Developing Critical Thinking Using the Geogebra Integrated Deep Learning Approach on Quadratic Equations Material for Elementary School Students

Abstract

Critical mathematical thinking is a higher-order cognitive ability that plays a crucial role in understanding abstract algebraic concepts, particularly quadratic equations, at the elementary school level. This study aimed to examine the effectiveness of a GeoGebra-integrated deep learning approach in improving fifth-grade students’ critical mathematical thinking skills on quadratic equations material. A quantitative pre-experimental method with a one-group pretest–posttest design was employed involving 30 elementary school students. The learning activities emphasized problem orientation, dynamic visualization of quadratic graphs, exploration of coefficient–graph relationships, analytical reasoning, reflective discussion, and generalization through GeoGebra-assisted exploration. Students’ critical mathematical thinking skills were assessed across five indicators: identifying problems, analyzing conceptual relationships, formulating solution strategies, evaluating solutions, and drawing conclusions based on digital exploration. Data were analyzed using descriptive statistics and a paired-samples t-test. The results indicated a substantial improvement in students’ critical thinking skills, as reflected by higher mean posttest scores compared to pretest scores. The paired-samples t-test revealed a statistically significant difference (p < 0.001), accompanied by a very large effect size (Cohen’s d in the very large category), indicating strong practical effectiveness. These findings suggest that the GeoGebra-integrated deep learning approach is highly effective in fostering students’ critical mathematical thinking and provides a meaningful instructional strategy for learning quadratic equations in elementary education.