Exploring High School Students' Mathematical Reasoning in Geometry Using GeoGebra-Assisted Problem-Based Learning
DOI:
https://doi.org/10.21009/jtp.v26i3.49887Keywords:
Mathematical Reasoning, Geometry, Problem-Based Learning, GeoGebra, Prior Mathematical AbilityAbstract
The significance of mathematical reasoning in mathematics instruction and the substantial incidence of inadequate mathematical reasoning among high school students prompted this study. This study intends to explore the mathematical reasoning of high school students about three-dimensional geometry using the GeoGebra-assisted Problem-Based Learning (GPBL) model. This research applied a quasi-experimental design including a non-equivalent pretest and posttest control group. The subjects of this research were specifically 12th-grade students from an upper secondary school in Subang. The research contained two classes, with 27 students as the experimental group and 27 as the control group. Interviews were conducted to identify the factors that explain students' difficulties in solving mathematical reasoning problems concerning three-dimensional geometry. The findings indicated that (1) overall, the enhancement of mathematical reasoning among students utilizing the GPBL model was significantly higher than that of students implementing the conventional learning model; (2) referring to students' prior mathematical ability (PMA), the enhancement in mathematical reasoning for students in high, medium, and low PMA groups utilizing the GPBL model was significantly higher than that of students implementing the conventional learning model; (3) the main obstacle discovered by students to solving mathematical reasoning problems involving three-dimensional geometry is their struggle in visualizing problems in a three-dimensional context. GeoGebra assists students in visually constructing three-dimensional geometry problems and evaluating the outcomes of algebraic algorithms with 3D graphical representations.
References
Andrews, D., van Lieshout, E., & Kaudal, B. B. (2023). How, Where, and When Do Students Experience Meaningful Learning?. International Journal of Innovation in Science and Mathematics Education, 31(3), 28-45. https://doi.org/10.30722/IJISME.31.03.003
Arends, R. I. (2012). Learn to Teach (Ninth Edition). Mc. Graw Hill.
Arnawa, I. M., & Fitriani, N. (2022). Constructing Calculus Concepts through Worksheet Based Problem-Based Learning Assisted by Geogebra Software. HighTech and Innovation Journal, 3(3), 282-296. https://doi.org/10.28991/HIJ-2022-03-03-04
Awaji, B. M. A. (2021). Investigating The Effectiveness of Using Geogebra Software on Students' Mathematical Proficiency [Unpublished doctoral dissertation]. University of Glasgow.
Birgin, O., & Topuz, F. (2021). Effect of The Geogebra Software-Supported Collaborative Learning Environment on Seventh Grade Students’ Geometry Achievement, Retention and Attitudes. The Journal of Educational Research, 114(5), 474-494. https://doi.org/10.1080/00220671.2021.1983505
Braak, D. T., Lenes, R., Purpura, D. J., Schmitt, S. A., & Størksen, I. (2022). Why Do Early Mathematics Skills Predict Later Mathematics and Reading Achievement? The Role of Executive Function. Journal of Experimental Child Psychology, 214. https://doi.org/10.1016/j.jecp.2021.105306
Buckley, J., Seery, N., & Canty, D. (2019). Investigating the Use of Spatial Reasoning Strategies in Geometric Problem Solving. International Journal of Technology and Design Education, 29(2), 341-362. https://doi.org/10.1007/s10798-018-9446-3
Cabello, V. M., Moreira, P. M., & Morales, P. G. (2021). Elementary Students’ Reasoning in Drawn Explanations Based on a Scientific Theory. Education Sciences, 11(10), 581. https://doi.org/doi.org/10.3390/educsci11100581
Carbonell-Carrera, C., Jaeger, A. J., Saorín, J. L., Melián, D., & de la Torre-Cantero, J. (2021). Minecraft as a Block Building Approach for Developing Spatial Skills. Entertainment Computing, 38. https://doi.org/10.1016/j.entcom.2021.100427
Condori, A. P., Velazco, D. J. M., & Fernández, R. A. (2020). In Conference on Information and Communication Technologies of Ecuador. Geogebra as a Technological Tool in The Process of Teaching and Learning Geometry. Springer International Publishing. https://doi.org/10.1007/978-3-030-62833-8_20
Creswell, J. W., & Creswell, J. D. (2018). Research Design: Qualitative, Quantitative, and Mixed Methods Approaches (Fifth Edition). SAGE Publications.
de Sousa, R. T., Alves, F. R. V., & de Azevedo, I. F. (2021). Categories of Intuitive Reasoning and GeoGebra 3D: An Experience with Brazilian Students. LUMAT: International Journal on Math, Science and Technology Education, 9(1), 622-642. https://doi.org/10.31129/LUMAT.9.1.1618
Departemen Pendidikan Nasional (Depdiknas). (2007). Kajian Kebijakan Kurikulum Mata Pelajaran Matematika. Badan Penelitian dan Pengembangan Pusat Kurikulum.
