A Structural Model of Factors Influencing Mathematical Thinking and Reasoning Competence in Vietnamese Upper Secondary Education
Keywords:
error-based pedagogy; mathematical discourse and communication; mathematical thinking and reasoning competence; self-regulated learning; upper secondary educationAbstract
Mathematical thinking and reasoning competence is essential in contemporary mathematics education, yet empirical evidence explaining how pedagogical and cognitive factors jointly influence this competence remains limited. This study developed and validated a structural model to examine the relationships among five latent constructs, including: (1) reasoning-oriented task design and learning environment, (2) error-based pedagogical practices, (3) mathematical discourse and communication, (4) students’ cognitive disposition and self-regulation, and (5) mathematical thinking and reasoning competence. Data were collected from 246 upper secondary mathematics teachers in Vietnam. Confirmatory factor analysis (CFA) and structural equation modeling (SEM) were used to evaluate the measurement model and examine the proposed relationships. The results showed that error-based pedagogical practices, students’ cognitive disposition and self-regulation, and mathematical discourse and communication significantly predicted mathematical thinking and reasoning competence. In addition, reasoning-oriented task design and learning environment positively influenced mathematical discourse and communication, which in turn was significantly associated with students’ cognitive disposition and self-regulation. These findings highlight the complementary roles of pedagogical and cognitive factors in developing mathematical thinking and reasoning competence and suggest that the intentional use of students’ errors, together with the fostering of mathematical discourse, can support mathematics teaching in upper secondary education.
https://doi.org/10.26803/ijlter.25.8.32
References
Adleff, A.-K., Ross, N., König, J., & Kaiser, G. (2023). Types of mathematical tasks in lower secondary classrooms in Germany: Statistical findings from a latent class analysis based on general mathematical competencies. Educational Studies in Mathematics, 114(3), 371–392, https://doi.org/10.1007/s10649-023-10254-9
Arnesen, K. K., & Rø, K. (2022). The complexity of supporting reasoning in a mathematics classroom of shared authority. Mathematical Thinking and Learning, 26(2), 159–184, https://doi.org/10.1080/10986065.2022.2059628
Begolli, K. N., Dai, T., McGinn, K. M., & Booth, J. L. (2021). Could probability be out of proportion? Self-explanation and example-based practice help students with lower proportional reasoning skills learn probability. Instructional Science, 49(4), 441–473, https://doi.org/10.1007/s11251-021-09550-9
B? Giáo d?c và ?ào t?o [Ministry of Education and Training]. (2018). Ch??ng trình Giáo d?c ph? thông môn Toán [General Education Curriculum for Mathematics] (Ban hành kèm theo Thông t? s? 32/2018/TT-BGD?T [Issued with Circular No. 32/2018/TT-BGD?T]). B? Giáo d?c và ?ào t?o [Ministry of Education and Training]. https://cdn.thuvienphapluat.vn//uploads/Hoidapphapluat/2024/TTTT/241017/GDPT/3.CT_Toan.doc
Borasi, R. (1994). Capitalizing on errors as “springboards for inquiry”: A teaching experiment. Journal for Research in Mathematics Education, 25(2), 166–208. https://doi.org/10.5951/jresematheduc.25.2.0166
Cesaria, A., & Herman, T. (2019). Mathematical reasoning in geometry learning using information and communication technology (ICT). Journal of Physics: Conference Series, 1157(4), 042101. https://doi.org/10.1088/1742-6596/1157/4/042101
Darmawijoyo, Zulkardi, Putri, R. I. I., Hapizah, & Syutaridho. (2025). How do students use mathematical reasoning to solve PISA-type mathematics problems based on making kite contexts? Infinity Journal, 14(4), 1065–1080. https://doi.org/10.22460/infinity.v14i4.p1065-1080
Ferrini-Mundy, J. (2000). Principles and standards for school mathematics: A guide for mathematicians. Notices of the American Mathematical Society, 47(8), 868–876. https://www.ams.org/notices/200008/comm-ferrini.pdf
Gedik Altun, S. D., Konyal?o?lu, A. C., & Tuncer, E. B. (2017). Mistake handling activities in mathematics education: Practice in class. Journal of Education and Human Development, 6(2), 86–95. https://doi.org/10.15640/jehd.v6n2a9
Gunes Uzun, A. (2024). The development of mathematical argumentation: A case study on two mathematics classrooms. International Electronic Journal of Mathematics Education, 19(2), em0778, https://doi.org/10.29333/iejme/14581
Hair, J. F., Babin, B. J., Anderson, R. E., & Black, W. C. (2018). Multivariate data analysis (8th ed.). Cengage.
