Enhancing Students’ Spatial Reasoning and Applied Geometry Problem-Solving through GeoGebra-Assisted Project-Based Learning
Keywords:
applied geometry, GeoGebra, project-based learning, spatial reasoning, problem-solvingAbstract
This study investigated the effectiveness of GeoGebra-assisted Project-Based Learning in improving students’ spatial reasoning and applied geometry problem-solving ability in an Applied Geometry course. The study employed a quantitative approach with a quasi-experimental pretest-posttest design involving 30 students. The intervention integrated dynamic geometry visualization through GeoGebra with project-based learning activities that required students to construct, analyze, revise, and present applied geometry models. Data were collected using spatial reasoning and applied geometry problem-solving tests administered before and after the intervention. The results showed that students’ spatial reasoning increased from a pretest mean score of 61.27 to a posttest mean score of 82.43, while their applied geometry problem-solving ability increased from 58.80 to 80.67. The normality test indicated that all data were normally distributed, and the paired-sample t-test showed significant improvements in both variables with p < 0.001. The normalized gain scores were 0.55 for spatial reasoning and 0.53 for applied geometry problem-solving, both categorized as moderate. These findings indicate that GeoGebra-assisted Project-Based Learning is an effective instructional approach for strengthening students’ visual-spatial understanding and contextual geometry problem-solving ability.
References
C. Zhu et al., “Fostering spatial ability development in and for authentic STEM learning,” Front. Educ. (Lausanne)., vol. 8, p. 1138607, Apr. 2023, doi: 10.3389/FEDUC.2023.1138607/FULL.
I. I. Supianti, P. Yaniawati, E. Bonyah, A. W. Hasbiah, and N. Rozalini, “STEAM approach in project-based learning to develop mathematical literacy and students’ character,” Infinity Journal, vol. 14, no. 2, pp. 283–302, May 2025, doi: 10.22460/INFINITY.V14I2.P283-302.
I. Muhammad, A. Jupri, and T. Herman, “Development of web-based learning media with a realistic mathematics education approach to increase student self-determination,” Infinity Journal, vol. 14, no. 2, pp. 303–322, May 2025, doi: 10.22460/INFINITY.V14I2.P303-322.
A. Yohannes and H. L. Chen, “GeoGebra in mathematics education: a systematic review of journal articles published from 2010 to 2020,” Interactive Learning Environments, vol. 31, no. 9, pp. 5682–5697, Dec. 2023, doi: 10.1080/10494820.2021.2016861.
R. M. M. Sari, N. Priatna, and D. Juandi, “Implementing Project-Based Blended Learning Model Using Cognitive Conflict Strategy to Enhance Students’ Mathematical Spatial Literacy,” European Journal of Educational Research, vol. 11, no. 4, pp. 2031–2041, Oct. 2022, doi: 10.12973/EU-JER.11.4.2031.
M. A. Almulla, “The Effectiveness of the Project-Based Learning (PBL) Approach as a Way to Engage Students in Learning,” Sage Open, vol. 10, no. 3, Jul. 2020, doi: 10.1177/2158244020938702;SUBPAGE:STRING:FULL.
W. R. Shadish, T. D. Cook, and D. T. Campbell, “EXPERIMENTAL AND QUASI-EXPERIMENTAL DESIGNS FOR GENERALIZED CAUSAL INFERENCE .jr-*"-** fr HOUGHTON MIFFLIN COMPANY Boston New York,” 2002.
Y. Zhang, P. Wang, W. Jia, A. Zhang, and G. Chen, “Dynamic visualization by GeoGebra for mathematics learning: a meta-analysis of 20 years of research,” Journal of Research on Technology in Education, vol. 57, no. 2, pp. 437–458, 2025, doi: 10.1080/15391523.2023.2250886.
F. Gurmu, C. Tuge, and A. B. Hunde, “Effects of GeoGebra-assisted instructional methods on students’ conceptual understanding of geometry,” Cogent Education, vol. 11, no. 1, Dec. 2024, doi: 10.1080/2331186X.2024.2379745.
C. W. Tsai, P. Di Shen, and R. A. Lin, “Exploring the effects of student-centered project-based learning with initiation on students’ computing skills: A quasi-experimental study of digital storytelling,” International Journal of Information and Communication Technology Education, vol. 11, no. 1, pp. 27–43, Jan. 2015, doi: 10.4018/IJICTE.2015010102.
K. Suastika, “Mathematics Learning Model of Open Problem Solving to Develop Students’ Creativity,” International Electronic Journal of Mathematics Education, vol. 12, no. 3, pp. 569–577, Dec. 2021, doi: 10.29333/IEJME/633.