Dong, A., Jong, M. S. Y., & King, R. B. (2020). How Does Prior Knowledge Influence Learning Engagement? The Mediating Roles of Cognitive Load and Help-Seeking. Frontiers in Psychology, 11. https://doi.org/10.3389/fpsyg.2020.591203
Fadlillah, M., Ali, M., Hernawan, A. H., & Riyana, C. (2023). Designing a Media Literacy Training Curriculum Framework for Junior High School Teachers. JTP-Jurnal Teknologi Pendidikan, 25(3), 414-429. https://doi.org/10.21009/jtp.v25i3.38928
Fisher, D. (2021). Kemampuan Pemecahan Masalah, Penalaran dan Self-Esteem Matematis Siswa SMP dalam Project-Based Learning dengan Pendekatan Authentic Learning Experiences [Unpublished doctoral dissertation]. Universitas Pendidikan Indonesia.
Fitriyah, M. I., Putro, N. H. P. S., & Apino, E. (2022). Meta Analysis Study: Effectiveness of Problem-Based Learning on Indonesian Students’ Mathematical Reasoning Ability. Jurnal Riset Pendidikan Matematika, 9(1), 36-45. https://doi.org/10.21831/jrpm.v9i1.46447
Gökçe, S., & Güner, P. (2022). Dynamics of GeoGebra Ecosystem in Mathematics Education. Education and Information Technologies, 27(4), 5301-5323. https://doi.org/10.1007/s10639-021-10836-1
Gunawan, I. (2017). Pengantar Statistika Inferensial. Rajawali Pers.
Hake, R. R. (1998). Interactive-Engagement versus Traditional Methods: A Six-Thousand-Student Survey of Mechanics Test Data for Introductory Physics Courses. American Journal of Physics, 66(1), 64-74. https://doi.org/10.1119/1.18809
Hanifah, M., Ishartono, N., Halili, S. H. B., & Razak, R. B. A. (2023). AIP Conference Proceedings of International Summit on Education, Technology, and Humanity (ISETH) 2021. Improving Secondary School Student’s Mathematics Critical Thinking in Geometry Transformation through Geogebra-Based Flipped Learning: An Experimental Study. AIP Publishing. https://doi.org/10.1063/5.0141401
Hermino, A., & Arifin, I. (2020). Contextual Character Education for Students in the Senior High School European. Journal of Educational Research, 9(3), 1009-1023. https://doi.org/10.12973/eu-jer.9.3.1009
Hjelte, A., Schindler, M., & Nilsson, P. (2020). Kinds of Mathematical Reasoning Addressed in Empirical Research in Mathematics Education: A Systematic Review. Education Sciences, 10(10), 289. https://doi.org/10.3390/educsci10100289
Indrapangastuti D., Surjono, H. D., & Yanto, B. E. (2021). Effectiveness of the Blended Learning Model to Improve Students' Achievement of Mathematical Concepts. Journal of Education and E-Learning Research, 8(4), 423-430. https://doi.org/10.20448/journal.509.2021.84.423.430
Jupri, A. (2017). AIP Conference Proceedings of The 4th International Conference on Mathematical Sciences (ICMS4), 1830(1). From Geometry to Algebra and Vice Versa: Realistic Mathematics Education Principles for Analyzing Geometry Tasks. AIP Publishing. https://doi.org/10.1063/1.4980938
Kamid, Sofnidar, Syafmen, W., Mujahidawati, Theis, R., & Anwar, K. (2020). The Influence of Computer-Based Learning Media Tutorials on Students' Spatial Abilities In Mathematics. JTP-Jurnal Teknologi Pendidikan, 22(3), 159-166. https://doi.org/10.21009/jtp.v22i3.16536
Kustiawati, D., & Siregar, N. (2022). AIP Conference Proceedings of The 6th National Conference on Mathematics and Mathematics Education, 2577(1). Problem-Solving with Geogebra: How The Relationship between Reasoning and Communication in Mathematics. AIP Publishing. https://doi.org/10.1063/5.0096136
