Tracing Students’ Cognitive Progression in Geometry: A Design-Based Research Through the Van Hiele Model of Instruction and Ethnomathematics
DOI:
https://doi.org/10.33394/j-ps.v14i1.18025Keywords:
cognitive progression, design-based research, ethnomathematics, geometry, Van Hiele model of instructionAbstract
This study investigated students’ cognitive progression in geometry based on Van Hiele levels. It used a design-based research approach that integrates the Van Hiele Model of Instruction with ethnomathematics, following the McKenney & Reeves design cycle (analysis and exploration, design and construction, and evaluation and reflection). Data were collected through Van Hiele tests, observations, teachers and students interview, and documentation, and analysed using qualitative methods (data reduction, data display, and conclusion drawing/verification). The pilot class (cycle 1) was conducted with 34 eighth-grade students at SMPN 6 Tasikmalaya in August 2025, while actual class (cycle 2) was carried out with 33 eighth-grade students at SMPN 13 Tasikmalaya in September 2025. The research results showed that students’ cognitive development peaked at the visualization phase in both the pilot class (85%) and the actual class (94%), with fewer students progressing to higher levels. However, the actual class (61% at the formal deduction level) demonstrated notable improvement compared to the pilot class (41% at the formal deduction level), due to refinements in instructional design. These findings suggest that integrating ethnomathematics with the Van Hiele model effectively enhances students’ geometric thinking.
References
Adeniji, S. M., & Baker, P. (2022). Worked-examples instruction versus Van Hiele teaching phases: A demonstration of students’ procedural and conceptual understanding. Journal on Mathematics Education, 13(2), 337–356. https://doi.org/10.22342/jme.v13i2.pp337-356
Akker, J. van den, Bannan, B., Kelly, A. E., Nieveen, N., & Plomp, T. (2006). Educational design research. In Netherlands Institute for Curriculum Development: SLO. Netherland Institute for Curriculum Development.
Arnal-Bailera, A., & Manero, V. (2024). A Characterization of Van Hiele’s Level 5 of Geometric Reasoning Using the Delphi Methodology. International Journal of Science and Mathematics Education, 22(3), 537–560. https://doi.org/10.1007/s10763-023-10380-z
Bernabeu, M., Moreno, M., & Llinares, S. (2024). Polygon class learning opportunities: interplay between teacher’s moves, children’s geometrical thinking, and geometrical task. International Journal of Science and Mathematics Education, 22(6), 1381–1403. https://doi.org/10.1007/s10763-023-10425-3
Burger, W. F., & Shaughnessy, J. M. (1986). Characterizing the van Hiele levels of development in Geometry. Journal for Research in Mathematics Education, 17(1), 31. https://doi.org/10.2307/749317
Cela-Ranilla, J., Esteve-Mon, F. M., & Sánchez-Caballé, A. (2025). Design-based research in higher education: A systematic literature review between 2019 and 2023. Australasian Journal of Educational Technology. https://doi.org/10.14742/ajet.10380
Chen, J., Li, L., & Zhang, D. (2021). Students with specific difficulties in geometry: exploring the timss 2011 data with plausible values and latent profile analysis. Learning Disability Quarterly, 44(1), 11–22. https://doi.org/10.1177/0731948720905099
Chen, W., & Reeves, T. C. (2020). Twelve tips for conducting educational design research in medical education. Medical Teacher, 42(9), 980–986. https://doi.org/10.1080/0142159X.2019.1657231
Cohen, L., Manion, L., & Morrison, K. (2017). Research Methods in Education. In Syria Studies (Vol. 7, Issue 1). Routledge. https://doi.org/10.4324/9781315456539
Cybulski, F. C., Oliveira, H., & de Costa Trindade Cyrino, M. C. (2024). Quadrilaterals hierarchical classification and properties of the diagonals: A study with pre-service mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education, 20(8). https://doi.org/10.29333/ejmste/14916