Jeannotte, D., & Kieran, C. (2017). A conceptual model of mathematical reasoning for school mathematics. Educational Studies in Mathematics, 96(1), 1–16. https://doi.org/10.1007/s10649-017-9761-8
Khasawneh, A.A., Al-Barakat, A.A., Almahmoud, S.A. (2022). The effect of error analysis-based learning on proportional reasoning ability of seventh-grade students. Frontiers in Education, 7, Article 899288. https://doi.org/10.3389/feduc.2022.899288
Kleitman, S., & Gibson, J. (2011). Metacognitive beliefs, self-confidence and primary learning environment of sixth grade students. Learning and Individual Differences, 21(6), 728–735, https://doi.org/10.1016/j.lindif.2011.08.003
Kleitman, S., Stankov, L., Allwood, C. M., Young, S., & Mak, K. K. L. (2012). Metacognitive self-confidence in school-aged children. In M. M. C. Mok (Ed.), Self-directed learning-oriented assessment in the Asia-Pacific (pp. 147–163). Springer. https://doi.org/10.1007/978-94-007-4507-0_8
Leong, K. E., Zulnaidi, H., & Chan, C. T. (2023). Undergraduate students’ attitudes and mathematical reasoning during the pandemic: The mediating role of metacognitive awareness. European Journal of Mathematics and Science Education, 4(3), 169–180. https://doi.org/10.12973/ejmse.4.3.169
Lestari, K.E., Utami, M.R., & Yudhanegara, M.R. (2022). Exploratory analysis on adaptive reasoning of undergraduate student in statistical inference. International Journal of Instruction, 15(4), 535–554, https://doi.org/10.29333/iji.2022.15429a
Lin, Y.-F., Yang, E.F.-Y., Wu, J.-S., Yeh, C.Y.C., Liao, C.-Y., Chan, T.-W. (2025). Enhancing students’ authentic mathematical problem-solving skills and confidence through error analysis of GPT-4 solutions. Research and Practice in Technology Enhanced Learning, 20, 034, https://doi.org/10.58459/rptel.2025.20034
Maulida, A. S., Wahyudin, W., Turmudi, T., & Nurlaelah, E. (2024). The effect of experiential learning and directed instructions assisted by augmented reality on students’ self-regulated learning. Infinity Journal, 13(2), 553–568. https://doi.org/10.22460/infinity.v13i2.p553-568
Miao, F., & Cukurova, M. (2024). AI competency framework for teachers. UNESCO. https://doi.org/10.54675/ZJTE2084
Mukuka, A., & Alex, J. K. (2024). Fostering students’ mathematical reasoning through a cooperative learning model. International Journal of Evaluation and Research in Education, 13(2), 1205–1215, https://doi.org/10.11591/ijere.v13i2.28010
Mumu, J., & Tanujaya, B. (2019). Measure reasoning skill of mathematics students. International Journal of Higher Education, 8(6), 85–91, https://doi.org/10.5430/ijhe.v8n6p85
Nguy?n V?n Thu?n, N. V. T., Nguy?n Th? M? H?ng, N. T. M. H., & Nguy?n Th? Trang, N. T. T. (2026). Phát tri?n n?ng l?c t? duy và l?p lu?n toán h?c c?a h?c sinh thông qua khai thác sai l?m trong d?y h?c toán [Developing students’ mathematical thinking and reasoning competence through error analysis in mathematics teaching]. T?p chí Giáo d?c, 26(4), 36–40. https://tcgd.tapchigiaoduc.edu.vn/index.php/tapchi/article/view/4861
Niss, M., & Højgaard, T. (2019). Mathematical competencies revisited. Educational Studies in Mathematics, 102(1), 9–28, https://doi.org/10.1007/s10649-019-09903-9
Nurrahmah, A., Kartono, Zaenuri, & Isnarto. (2023). The process of mathematics students’ reflective abstraction in solving continuous random variable problems in the probability course. International Journal of Education and Practice, 11(4), 727–738, https://doi.org/10.18488/61.v11i4.3497
OECD. (2017). PISA 2015 results (Volume V): Collaborative problem solving. OECD Publishing. https://doi.org/10.1787/9789264285521-en https://doi.org/10.1787/9789264285521-en
Polya, G. (1954). Mathematics and plausible reasoning: Volume I, Induction and analogy in mathematics. Princeton University Press.
