Document Type : Original Research Paper-English Issue
Authors
1 Department of Mathematics and Computer Science, Central Tehran branch, Islamic Azad University, Tehran, Iran
2 Department of Mathematics, Faculty of Sciences, Shahid Rajaei Teacher Training University, Tehran, Iran
Abstract
Background and Objectives: This comprehensive study delves into the comparative effectiveness of diverse educational approaches in enhancing students' comprehension and learning skills, specifically in the domain of geometric theorem proofs. The research focuses particularly on the section related to longitudinal relationships within triangles, a crucial component of the 11th-grade geometry curriculum. To identify the most impactful teaching strategies, this investigation meticulously compares three distinct pedagogical methods: (1) using illustrated examples formulated by the researcher through GeoGebra software, (2) exclusive use of examples, and (3) adherence to traditional teaching methods.
Materials and Methods: This research employs a quasi-experimental design with two experimental groups and one control group, including pre-test and post-test assessments. In terms of its objective, it is considered an applied study. The study population comprised 332 female 11th-grade students from District 3 of Isfahan during the second half of the 2021-2022 academic year. For the selection of the statistical sample, 60 students from three schools in District 3 of Isfahan were chosen using a purposive sampling method. All participants completed Cattell's Culture Fair Intelligence Test and a pre-test in Geometry 1 with identical questions. The first experimental group received an instructional video on constructing simple shapes and measuring shape components using GeoGebra software, along with virtual instructions on effective software use. The first author addressed their issues in five one-hour sessions. Additionally, five practical examples related to longitudinal relationships in triangles from the 11th-grade geometry textbook were presented, with responses designed using GeoGebra. Content validity was ensured through feedback from five experienced professors and teachers, who also reviewed aspects such as adherence to Persian grammar. The test questions demonstrated good reliability (Cronbach's alpha = 0.81). Given that this number exceeded 0.7, the test questions demonstrate good reliability. After confirmation and correction, the examples were provided to both experimental groups consecutively over five weeks, with 90-minute sessions conducted in the classroom. Examples were given to students without answers. The first group used GeoGebra to solve examples, hypothesize relationships between components, and verify them. Subsequently, correct answers were provided, and students were required to infer and prove the principles of relevant theorems with teacher guidance. Data analysis was conducted using SPSS 25 software, including ANCOVA analysis, Kolmogorov-Smirnov test, and Levene's test.
Findings: ANCOVA (Analysis of Covariance) results revealed statistically significant differences among the groups. Notably, the primary experimental group, which utilized a combination of carefully selected examples and interactive GeoGebra software, demonstrated superior performance compared to the second experimental group. This enhanced performance was particularly evident in two critical areas of geometric understanding: the accurate identification of relevant geometric theorems and the subsequent application of these theorems to complex problem-solving scenarios.
Conclusions: This comprehensive research underscores the significant benefits of integrating examples and GeoGebra software in geometry education. The findings demonstrate that this combined approach not only enhances students' understanding but also fosters their creativity and promotes active participation in the learning process. By engaging with interactive, visual representations of geometric concepts, students are empowered to explore, hypothesize, and verify mathematical ideas independently. This increased engagement ultimately leads to a more robust and lasting comprehension of geometric principles. It is recommended that educators actively encourage students to install GeoGebra software on their personal devices and allocate specific time for students to gain proficiency in its use.
Keywords
Main Subjects
COPYRIGHTS
© 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/)
', './data/jte/coversheet/cover_en.jpg'))
Send comment about this article