Year: 2026 | Month: May | Volume: 13 | Issue: 5 | Pages: 722-729
DOI: https://doi.org/10.52403/ijrr.20260572
Effectiveness of Smartphone-Based GeoGebra Integrated with Problem-Based Learning in Enhancing Students’ Critical Thinking on Function Transformations
Farah Diba1, Irvan2
1,2Postgraduate School of Mathematics Education, Universitas Muhammadiyah Sumatera Utara, Medan, Indonesia
Corresponding Author: Irvan
ABSTRACT
Students' mathematical critical thinking skills, particularly regarding function transformations, are currently below expected standards, largely due to the abstract nature of the topic, which requires students to connect algebraic expressions with graphical representations. In order to improve these abilities, this study examines how effectively smartphone-based GeoGebra may be incorporated into a Problem-Based Learning (PBL) framework. A validated critical thinking test that aligned with Facione's paradigm was used to collect data using a quantitative one-group pretest–posttest design with 46 twelfth-grade students. The results showed an adequate reliability (α = 0.78). Normalized gain (N-Gain), paired sample t-tests, and descriptive statistics were used in the analysis. The results showed that critical thinking abilities had significantly improved, with mean scores increasing from 49.46 in the pre-test to 79.37 in the post-test (p < 0.001). The N-Gain value of 0.59 indicates a moderate degree of progress. GeoGebra's dynamic visualization features, which let students view graphical changes in real time, and the PBL methodology, which promotes active inquiry and reflective thinking, are credited with this improvement. In conclusion, incorporating smartphone-based GeoGebra within a PBL environment effectively develops students' critical thinking skills in function transformation, underscoring the value of merging pedagogical strategies with interactive digital tools for deeper mathematical comprehension.
Keywords: GeoGebra; Mobile Learning; Function Transformation; Critical Thinking; Problem-Based Learning; Mathematical Visualization.
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