Laurens, T., Batlolona, F. A., Batlolona, J. R., & Leasa, M. (2017). How Does Realistic Mathematics Education (RME) Improve Students’ Mathematics Cognitive Achievement?. Eurasia Journal of Mathematics, Science and Technology Education, 14(2), 569-578. https://doi.org/10.12973/ejmste/76959
Liburd, K. K. D., & Jen, H. Y. (2021). Investigating the Effectiveness of Using a Technological Approach on Students’ Achievement in Mathematics–Case Study of a High School in a Caribbean Country. Sustainability, 13(10), 5586. https://doi.org/10.3390/su13105586
Mandasari, N. (2021). Journal of gers: Conference Series in Mathematics and Science Education International Seminar (MASEIS) 2019, 1731(1). Problem-Based Learning Model to Improve Mathematical Reasoning Ability. IOP Publishing. https://doi.org/10.1088/1742-6596/1731/1/012041
Muchlis, E. E., Priatna, N., Herman, T., & Juandi, D. (2023). Geogebra-Assisted Inductive Reasoning in Project-Based Learning through a Web-Based System. Journal of Engineering, Science and Technology, 18, 224-238. https://jestec.taylors.edu.my/Special%20Issue%20ISCoE%202022_1/ISCoE%201_19.pdf
Napitupulu, E. E., Suryadi, D., & Kusumah, Y. S. (2016). Cultivating Upper Secondary Students' Mathematical Reasoning-Ability and Attitude Towards Mathematics through Problem-Based Learning. Journal on Mathematics Education, 7(2), 117-128. https://doi.org/10.22342/jme.7.2.3542.117-128
National Council of Teachers of Mathematics (NCTM). (2000). Principles and Standards for School Mathematics. NCTM.
Nurjanah, Latif, B., Yuliardi, R., & Tamur, M. (2020). Computer-Assisted Learning Using The Cabri 3D for Improving Spatial Ability and Self-Regulated Learning. Heliyon, 6(11). https://doi.org/10.1016/j.heliyon.2020.e05536
Organisation for Economic Co-operation and Development (OECD). (2023). PISA 2022 Results (Volume I): The State of Learning and Equity in Education. OECD Publishing.
Oslington, G., Mulligan, J., & Bergen, P. V. (2020). Third-Graders’ Predictive Reasoning Strategies. Educational Studies in Mathematics, 104, 5-24. https://doi.org/10.1007/s10649-020-09949-0
Pérez, H. G., & Ortega, M. V. (2019). Journal of Physics: Conference Series in III International Meeting of Mathematical Education, 1408(1). Development of Math Skills in First Semester Students of Public Accounting. IOP Publishing. https://doi.org/10.1088/1742-6596/1408/1/012021
Rach, S. & Ufer, S. (2020). Which Prior Mathematical Knowledge is Necessary for Study Success in the University Study Entrance Phase? Results on a New Model of Knowledge Levels Based on a Reanalysis of Data from Existing Studies. International Journal of Research in Undergraduate Mathematics Education, 6(3), 375-403. https://doi.org/10.1007/s40753-020-00112-x
Ramírez-Uclés, R., & Ruiz-Hidalgo, J. F. (2022). Reasoning, Representing, and Generalizing in Geometric Proof Problems among 8th Grade Talented Students. Mathematics, 10(5), 789. https://doi.org/10.3390/math10050789
Retnawati, H., Apino, E., & Santoso, A. (2020). High School Students' Difficulties in Making Mathematical Connections when Solving Problems. International Journal of Learning, Teaching and Educational Research, 19(8), 255-277. https://doi.org/10.26803/ijlter.19.8.14
Santos-Trigo, M. (2019). Mathematical Problem Solving and The Use of Digital Technologies. Springer Cham.
