Document Type : Original Research Paper
Authors
Department of Mathematics Education, Farhangian University, P. O. Box 14665-889, Tehran, Iran
Abstract
Methods: This study is a mixed-methods research with a quantitative-qualitative approach, in which the quantitative part used a quasi-experimental research method with a single-group pre-test and post-test design. The statistical population consisted of 110 second-semester mathematics students in 2023 at one of the country's public universities, of whom 35 students participated in this study using a convenience sampling method. Data were collected through two researcher-developed questionnaires administered before and after the intervention to measure students' understanding of the purposes of proof, as well as an electronic dynamic assessment test. The test was developed using C++ and included five multiple-choice items accompanied by targeted, instructional feedback. The reliability of the questionnaires was confirmed using Cronbach's alpha (α = 0.7), and their validity was reviewed by expert faculty members. Quantitative data were analyzed using McNemar’s test to assess the significance of changes in students’ awareness of proof purposes. In addition, semi-structured interviews were conducted with 10 students to complete qualitative data analysis.
Findings: Statistical analysis revealed significant differences between students' responses in the pre- and post-intervention questionnaires for seven out of eight proof purposes (p < 0.05). The most notable improvement was observed in the “organization” purpose, with the number of students recognizing it rising from 15 in the pretest to 31 in the posttest. Other purposes, such as ‘explanation and clarification,’ ‘discovery of new results,’ ‘application in other contexts,’ and ‘problem solving,’ also showed significant gains. The only purpose that did not exhibit a statistically significant change was ‘verification of truth,’ which was already well understood before the intervention. Interview analysis confirmed that electronic dynamic assessment helped students recognize conceptual relationships, internal structures of proofs, and better understand the educational aims of proof. Students reported that the test questions and feedback provided a novel and insightful experience in understanding proofs.
Conclusion: The present study demonstrated that electronic dynamic assessment can serve as an effective tool for enhancing students’ awareness of the diverse functions of mathematical proof. Beyond mere evaluation, this type of assessment facilitates deeper learning of proof concepts and structures through instructional and interactive feedback. The findings align with previous research in mathematics education and highlight the pivotal role of assessments grounded in Vygotsky’s Zone of Proximal Development theory. It is recommended that mathematics educators incorporate interactive and feedback-driven models in the design of instructional and assessment activities to foster conceptual and purposeful understanding of proof among students. Such an approach not only helps students perceive proofs as tools for explanation, organization, discovery, and problem-solving, but also lays the foundation for developing mathematical reasoning and cultivating critical thinking. In doing so, students’ understanding of the nature and purpose of proof is transformed from a rule-based and repetitive view to a dynamic, analytical, and deeply applicable perspective.
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© 2025 The Author(s). This is an open-access article distributed under the terms and conditions of the Creative Attribution-NonCommercial 4.0 International (CC BY-NC 4.0) (https://creativecommons.org/licenses/by-nc/4.0/)
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