Dunn, R., Hattie, J., & Bowles, T. (2019). Exploring the experiences of teachers undertaking Educational Design Research (EDR) as a form of teacher professional learning. Professional Development in Education, 45(1), 151–167. https://doi.org/10.1080/19415257.2018.1500389
Fink, M. C., Radkowitsch, A., Bauer, E., Sailer, M., Kiesewetter, J., Schmidmaier, R., Siebeck, M., Fischer, F., & Fischer, M. R. (2021). Simulation research and design: a dual-level framework for multi-project research programs. Educational Technology Research and Development, 69(2), 809–841. https://doi.org/10.1007/s11423-020-09876-0
Fouze, A. Q., & Amit, M. (2021). Teaching Geometry by Integrating Ethnomathematics of Bedouin Values. Creative Education, 12(02), 402–421. https://doi.org/10.4236/ce.2021.122029
Fowler, S., Cutting, C., Fiedler, S. H. D., & Leonard, S. N. (2023). Design-based research in mathematics education: trends, challenges and potential. Mathematics Education Research Journal, 35(3), 635–658. https://doi.org/10.1007/s13394-021-00407-5
Fujita, T., Kondo, Y., Kumakura, H., Kunimune, S., & Jones, K. (2020). Spatial reasoning skills about 2D representations of 3D geometrical shapes in grades 4 to 9. Mathematics Education Research Journal, 32(2), 235–255. https://doi.org/10.1007/s13394-020-00335-w
Gridos, P., Avgerinos, E., Mamona-Downs, J., & Vlachou, R. (2022). Geometrical figure apprehension, construction of auxiliary lines, and multiple solutions in problem solving: aspects of mathematical creativity in school geometry. International Journal of Science and Mathematics Education, 20(3), 619–636. https://doi.org/10.1007/s10763-021-10155-4
Gusfitri, W., Abdurrahman, Andrian, D., Nofriyandi, & Rezeki, S. (2022). Development of mathematics learning tools based on ethnomathematics on rectangular and triangles in junior high school. Prisma Sains : Jurnal Pengkajian Ilmu Dan Pembelajaran Matematika Dan IPA IKIP Mataram, 10(3), 609. https://doi.org/10.33394/j-ps.v10i3.5310
Haj-Yahya, A. (2023). Can a number of diagrams linked to a proof task in 3D geometry improve proving ability? Mathematics Education Research Journal, 35(1), 215–236. https://doi.org/10.1007/s13394-021-00385-8
Harris, D., Logan, T., & Lowrie, T. (2021). Unpacking mathematical-spatial relations: Problem-solving in static and interactive tasks. Mathematics Education Research Journal, 33(3), 495–511. https://doi.org/10.1007/s13394-020-00316-z
Hwang, W.-Y., Zhao, L., Shadiev, R., Lin, L.-K., Shih, T. K., & Chen, H.-R. (2020). Exploring the effects of ubiquitous geometry learning in real situations. Educational Technology Research and Development, 68(3), 1121–1147. https://doi.org/10.1007/s11423-019-09730-y
Kabuye Batiibwe, M. S. (2024). The role of ethnomathematics in mathematics education: A literature review. Asian Journal for Mathematics Education, 3(4), 383–405. https://doi.org/10.1177/27527263241300400
Kusaeri, A., Pardi, H. H., & Ependi, E. (2024). Scientific horizon: Basis for developing basic mathematics teaching materials. Prisma Sains: Jurnal Pengkajian Ilmu Dan Pembelajaran Matematika Dan IPA IKIP Mataram, 12(4), 677–688. https://doi.org/10.33394/j-ps.v12i4.13380
Kyeremeh, P., Awuah, F. K., & Dorwu, E. (2023). Integration of ethnomathematics in teaching geometry: a systematic review and bibliometric report. Journal of Urban Mathematics Education, 16(2), 68–89. https://doi.org/10.21423/JUME-V16I2A519
Maqoqa, T. (2024). An Exploration of Learners’ Understanding of Euclidean Geometric Concepts: A Case Study of Secondary Schools in the OR Tambo Inland District of the Eastern Cape. E-Journal of Humanities, Arts and Social Sciences, 5(5), 658–675. https://doi.org/10.38159/ehass.2024557
McKenney, S. E., & Reeves, T. C. (2012). Conducting Educational Design Research. Routledge.
