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.
Published Version
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