Mapping Geometric Minds: Exploring 3D Thinking Skills of Elementary School Students Using the Van Hiele Model
DOI:
https://doi.org/10.56916/jesi.v2i1.806Keywords:
3D thinking skill, elementary school student, Van Hiele ModelAbstract
This study investigates elementary school students' 3D geometric thinking skills using the Van Hiele model. The research employed a grounded theory approach, utilizing tests, observations, and interviews to assess students' geometric thinking levels across two elementary schools in West Java and Central Java, Indonesia. A total of 6 test items were developed based on Van Hiele's theory, targeting the visualization, analysis, and informal deduction levels. Results showed varied performance between the two schools. Students from the Majalengka school demonstrated stronger visualization skills (77.14%), while those from the Surakarta school showed better performance in analysis (67.86%) and informal deduction (53.57%). Overall, students exhibited a good foundational understanding of 3D shapes, with most achieving the visualization and analysis levels. However, challenges emerged at the informal deduction level, where students often opted for simpler problem-solving methods over more systematic approaches. The study highlights the effectiveness of the Van Hiele model in assessing geometric thinking development and provides valuable insights for curriculum development and teaching strategies. It emphasizes the need to reinforce visualization and analysis skills while gradually introducing more abstract and systematic thinking in geometry education. The findings contribute to the understanding of elementary students' 3D geometric thinking skills and offer a basis for improving geometry instruction at the primary level.
References
Abdullah, A. H., & Zakaria, E. (2013). The Effects of Van Hiele’s Phases of Learning Geometry on Students’ Degree of Acquisition of Van Hiele Levels. Procedia - Social and Behavioral Sciences, 102, 251–266. https://doi.org/10.1016/j.sbspro.2013.10.740
Abu, M. S., & Abidin, Z. Z. (2013). Improving the levels of geometric thinking of secondary school students using geometry learning video based on Van Hiele theory. International Journal of Evaluation and Research in Education (IJERE), 2(1), 16–22.
Abu, M. S., Ali, M. B., & Hock, T. T. (2012). Assisting Primary School Children to Progress through Their van Hiele’s Levels of Geometry Thinking using Google SketchUp. Procedia - Social and Behavioral Sciences, 64, 75–84. https://doi.org/10.1016/j.sbspro.2012.11.010
Adolphus, T. (2011). Problems of teaching and learning of geometry in secondary schools in Rivers State, Nigeria. International Journal of Emerging Sciences, 1(2), 143–152.
Alex, J. K., & Mammen, K. J. (2012). A survey of South African grade 10 learners’ geometric thinking levels in terms of the Van Hiele theory. The Anthropologist, 14(2), 123-129.
Alex, J. K. (2019). The Preparation of Secondary School Mathematics Teachers in South Africa: Prospective Teachers’ Student Level Disciplinary Content Knowledge. EURASIA Journal of Mathematics, Science and Technology Education, 15(12). https://doi.org/10.29333/ejmste/105782
Armah, R. B., & Kissi, P. S. (2019). Use of the van Hiele Theory in Investigating Teaching Strategies used by College of Education Geometry Tutors. EURASIA Journal of Mathematics, Science and Technology Education, 15(4). https://doi.org/10.29333/ejmste/103562
Ayuningrum, D. (2017). Strategi Pemecahan Masalah Matematika Siswa SMP Ditinjau Dari Tingkat Berpikir Geometri Van Hiele. Kreano, Jurnal Matematika Kreatif-Inovatif, 8(1), 27–34. https://doi.org/10.15294/kreano.v8i1.6851
Baiduri, B., Ismail, A. D., & Sulfiyah, R. (2020). Understanding the concept of visualization phase student in geometry learning. International Journal of Scientific & Technology Research, 9(2), 2353-2359.
Barkai, R., & Patkin, D. (2012). Geometric thinking levels of in-service and pre-service mathematics teachers at various stages during their training. The Kibbutzim Education College Yearly, 34, 83-96.
Battista, M. T. (2003). Levels of Sophistication in Elementary Students Reasoning about Length. International Group for the Psychology of Mathematics Education, 2, 73–80.
Battista, M. T. (2007). The development of geometric and spatial thinking. Second Handbook of Research on Mathematics Teaching and Learning, 2, 843–908.
Cesaria, A., Herman, T., & Dahlan, J. A. (2021). Level berpikir geometri peserta didik berdasarkan teori van hiele pada materi bangun ruang sisi datar. Jurnal Elemen, 7(2), 267-279.
Clements, D. H., & Battista, M. T. (1992). Geometry and spatial reasoning. Handbook of Research on Mathematics Teaching and Learning, 420, 464.