Pratiwi, V., Herman, T., & Lidinillah, D. A. M. (2017). Upper elementary grades students’ algebraic thinking ability in Indonesia. IJAEDU—International E-Journal of Advances in Education, 3(9), 705–715. https://doi.org/10.18768/ijaedu.390554
Santagata, R. (2005). Practices and beliefs in mistake-handling activities: A video study of Italian and US mathematics lessons. Teaching and Teacher Education, 21(5), 491-508. https://doi.org/10.1016/j.tate.2005.03.004
Santana-Ramírez, H. F., Salgado-Beltrán, G., García-García, J., & López-González, A. (2025). Alternative conceptions about proportional reasoning in high school students. Infinity Journal, 14(3), 781–796, https://doi.org/10.22460/infinity.v14i3.p781-796
Schoenfeld, A. H. (1985). Mathematical problem solving. Academic Press. https://doi.org/10.1016/C2013-0-05012-8
Shaughnessy, M., & Boerst, T. A. (2018). Uncovering the skills that preservice teachers bring to teacher education: The practice of eliciting a student’s thinking. Journal of Teacher Education, 69(1), 40–55, https://doi.org/10.1177/0022487117702574
Shimizu, Y., & Kang, H. (2025). Research on classroom practice and students’ errors in mathematics education: a scoping review of recent developments for 2018– 2023. ZDM – Mathematics Education, 57(3), 695–710, https://doi.org/10.1007/s11858-025-01704-0
Siregar, N.C., Rosli, R., & Maat, S.M. (2020). The effects of a discovery learning module on geometry for improving students’ mathematical reasoning skills, communication and self-confidence. International Journal of Learning, Teaching and Educational Research, 19(3), 214–228, https://doi.org/10.26803/ijlter.19.3.12
Smit, R., Dober, H., Hess, K., Bachmann, P., & Birri, T. (2023). Supporting primary students’ mathematical reasoning practice: the effects of formative feedback and the mediating role of self-efficacy. Research in Mathematics Education, 25(3), 277–300, https://doi.org/10.1080/14794802.2022.2062780
Stylianides, A.J. (2007). Proof and proving in school mathematics. Journal for research in Mathematics Education, 38(3), 289–321, https://www.jstor.org/stable/30034869
Tak, C. C., Zulnaidi, H., Eu, L. K., & Feng, S. P. (2023). Mediating role of metacognitive awareness between self-efficacy and mathematics reasoning among education undergraduate students during pandemic. Journal of Higher Education Theory and Practice, 23(6), 36–46. https://doi.org/10.33423/jhetp.v23i6.5959
Tall, D. (2002). The psychology of advanced mathematical thinking. In D. Tall (Ed.), Advanced mathematical thinking (pp. 3–21). Springer. https://doi.org/10.1007/0-306-47203-1_1
Uyen, B.P., Ngan, L.K., Thao, N.P., Tong, D.H. (2021). Impulsing the development of students’ competency related to mathematical thinking and reasoning through teaching straight-line equations. International Journal of Learning, Teaching and Educational Research, 20(6), 38–65, https://doi.org/10.26803/ijlter.20.6.3
Wu, T.-T., Asmara, A., Huang, Y.-M., & Permata Hapsari, I. (2024). Identification of problem-solving techniques in computational thinking studies: Systematic literature review. SAGE Open, 14(2). https://doi.org/10.1177/21582440241249897
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