McKenney, S., & Reeves, T. C. (2021). Educational design research: Portraying, conducting, and enhancing productive scholarship. Medical Education, 55(1), 82–92. https://doi.org/10.1111/medu.14280
Michael–Chrysanthou, P., Panaoura, A., Gagatsis, A., & Elia, I. (2024). Exploring secondary school students’ geometrical figure apprehension: cognitive structure and levels of geometrical ability. Educational Studies in Mathematics, 117(1), 23–42. https://doi.org/10.1007/s10649-024-10317-5
Moru, E. K., Malebanye, M., Morobe, N., & George, M. J. (2020). A Van Hiele Theory analysis for teaching volume of threedimensional geometric shapes. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 6(1), 17–31. https://doi.org/10.23917/jramathedu.v6i1.11744
Mudhefi, F., Mabotja, K., & Muthelo, D. (2024). The use of Van Hiele’s geometric thinking model to interpret Grade 12 learners’ learning difficulties in Euclidean Geometry. Perspectives in Education, 42(2), 162–175. https://doi.org/10.38140/pie.v42i2.8350
Nathan, M. J., Schenck, K. E., Vinsonhaler, R., Michaelis, J. E., Swart, M. I., & Walkington, C. (2021). Embodied geometric reasoning: Dynamic gestures during intuition, insight, and proof. Journal of Educational Psychology, 113(5), 929–948. https://doi.org/10.1037/edu0000638
Özçakır, B., & Çakıroğlu, E. (2022). Fostering spatial abilities of middle school students through augmented reality: Spatial strategies. Education and Information Technologies, 27(3), 2977–3010. https://doi.org/10.1007/s10639-021-10729-3
Patahuddin, S. M., Rokhmah, S., & Ramful, A. (2020). What does teaching of spatial visualisation skills incur: an exploration through the visualise-predict-check heuristic. Mathematics Education Research Journal, 32(2), 307–329. https://doi.org/10.1007/s13394-020-00321-2
Rahmayani, R., Sukayasa, Ismaimuza, D., & Meinarni, W. (2024). Analysis of mathematical literacy skills of students in class VIII SMP Negeri 3 Dampelas in solving geometry problems in terms of Van Hiele level. Prima: Jurnal Pendidikan Matematika, 8(2), 282–292. https://doi.org/10.31000/prima.v8i2.10888
Santos, M. S. M. D., Sobretodo, M. L., & Hortillosa, A. D. (2022). The Van Hiele model in teaching geometry. World Journal of Vocational Education and Training, 4(1), 10–22. https://doi.org/10.18488/119.v4i1.3087
Spiller, J., Clayton, S., Cragg, L., Johnson, S., Simms, V., & Gilmore, C. (2023). Higher level domain specific skills in mathematics; The relationship between algebra, geometry, executive function skills and mathematics achievement. PLOS ONE, 18(11), e0291796. https://doi.org/10.1371/journal.pone.0291796
Sunardi, S., Yudianto, E., Susanto, S., Kurniati, D., Cahyo, R. D., & Subanji, S. (2019). Anxiety of students in visualization, analysis, and informal deduction levels to solve geometry problems. International Journal of Learning, Teaching and Educational Research, 18(4), 171–185. https://doi.org/10.26803/ijlter.18.4.10
Tamur, M., Wijaya, T., Nurjaman, A., Siagian, M., & Perbowo, K. (2023). Ethnomathematical Studies in the Scopus Database Between 2010-2022: A Bibliometric Review. https://doi.org/10.4108/eai.21-10-2022.2329666
Tawfik, A. A., Schmidt, M., & Hooper, C. P. (2020). Role of conjecture mapping in applying a game-based strategy towards a case library: a view from educational design research. Journal of Computing in Higher Education, 32(3), 655–681. https://doi.org/10.1007/s12528-020-09251-1
Zeybek, Z. (2018). Understanding inclusion relations between quadrilaterals. International Journal of Research in Education and Science, 4(2), 595–612. https://doi.org/10.21890/ijres.428968
Zhang, Y., Wang, P., Jia, W., Zhang, A., & Chen, G. (2025). Dynamic visualization by GeoGebra for mathematics learning: a meta-analysis of 20 years of research. Journal of Research on Technology in Education, 57(2), 437–458. https://doi.org/10.1080/15391523.2023.2250886
Zhu, M., & Zhang, K. (2023). Promote collaborations in online problem-based learning in a user experience design course: Educational design research. Education and Information Technologies, 28(6), 7631–7649. https://doi.org/10.1007/s10639-022-11495-6
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