Corbin, J. M., & Strauss, A. (1990). Grounded theory research: Procedures, canons, and evaluative criteria. Qualitative Sociology, 13(1), 3–21. https://doi.org/10.1007/BF00988593
Crowley, M. L. (1987). The van Hiele model of the development of geometric thought. Learning and Teaching Geometry, K-12, 1, 16.
Ding, L., & Jones, K. (2006). Teaching geometry in lower secondary school in Shanghai, China. Proceedings of the British Society for Research into Learning Mathematics, 26(1), 41–46.
Duranovic, M., & Didic, E. (2023). Prevalence and characteristics of geometric difficulties in elementary school children. Asia Pacific Journal of Developmental Differences, 10(1), 5–26.
Fuys, D., Geddes, D., & Tischler, R. (1988). The Van Hiele Model of Thinking in Geometry among Adolescents. Journal for Research in Mathematics Education. Monograph, 3, i. https://doi.org/10.2307/749957
Gilar Jatisunda, M., & Nahdi, D. S. (2020). Kemampuan Pemecahan Masalah Matematis melalui Pembelajaran Berbasis Masalah dengan Scaffolding. Jurnal Elemen, 6(2), 228–243. https://doi.org/10.29408/jel.v6i2.2042
Hassan, M. N., Abdullah, A. H., & Ismail, N. (2020). Effects of integrative interventions with van hiele phase on students’ geometric thinking: A systematic review. Journal of Critical Reviews, 7(13), 1133–1140.
Haviger, J., & Vojkůvková, I. (2014). The Van Hiele Geometry Thinking Levels: Gender and School Type Differences. Procedia - Social and Behavioral Sciences, 112, 977–981. https://doi.org/10.1016/j.sbspro.2014.01.1257
Haviger, J., & Vojkůvková, I. (2015). The van Hiele Levels at Czech Secondary Schools. Procedia - Social and Behavioral Sciences, 171, 912–918. https://doi.org/10.1016/j.sbspro.2015.01.209
Heathcote, D. (1994). The role of visuo-spatial working memory in the mental addition of multi-digit addends. Cahiers de Psychologie Cognitive/Current Psychology of Cognition.
Hershkowitz, R. (1987). The acquisition of concepts and misconceptions in basic geometry-or when" A little learning is dangerous thing". In Proceedings of the Second International Seminar Misconceptions and Educational Strategies in Science and Mathematics.
Hershkowitz, R. (1990). Psychological aspects of learning geometry. In Mathematics and cognition (pp. 70-95). Cambridge University Press.
İbili, E., Çat, M., Resnyansky, D., Şahin, S., & Billinghurst, M. (2020). An assessment of geometry teaching supported with augmented reality teaching materials to enhance students’ 3D geometry thinking skills. International Journal of Mathematical Education in Science and Technology, 51(2), 224–246. https://doi.org/10.1080/0020739X.2019.1583382
Idris, N. (1999). Linguistic aspects of mathematical education: How precise do teachers need to be. Cultural and Language Aspects of Science, Mathematics, and Technical Education, 280–289.
Ismail, Z., & Rahman, S. N. A. (2017). Learning 2-Dimensional and 3-Dimensional Geometry with Geogebra: Which Would Students Do Better? International Journal on Emerging Mathematics Education, 1(2), 121. https://doi.org/10.12928/ijeme.v1i2.5541
Karakuş, F., & Peker, M. (2015). The effects of dynamic geometry software and physical manipulatives on pre-service primary teachers’ van Hiele levels and spatial abilities. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 6(3), 338-365.
Marchis, I. (2012). Preservice Primary School Teachers' Elementary Geometry Knowledge. Acta Didactica Napocensia, 5(2), 33-40.
Markopoulos, C., Potari, D., Boyd, W., Petta, Κ., & Chaseling, M. (2015). The Development of Primary School Students’ 3D Geometrical Thinking within a Dynamic Transformation Context. Creative Education, 06(14), 1508–1522. https://doi.org/10.4236/ce.2015.614151
Martin, J. D. (2007). Children’s understanding of area of rectangular regions and volumes of rectangular shapes and the relationship of these measures to their linear dimensions. Unpublished PhD thesis. Retrieved from http://hdl. handle.net/10427/53098
Meng, C. C., & Sam, L. C. (2013). Enhancing primary pupils’ geometric thinking through phase-based instruction using the geometer’s sketchpad. Asia Pacific Journal of Educators and Education, 28, 33–51.
