Reconstructing Multivariable Calculus Learning through Mathematical Discourse for Conceptual and Procedural Understanding
Keywords:
Multivariable Calculus Mathematical Discourse Conceptual Understanding Procedural Application Collaborative Learning
Abstract
Purpose of the study: This study aims to evaluate the effectiveness of a mathematical discourse methodology in enhancing conceptual understanding and procedural application in Multivariable Calculus among undergraduate mathematics education students.
Methodology: A mixed-methods study design was employed, combining pre-tests, post-tests, classroom recordings, and focus group discussions. Quantitative analysis included paired t-tests and MANOVA, while qualitative data were analyzed using Sfard’s (2008) coding framework. A pilot study validated the instruments with high internal consistency (Cronbach’s alpha: 0.87 for procedural, 0.84 for conceptual understanding).
Main Findings: The mathematical discourse methodology significantly improved conceptual understanding (mean increase: 26.2, p < 0.01) and procedural application (mean increase: 28.4, p < 0.01) in the experimental group compared to minimal improvements in the control group. Qualitative findings revealed increased engagement, critical thinking, and connections to real-world applications.
Novelty/Originality of this study: This study introduces the application of mathematical discourse specifically to Multivariable Calculus, bridging conceptual and procedural understanding through active, dialogic learning. It provides a scalable framework for integrating structured discourse into higher mathematics education, advancing student-centered and collaborative pedagogical practices.
References
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[2] T. Fujii, “Misconceptions and Alternative Conceptions in Mathematics Education,” in Encyclopedia of Mathematics Education, Dordrecht: Springer Netherlands, 2014, pp. 453–455. doi: 10.1007/978-94-007-4978-8_114.
[3] L. Mebert et al., “Fostering student engagement through a real-world, collaborative project across disciplines and institutions,” High Educ Pedagog, vol. 5, no. 1, pp. 30–51, Jan. 2020, doi: 10.1080/23752696.2020.1750306.
[4] A. Haleem, M. Javaid, M. A. Qadri, and R. Suman, “Understanding the role of digital technologies in education: A review,” Sustainable Operations and Computers, vol. 3, pp. 275–285, 2022, doi: 10.1016/j.susoc.2022.05.004.
[5] M. Firdaus and Mukhtar, “Critical Thinking Skills of Mathematics Prospective Teachers: An Exploration Study at Medan State University,” J Phys Conf Ser, vol. 1462, no. 1, p. 012005, Feb. 2020, doi: 10.1088/1742-6596/1462/1/012005.
[6] S. Prediger, J. Dröse, R. Stahnke, and C. Ademmer, “Teacher expertise for fostering at-risk students’ understanding of basic concepts: conceptual model and evidence for growth,” Journal of Mathematics Teacher Education, vol. 26, no. 4, pp. 481–508, Aug. 2023, doi: 10.1007/s10857-022-09538-3.
[7] D. Kollosche, “Styles of reasoning for mathematics education,” Educational Studies in Mathematics, vol. 107, no. 3, pp. 471–486, Jul. 2021, doi: 10.1007/s10649-021-10046-z.
[8] D. Navarro-Mateu, T. Gómez-Domínguez, M. Padrós Cuxart, and E. Roca-Campos, “Dialogic Learning Environments That Enhance Instrumental Learning and Inclusion of Students With Special Needs in Secondary Education,” Front Psychol, vol. 12, Jun. 2021, doi: 10.3389/fpsyg.2021.662650.
[9] A. Rodríguez-Oramas, P. Alvarez, M. Ramis-Salas, and L. Ruiz-Eugenio, “The Impact of Evidence-Based Dialogic Training of Special Education Teachers on the Creation of More Inclusive and Interactive Learning Environments,” Front Psychol, vol. 12, Mar. 2021, doi: 10.3389/fpsyg.2021.641426.
[10] M. Kolovou, “Embracing Culturally Relevant Education in Mathematics and Science: A Literature Review,” Urban Rev, vol. 55, no. 1, pp. 133–172, Mar. 2023, doi: 10.1007/s11256-022-00643-4.
[11] F. Reuter, “Explorative mathematical argumentation: a theoretical framework for identifying and analysing argumentation processes in early mathematics learning,” Educational Studies in Mathematics, vol. 112, no. 3, pp. 415–435, Mar. 2023, doi: 10.1007/s10649-022-10199-5.
[12] R. Cui and P. Teo, “Dialogic education for classroom teaching: a critical review,” Language and Education, vol. 35, no. 3, pp. 187–203, May 2021, doi: 10.1080/09500782.2020.1837859.
[13] R. García-Carrión, G. López de Aguileta, M. Padrós, and M. Ramis-Salas, “Implications for Social Impact of Dialogic Teaching and Learning,” Front Psychol, vol. 11, Feb. 2020, doi: 10.3389/fpsyg.2020.00140.
[14] B. Koichu, B. B. Schwarz, E. Heyd-Metzuyanim, M. Tabach, and A. Yarden, “Design practices and principles for promoting dialogic argumentation via interdisciplinarity,” Learn Cult Soc Interact, vol. 37, p. 100657, Dec. 2022, doi: 10.1016/j.lcsi.2022.100657.
[15] E. Er, Y. Dimitriadis, and D. Gašević, “A collaborative learning approach to dialogic peer feedback: a theoretical framework,” Assess Eval High Educ, vol. 46, no. 4, pp. 586–600, May 2021, doi: 10.1080/02602938.2020.1786497.
