Investigating the Impact of Mason, Burton, and Stacey's Problem-Solving Method Based on Mathematical Modeling on the Learning and Comprehension of Proof and Reasoning Skills: An Experimental Study in Virtual Education of Ninth-Grade Students

Abstract Extended
Aim and Introduction: The rapid shift to virtual education due to the COVID-19 pandemic has underscored the need for effective teaching methodologies in mathematics, particularly in developing proof and reasoning skills amongst students. This study aims to investigate the efficacy of the Mason, Burton, and Stacey problem-solving approach in enhancing ninth-grade students' understanding and capabilities in proof and reasoning within a virtual learning framework. Given that reasoning and proof are crucial components of mathematical understanding, the research seeks to determine whether these skills can contribute to solving mathematical problems through modeling real-life contexts. The study addresses the following research question: Can proficiency in proof and reasoning enhance students’ abilities to apply mathematical modeling in real-life problem-solving scenarios?
Methodology: The research employs a quasi-experimental design with a static group comparison, integrating a pre-test and post-test evaluation to measure student performance before and after the intervention. The sample consists of 34 ninth-grade female students from one of the 19 educational districts in Tehran during the academic year 2020-2021. A multi-stage cluster sampling technique was adopted to select participants, resulting in two classes of 17 students each: one designated as the experimental group and the other as the control group. The experimental group engaged in learning the third chapter of the ninth-grade mathematics curriculum through the Mason, Burton, and Stacey problem-solving method, explicitly focusing on the skills of proof and reasoning. Conversely, the control group received traditional lecture-based instruction on the same topic.
Data were collected through a four-option questionnaire designed to assess students' understanding of mathematical modeling in relation to proof and reasoning skills. The questionnaire included questions aligned with various cognitive learning levels, ensuring that it adequately captured the depth of students’ understanding. Validity was verified through expert evaluations by university professors in the field of mathematics education, while reliability was confirmed with Cronbach's alpha coefficients, showing values of 0.821 for the pre-test and 0.786 for the post-test, both falling within acceptable ranges for educational research.
Statistical analyses were conducted using SPSS software. The normality of the data permitted the use of independent two-sample t-tests and one-way analysis of covariance (ANCOVA) to compare the outcomes between experimental and control group participants.
Finding: The results of the statistical analysis revealed that there were significant differences in the performance of students between the experimental and control groups (p = 0.0006), indicating that the students taught through the Mason, Burton, and Stacey method achieved higher scores on assessment measures compared to their counterparts in the control group. Specifically, the findings of the t-test suggest that not only was the intervention effective in improving students' understanding of proof and reasoning, but it also fostered a more positive attitude towards learning these skills.
Further analysis using one-way ANCOVA provided additional evidence supporting the hypothesis that the Mason, Burton, and Stacey problem-solving method significantly enhances students’ cognitive engagement with proof and reasoning. The experimental group demonstrated improved learning outcomes, evidenced by higher mean scores on both the pre-test and post-test assessments, confirming the methodology's effectiveness in promoting mathematical reasoning.
Discussion and Conclusion: The findings of this study have substantial implications for mathematics education, particularly in the context of virtual learning environments. The positive impact of the Mason, Burton, and Stacey method on students' proficiency in proof and reasoning suggests that this instructional approach can effectively bridge the gap between theoretical mathematical constructs and practical applications, enhancing students’ abilities to tackle real-world problems through mathematical modeling.
The study emphasizes the necessity for educators to adapt innovative and engaging teaching methodologies that promote active participation and deeper cognitive engagement, especially in subjects like mathematics that typically require conceptual understanding rather than rote memorization. The COVID-19 pandemic has presented unique challenges in delivering mathematics education, making it imperative to explore and implement teaching strategies that can retain student engagement in a virtual context.
Moreover, the research highlights the critical role that proof and reasoning play in fostering students' logical thinking and problem-solving capabilities, which are essential skills not only in mathematics but across various disciplines. By integrating the Mason, Burton, and Stacey problem-solving method into the curriculum, educators can cultivate an environment where students not only learn mathematical concepts but also develop the skills needed to apply these concepts in practical situations.
In summary, this study concludes that the Mason, Burton, and Stacey problem-solving approach significantly improves the acquisition of proof and reasoning skills among ninth-grade students in virtual educational settings. As educational institutions continue to navigate the complexities of remote learning, there is an urgent need for further research and development of innovative teaching strategies that focus on student engagement and real-world applicability in mathematics education.
Keywords: Problem-solving, Proof and reasoning, Cognitive learning, Mathematics education, Mathematical modeling.