USING GEOGEBRA FOR TEACHING PROBLEMS ON FIXED POINTS OF FAMILIES OF LINES AND CIRCLES IN SECONDARY SCHOOL GEOMETRY

This paper explores the application of GeoGebra software to assist teachers and students in lessons on fixed points of families of lines and circles, a relatively complex topic in secondary school geometry that requires logical reasoning and advanced proof skills. GeoGebra, as a visual modeling tool, enables the discovery and proof of fixed points in problems involving families of lines and circles. The selected illustrations are derived from problems featured in competitions for high-achieving students and specialized 10th-grade entrance exams in recent years. To evaluate the effectiveness of this teaching method, experiments were conducted with 59 Grade 9 students at Newton Secondary and High School (Bac Tu Liem, Ha Noi). A t-test on students’ test scores after being taught fixed-point problems showed statistically significant differences between the GeoGebra method group (M = 7.07, SD = 1.64) and the traditional method group (M = 5.6, SD = 1.3) [t(59) = 1.987934, p = 0.001134 < 0.05]. Additionally, students in the experimental group demonstrated greater interest in the presented problems. The findings from this study highlight the potential of using GeoGebra to teach advanced geometrical problems within the Vietnamese educational context.