Musa, L. A. D. (2018). Level Berpikir Geometri Menurut Teori Van Hiele Berdasarkan Kemampuan Geometri dan Perbedaan Gender Siswa Kelas VII SMPN 8 Pare-Pare. Al-Khwarizmi: Jurnal Pendidikan Matematika Dan Ilmu Pengetahuan Alam, 4(2), 103–116. https://doi.org/10.24256/jpmipa.v4i2.255
Naufal, M. A., Abdullah, A. H., Osman, S., Abu, M. S., Ihsan, H., & Rondiyah, R. (2021). Reviewing the Van Hiele model and the application of metacognition on geometric thinking. International Journal of Evaluation and Research in Education (IJERE), 10(2), 597. https://doi.org/10.11591/ijere.v10i2.21185
Ocal, T., & Halmatov, M. (2021). 3D geometric thinking skills of preschool children: 3D geometric thinking skills. International Journal of Curriculum and Instruction, 13(2), 1508–1526.
Olkun, S. (2003). When does the volume formula make sense to students. Hacettepe Üniversitesi Eğitim Fakültesi Dergisi, 25, 160–165.
Passolunghi, M. C., & Mammarella, I. C. (2010). Spatial and visual working memory ability in children with difficulties in arithmetic word problem solving. European Journal of Cognitive Psychology, 22(6), 944–963. https://doi.org/10.1080/09541440903091127
Patkin, D. (2011). The interplay of language and mathematics. Pythagoras: Journal of the Association for Mathematics Education of South Africa, 32(2), 7.
Pavlovičová, G., & Švecová, V. (2015). The Development of Spatial Skills through Discovering in the Geometrical Education at Primary School. Procedia - Social and Behavioral Sciences, 186, 990–997. https://doi.org/10.1016/j.sbspro.2015.04.189
Pebruariska, A., & Fachrudin, A. D. (2018). Kemampuan Pemecahan Masalah Siswa Kelas VII pada Materi Segiempat ditinjau dari Tingkat Berpikir Geometri Van Hiele. AKSIOMA : Jurnal Matematika Dan Pendidikan Matematika, 9(1), 21. https://doi.org/10.26877/aks.v9i1.2461
Piaget, J., & Inhelder, B. (1969). The psychology of the child. Routledge.
Rott, B. (2021). Inductive and deductive justification of knowledge: epistemological beliefs and critical thinking at the beginning of studying mathematics. Educational Studies in Mathematics, 106(1), 117–132. https://doi.org/10.1007/s10649-020-10004-1
Sam, L. C., & Yong, H. T. (2006, December). Promoting mathematical thinking in the Malaysian classroom: Issues and challenges. In Meeting of the APEC-Tsukuba International Conference. meeting of the APEC-Tsukuba International Conference, Japan.
Sholihah, S. Z., & Afriansyah, E. A. (2018). Analisis Kesulitan Siswa dalam Proses Pemecahan Masalah Geometri Berdasarkan Tahapan Berpikir Van Hiele. Mosharafa: Jurnal Pendidikan Matematika, 6(2), 287–298. https://doi.org/10.31980/mosharafa.v6i2.317
Siew, N. M., Chong, C. L., & Abdullah, M. R. (2013). Facilitating Students’geometric Thinking Through Van Hiele’s Phase-Based Learning Using Tangram. Journal of Social Sciences, 9(3), 101.
Silva, C. C., Da Silva, J. A. C., Costa, M. B., & De Carvalho, R. B. F. (2015). Lava-Luz’luminaire: A pedagogical proposal for science teaching. Periodico Tche Quimica, 12(23), 22–27.
Stols, G., Long, C., & Dunne, T. (2015). An application of the Rasch measurement theory to an assessment of geometric thinking levels. African Journal of Research in Mathematics, Science and Technology Education, 19(1), 69-81.
Supli, A. A., & Yan, X. (2024). Exploring the effectiveness of augmented reality in enhancing spatial reasoning skills: A study on mental rotation, spatial orientation, and spatial visualization in primary school students. Education and information technologies, 29(1), 351-374.
Tieng, P. G., & Eu, L. K. (2014). Improving Students’ Van Hiele Level of Geometric Thinking Using Geometer’s Sketchpad. Malaysian Online Journal of Educational Technology, 2(3), 20–31.
Usiskin, Z. (1982). Van Hiele Levels and Achievement in Secondary School Geometry. CDASSG Project.
Utami, A. K. D., Mardiyana, M., & Pramudya, I. (2017, August). Analysis of junior high school students’ difficulty in resolving rectangular conceptual problems. In AIP Conference proceedings (Vol. 1868, No. 1). AIP Publishing.
Van Hiele, P. M. (1986). Structure and insight: A theory of mathematics education. Academic Press.
Van Hiele, Pierre M. (1999). Developing geometric thinking through activities that begin with play. Teaching Children Mathematics, 5(6), 310–316.
Wu, D., & Ma, H. (2005). A study of the geometric concepts of the elementary school students who are assigned to the van Hiele level one. PME CONFERENCE, 29(4), 4.
Yunus, M., & AS, M. A. (n.d.). AF, & Hock, TT (2019). Geometric Thinking of Malaysian Elementary School Students. International Journal of Instruction, 12(1), 1095–1112.
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