APPLICATIONS OF COMPUTER ALGEBRA SYSTEMS IN TEACHING MATHEMATICS
DOI:
https://doi.org/10.18173/2354-1075.2025-0078Keywords:
information and communication technology, computer algebra systems, Wolfram AlphaAbstract
The application of Information and Communication Technology (ICT) in education, particularly in Mathematics teaching, is an irreversible trend, as emphasized in the 2018 Mathematics curriculum. This paper presents the results of theoretical research on the use of Computer Algebra Systems (CAS) in teaching mathematics, including their historical development, potential, and significant pedagogical implications. Alongside theoretical exploration, the authors conducted practical investigations, summarizing experiences with CAS, exemplified by the Wolfram Alpha system. Based on these findings, several strategies for integrating CAS into teaching are proposed. Initial experiments show these approaches are feasible and yield positive results, promising effective implementation in practice.
Downloads
References
[1] Ardıç, M. A., & İşleyen, T. (2018). The effect of mathematics instruction through computer algebra systems on the academic achievements of secondary education students: The Turkish example. Journal of Education and e-Learning Research, 5(3), 165–173. https://doi.org/10.20448/journal.509.2018.53.165.173
[2] Buteau, C., Marshall, N., Jarvis, D. H., & Lavicza, Z. (2010). Integrating computer algebra systems in post-secondary mathematics education: Preliminary results of a literature review. International Journal for Technology in Mathematics Education, 17(2), 57–68.
[3] Marshall, N., Buteau, C., Jarvis, D. H., & Lavicza, Z. (2012). Do mathematicians integrate computer algebra systems in university teaching? Comparing a literature review to an international survey study. Computers & Education, 58(1), 423–434.
[4] Alhumaid, K. (2019). Four ways technology has negatively changed education. Journal of Educational and Social Research, 9(4), 10–20.
[5] Ditzler, C., Hong, E., & Strudler, N. (2016). How tablets are utilized in the classroom. Journal of Research on Technology in Education, 48(3), 181–193.
[6] Dien, P. H. (2002). Computation, Programming, and Mathematics Teaching with Maple. Science and Technology Publishing House (in Vietnamese).
[7] Phan, D. C. (2005). Using Maple in Elementary and Advanced Mathematics. Science and Technology Publishing House (in Vietnamese).
[8] Pham, A. T., & Nguyen, N. G. (2015). Applying Maple software in exploratory teaching of function analysis. Educational Equipment Journal, 123, 30–33 (in Vietnamese).
[9] Pham, M. H., & Tran, T. N. G. (2019). Applying Maple software in teaching advanced mathematics through applied problems. Dong Thap University Journal of Science, 37, 16–20. https://doi.org/10.52714/dthu.37.4.2019.676 (in Vietnamese).
[10] Nguyen, T. N. (2024). Application of Maple in teaching the concept of definite integrals. Educational Equipment - Special Issue on the New General Education Curriculum, 2(313), 25–30 (in Vietnamese).
[11] Dinh, T. G. (2024). Application of Wolfram|Alpha in Calculus teaching at Vinh University. Educational Equipment Journal, 2(319), 86–88 (in Vietnamese).
[12] Le, T. B. T. T., Tang, M. D., & Tran, D. K. (2024). Organizing students' self-study of linear equations via mobile learning using Microsoft Math Solver on smartphones. Ho Chi Minh City University of Education Journal of Science, 21(4), 759. https://doi.org/10.54607/hcmue.js.21.4.4116 (in Vietnamese).
[13] Evans, B. (2006). History of computer algebra systems. Georgia Institute of Technology.
[14] Arnold, S. (2004). Classroom computer algebra: Some issues and approaches. Australian Mathematics Teacher, 60(2), 17–21.
[15] Nunes-Harwitt, A. (2004). Opportunities and limitations of computer algebra in education. Journal of Educational Technology Systems, 33(2), 157–163.
[16] Heid, M. K., & Edwards, M. T. (2001). Computer algebra systems: Revolution or retrofit for today's mathematics classrooms? Theory Into Practice, 40(2), 128–136.
[17] Lagrange, J. B., Artigue, M., Laborde, C., & Trouche, L. (2003). Technology and mathematics education: A multidimensional study of the evolution of research and innovation. In Springer International Handbooks of Education (Vol. 10, pp. 237–269).
[18] National Council of Teachers of Mathematics (NCTM). (1989). Curriculum and evaluation standards for school mathematics. Reston, VA: NCTM.
[19] Bawatneh, Z. (2012). The impact of using a computer algebra system in high school calculus on high-performing students' conceptual and procedural understanding. Electronic Theses and Dissertations.
[20] Pierce, R., & Stacey, K. (2010). Mapping pedagogical opportunities provided by mathematics analysis software. International Journal of Computers for Mathematical Learning, 15, 1–20.
[21] Ball, L., & Stacey, K. (2003). What should students record when solving problems with CAS? Reasons, information, the plan and some answers. In Computer Algebra Systems in Secondary School Mathematics Education (pp. 289–303). Reston: The National Council of Teachers of Mathematics.
[22] Pierce, R., & Stacey, K. (2002). Monitoring effective use of computer algebra systems. In Proceedings of the 25th Annual Conference of the Mathematics Education Research Group of Australasia, Auckland.
[23] Pierce, R. U., & Stacey, K. C. (2002). Algebraic insight: The algebra needed to use computer algebra systems. The Mathematics Teacher, 95(8), 622–627.
[24] National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. Reston, VA: NCTM.
[25] Stacey, K. (2003). Using computer algebra systems in secondary school mathematics: Issues of curriculum, assessment and teaching.
[26] Santos, J. V. (2022). Comparative analysis of mobile applications for its integration in college mathematics subjects. Journal of Education, 6(4), 324–345.
[27] Dimiceli, V. E., Lang, A. S. I. D., & Locke, L. (2010). Teaching calculus with Wolfram Alpha. International Journal of Mathematical Education in Science and Technology, 1–11.
[28] Rosly, W., Abdullah, S., & Shukri, F. (2020). The uses of Wolfram Alpha in Mathematics. Teaching and Learning in Higher Education, 1.
[29] Abramovich, S. (2021). Using Wolfram Alpha with elementary teacher candidates: From more than one correct answer to more than one correct solution. Mathematics, 9(7), 2112.
[30] Nguyen, H. C., Tran, C., Nguyen, T. T. T., Dinh, T. H., Nguyen, T. T. L., & Nguyen, T. T. D. (2021). Designing Mathematics Lessons for Grade 6 (According to the 2018 Curriculum). University of Education Publishers, Hanoi.