Sari, M. P., Susanto, Yuliati, N., Imamah, E. N., & Laily, N. I. (2020). Journal of Physics: Conference Series in The Third International Conference of Combinatorics, Graph Theory, and Network Topology (ICCGANT) 2019, 1538(1). The Students’ Mathematical Reasoning Ability based on Problem-Based Learning Model. IOP Publishing. https://doi.org/10.1088/1742-6596/1538/1/012078
Sary, R. F., & Fatimah, S. (2023). AIP Conference Proceedings of International Seminar on Mathematics, Science, and Computer Science Education (MSCEIS) 2021, 2734(1). Does Problem-Based Learning Model Enhance Mathematical Reasoning Ability? A Meta-Analysis Study. AIP Publishing. https://doi.org/10.1063/5.0155347
Schmid, A., Korenova, L., Cahyono, A. N., Hvorecky, J., & Lavicza, Z. Geogebra as a Constructivism Teaching Tool for Visualization Geometry Using VR And AR. Scientific Editor Eugenia Smyrnova-Trybulska, 15, 253-264. https://doi.org/10.34916/el.2023.15.20
Schlesinger, L., Jentsch, A., Kaiser, G., König, J., & Blömeke, S. (2018). Subject-Specific Characteristics of Instructional Quality in Mathematics Education. ZDM, 50, 475-490. https://doi.org/10.1007/s11858-018-0917-5
Septian, A., Inayah, S., Suwarman, R. F., & Nugraha, R. (2020). In SEMANTIK Conference of Mathematics Education (SEMANTIK 2019). GeoGebra-Assisted Problem Based Learning to Improve Mathematical Problem Solving Ability. Atlantis Press. https://doi.org/10.2991/assehr.k.200827.119
Siswono, E. T. Y. (2018). Pembelajaran Matematika berbasis Pengajuan dan Pemecahan Masalah Fokus pada Berpikir Kritis dan Berpikir Kreatif. Remaja Rosdakarya.
Sugiman, Retnowati, E., Ayres, P., & Murdanu. (2019). Learning Goal-Free Problems: Collaboratively or Individually?. Cakrawala Pendidikan, 38(3), 590-600. https://doi.org/10.21831/cp.v38i3.26914
Ukobizaba, F., Ndihokubwayo, K., Mukuka, A., & Uwamahoro, J. (2021). From What Makes Students Dislike Mathematics towards its Effective Teaching Practices. Bolema: Boletim de Educação Matemática, 35(70), 1200-1216. https://doi.org/10.1590/1980-4415v35n70a30
Walkington, C., Woods, D., Nathan, M. J., Chelule, G., & Wang, M. (2019). Does Restricting Hand Gestures Impair Mathematical Reasoning. Learning and Instruction, 64. https://doi.org/10.1016/j.learninstruc.2019.101225
Widada, W., Herawaty, D., Nugroho, K. U. Z., & Anggoro, A. F. D. (2021). Journal of Physics: Conference Series in Mathematics and Science Education International Seminar (MASEIS) 2019, 1731(1). Augmented Reality Assisted by GeoGebra 3-D for Geometry Learning. IOP Publishing. https://doi.org/10.1088/1742-6596/1731/1/012034
Wittmann, E. C. (2021). Connecting Mathematics and Mathematics Education: Collected Papers on Mathematics Education as a Design Science. Springer Open. https://doi.org/10.1007/978-3-030-61570-3
Žakelj, A., & Klancar, A. (2022). The Role of Visual Representations in Geometry Learning. European Journal of Educational Research, 11(3), 1393-1411. https://doi.org/10.12973/eu-jer.11.3.1393
Zapata, M., Ramos-Galarza C., Aragón K. V., & Guachi L. (2024). Enhancing Mathematics Learning with 3D Augmented Reality Escape Room. International Journal of Educational Research Open, 7. https://doi.org/10.1016/j.ijedro.2024.100389
Ziatdinov, R., & Valles Jr, J. R. (2022). Synthesis of Modeling, Visualization, and Programming in GeoGebra as an Effective Approach for Teaching and Learning STEM Topics. Mathematics, 10(3), 398. https://doi.org/10.3390/math10030398
Zulnaidi, H., Oktavika, E., & Hidayat, R. (2020). Effect of Use of GeoGebra on Achievement of High School Mathematics Students. Education and Information Technologies, 25(1), 51-72. https://doi.org/10.1007/s10639-019-09899-y
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2024 Humam Nuralam, Al Jupri, Wenda Alifulloh
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.
Jurnal Teknologi Pendidikan is an Open Access Journal. The authors who publish the manuscript in Jurnal Teknologi Pendidikan agree to the following terms.
Attribution-ShareAlike 4.0 International (CC BY-SA 4.0)
-
Attribution — You must give appropriate credit, provide a link to the license, and indicate if changes were made. You may do so in any reasonable manner, but not in any way that suggests the licensor endorses you or your use.
-
ShareAlike — If you remix, transform, or build upon the material, you must distribute your contributions under the same license as the original.
- No additional restrictions — You may not apply legal terms or technological measures that legally restrict others from doing anything the license permits.
Notices:
- You do not have to comply with the license for elements of the material in the public domain or where your use is permitted by an applicable exception or limitation.
- No warranties are given. The license may not give you all of the permissions necessary for your intended use. For example, other rights such as publicity, privacy, or moral rights may limit how you use the material.