[16] M. T. Kalkbrenner, “Alpha, Omega, and H Internal Consistency Reliability Estimates: Reviewing These Options and When to Use Them,” Counseling Outcome Research and Evaluation, vol. 14, no. 1, pp. 77–88, Jan. 2023, doi: 10.1080/21501378.2021.1940118.
[17] A. J. Kleinheksel, N. Rockich-Winston, H. Tawfik, and T. R. Wyatt, “Demystifying Content Analysis,” Am J Pharm Educ, vol. 84, no. 1, p. 7113, Jan. 2020, doi: 10.5688/ajpe7113.
[18] D. Lombardi et al., “The Curious Construct of Active Learning,” Psychological Science in the Public Interest, vol. 22, no. 1, pp. 8–43, Apr. 2021, doi: 10.1177/1529100620973974.
[19] K. A. Nguyen et al., “Instructor strategies to aid implementation of active learning: a systematic literature review,” Int J STEM Educ, vol. 8, no. 1, p. 9, Dec. 2021, doi: 10.1186/s40594-021-00270-7.
[20] S. L. Chew and W. J. Cerbin, “The cognitive challenges of effective teaching,” J Econ Educ, vol. 52, no. 1, pp. 17–40, Jan. 2021, doi: 10.1080/00220485.2020.1845266.
[21] Y. Shi, M. Tong, and T. Long, “Investigating relationships among blended synchronous learning environments, students’ motivation, and cognitive engagement: A mixed methods study,” Comput Educ, vol. 168, p. 104193, Jul. 2021, doi: 10.1016/j.compedu.2021.104193.
[22] S. Liu, S. Liu, Z. Liu, X. Peng, and Z. Yang, “Automated detection of emotional and cognitive engagement in MOOC discussions to predict learning achievement,” Comput Educ, vol. 181, p. 104461, May 2022, doi: 10.1016/j.compedu.2022.104461.
[23] M. Kokoç and A. Altun, “Effects of learner interaction with learning dashboards on academic performance in an e-learning environment,” Behaviour & Information Technology, vol. 40, no. 2, pp. 161–175, Jan. 2021, doi: 10.1080/0144929X.2019.1680731.
[24] J. Díez-Palomar, R. García-Carrión, L. Hargreaves, and M. Vieites, “Transforming students’ attitudes towards learning through the use of successful educational actions,” PLoS One, vol. 15, no. 10, p. e0240292, Oct. 2020, doi: 10.1371/journal.pone.0240292.
[25] P. Wright, “Transforming mathematics classroom practice through participatory action research,” Journal of Mathematics Teacher Education, vol. 24, no. 2, pp. 155–177, Apr. 2021, doi: 10.1007/s10857-019-09452-1.
[26] S. Saneinia, X. Zhai, R. Zhou, A. Gholizadeh, R. Wu, and S. Zhu, “Beyond virtual boundaries: the intersection of the metaverse technologies, tourism, and lifelong learning in China’s digital discourse,” Humanit Soc Sci Commun, vol. 11, no. 1, p. 1287, Sep. 2024, doi: 10.1057/s41599-024-03624-y.
[27] R. W. Pretorius, S. Carow, G. Wilson, and P. Schmitz, “Using real-world engagements for sustainability learning in ODeL in the Global South: challenges and opportunities,” International Journal of Sustainability in Higher Education, vol. 22, no. 6, pp. 1316–1335, Aug. 2021, doi: 10.1108/IJSHE-08-2020-0287.
[28] A. Grotlüschen, A. Belzer, M. Ertner, and K. Yasukawa, “The role of adult learning and education in the Sustainable Development Goals,” International Review of Education, vol. 70, no. 2, pp. 205–221, Apr. 2024, doi: 10.1007/s11159-024-10066-w.
[29] N. Kerimbayev, Z. Umirzakova, R. Shadiev, and V. Jotsov, “A student-centered approach using modern technologies in distance learning: a systematic review of the literature,” Smart Learning Environments, vol. 10, no. 1, p. 61, Nov. 2023, doi: 10.1186/s40561-023-00280-8.
[30] E. Xu, W. Wang, and Q. Wang, “The effectiveness of collaborative problem solving in promoting students’ critical thinking: A meta-analysis based on empirical literature,” Humanit Soc Sci Commun, vol. 10, no. 1, p. 16, Jan. 2023, doi: 10.1057/s41599-023-01508-1.
[31] J. Digout and H. El Samra, “Interactivity and Engagement Tactics and Tools,” in Governance in Higher Education, Cham: Springer Nature Switzerland, 2023, pp. 151–169. doi: 10.1007/978-3-031-40586-0_8.
[32] G. Fischer, J. Lundin, and J. O. Lindberg, “Rethinking and reinventing learning, education and collaboration in the digital age—from creating technologies to transforming cultures,” The International Journal of Information and Learning Technology, vol. 37, no. 5, pp. 241–252, Sep. 2020, doi: 10.1108/IJILT-04-2020-0051.
Published
2025-01-04
How to Cite
[1]
M. Firdaus and M. Mukhtar, “Reconstructing Multivariable Calculus Learning through Mathematical Discourse for Conceptual and Procedural Understanding”, Jor. Eva. Edu, vol. 6, no. 1, Jan. 2025.
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