:

Linear Algebra, Interactive media, Matrix transformation, Linear combinations, Applied mathematics

Abstract

This study aims to analyse mathematical representations in two interactive media: vector unknown and GeoGebra-based linear transformation simulation, within the context of applied linear algebra learning. Using a qualitative-descriptive approach, this study examines the consistency of symbolic structure, spatial visualisation, and applicative relevance across the two media. The results of the analysis show that Vector Unknown is effective at representing a combination of linear and result spaces, whereas GeoGebra excels at visualising matrix and determinant transformations. Both support conceptual understanding and modelling skills that are essential in the fields of Engineering, computer graphics, and spatial systems. The study confirms that interactive media can bridge the gap between abstraction and real-world applications, encouraging inquiry-based learning. The limitations of this study include the limited scope of the concept and the absence of empirical validation based on user performance. Therefore, further research is recommended to expand the media and the scope of concepts.

Downloads

Download data is not yet available.

Author Biographies

  • Ade Lia Rahmaningrum, Universitas Islam Negeri Siber Syekh Nurjati Cirebon

    Mathematics Department 

  • Tasya Agustin Hermawati, Universitas Islam Negeri Siber Syekh Nurjati Cirebon

    Mathematics Department 

  • Fatimah Azzahra, Universitas Islam Negeri Siber Syekh Nurjati Cirebon

    Mathematics Department 

  • Habib Giynastiar, Universitas Islam Negeri Siber Syekh Nurjati Cirebon

    Mathematics Department 

References

[1] P. Vankúš, “Influence of game-based learning in mathematics education on students’ affective domain: A systematic review”, Mathematics, vol. 9, no. 9, p. 986, Apr. 2021, doi: 10.3390/math9090986.

[2] A. G. González Peralta and M. S. Aguilar, “A linear algebra quiz game as a supplementary learning tool in tertiary-level,” Pedagog. Res., vol. 9, no. 1, p.177, Jan. 2024, doi: 10.29333/pr/14029.

[3] V. Y. K. Gusti, “Teaching algebra through games: a literature review” Al-Irsyad J. Math. Educ., vol. 4, Jul. 2025, doi: 10.58917/ijme.v4i2.177.

[4] A. J. Pinon and D.-M. Cordova-Esparza, “Analysis of teaching strategies and learning challenges in linear algebra,” CLEI Electron. J., vol. 28, no. 2, Apr. 2025, doi: 10.19153/cleiej.28.2.11.

[5] S. Laudari and N. Karjanto, “Enhancing flipped classroom pedagogy in linear algebra through machine learning,” Sep. 29, 2023, arXiv: arXiv:2309.16259. doi: 10.48550/arXiv.2309.16259.

[6] M. Mauntel, J. Sipes, M. Zandieh, D. Plaxco, and B. Levine, “Let’s See” – Students play vector unknown, an inquiry-oriented linear algebra digital game” presented at the 22nd Annual Conference on Research in Undergraduate Mathematics Education, Research in Undergraduate Mathematics Education (RUME) Conference, 2019, pp. 959–965.

[7] “Unity WebGL Player | vector_unknown,” Unity WebGL. Accessed: Nov. 27, 2025. [Online]. Available: https://tinyurl.com/linearbunny

[8] F. A. Tejada Ramirez, “Impacto del uso de GeoGebra en el aprendizaje universitario de transformaciones lineales en geometría dinámica,” Pedagog. Constell., vol. 4, no. 1, pp. 166–186, May 2025, doi: 10.69821/constellations.v4i1.90.

[9] M. Turgut, “Reinventing geometric linear transformations in a dynamic geometry environment: Multimodal analysis of student reasoning” Int. J. Sci. Math. Educ., vol. 20, no. 6, pp. 1203–1223, Aug. 2022, doi: 10.1007/s10763-021-10185-y.

[10] “GeoGebra material pDU4peV5,” GeoGebra. Accessed: Nov. 27, 2025. [Online]. Available: https://www.geogebra.org/m/pDU4peV5?utm.com

[11] C. Murphy, “Exploring the role of visual imagery in learning mathematics,” in Proceedings of the 42nd Annual Conference of the Mathematics Education Research Group of Australasia (MERGA), Australia: MERGA, 2019. [Online]. Available: https://files.eric.ed.gov/fulltext/ED604294.pdf

[12] G. Strang, Introduction to linear algebra, 5th edition. Wellesley, MA: Cambridge press, 2016. [Online]. Available: https://math.mit.edu/~gs/linearalgebra/ila5/indexila5.html

[13] V. Antohe, “Limits of Educational Soft ‘GeoGebra’ in a Critical Constructive Review,” ArXiv Prepr., 2009, [Online]. Available: https://arxiv.org/abs/0905.4430

[14] R. Dekker, “Mathematics and Common Sense — The Dutch School,” Springer, doi: 10.1007/978-3-030-33824-4_4.

[15] P. Adjiman, P. Chatalic, F. Goasdoue, M.-C. Rousset, and L. Simon, “Scalability study of peer-to-peer consequence finding” in Proceedings of IJCAI, Edinburgh, Scotland: IJCAI, 2005. [Online]. Available: https://www.ijcai.org/Proceedings/05/Papers/1144.pdf

[16] R. A. Syafnuri, N. Netriwati, and D. D. Pratiwi, “Pengembangan bahan ajar aljabar linear dengan menggunakan model pembelajaran matematika Knisley” Numer. J. Mat. Dan Pendidik. Mat., pp. 43–62, Jun. 2019, doi: 10.25217/numerical.v3i1.417.

[17] R. Ziatdinov and J. R. Valles, “Synthesis of Modeling, Visualization, and programming in geogebra as an effective approach for teaching and learning stem topics” Mathematics, vol. 10, no. 3, p. 398, Jan. 2022, doi: 10.3390/math10030398.

[18] M. Mauntel and M. Zandieh, “Forms of structuring space by linear algebra students with video games and GeoGebra” Int. J. Res. Undergrad. Math. Educ., vol. 10, no. 3, pp. 754–780, Dec. 2024, doi: 10.1007/s40753-024-00246-2.

Downloads

Published

2026-06-01

Issue

Section

Articles

How to Cite

[1]
“Mathematical conceptual analysis of two linear algebra-based learning games”, Perspect. Math. Appl., vol. 2, no. 01, pp. 1–11, Jun. 2026, doi: 10.66256/permata.v2i1.27.

Similar Articles

You may also start an advanced similarity search for this article.