Epistemological Obstacle in Transformation Geometry Based on van Hiele’s Level

Thesa Kandaga; Rizky Rosjanuardi; Dadang Juandi

doi:10.29333/ejmste/11914

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Thesa Kandaga ¹ ² ^* , Rizky Rosjanuardi ³ , Dadang Juandi ³

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¹ Mathematics Education Study Program, School of Postgraduate Studies, Universitas Pendidikan Indonesia, INDONESIA² Mathematics Education, Faculty of Teacher Training and Education, Universitas Pasundan, INDONESIA³ Department of Mathematics Education, Universitas Pendidikan Indonesia, INDONESIA^* Corresponding Author

Abstract

Each level on van Hiele’s model has its characteristics, such as terminology, concept, and reasoning strategies. This study attempts to reveal epistemological obstacles on all van Hiele’s levels of geometric thinking in the topic of geometric transformation. Thus, a student could overcome the epistemological obstacles in transformation geometry and develop appropriate reasoning strategies. That way, van Hiele’s geometric thinking could promote level by level. This research is a case study that investigates and analyzes the epistemological obstacles on the topic of transformation geometry for each level of thinking of the van Hiele model of geometry. The study was conducted on ten prospective mathematics teachers who had received lectures in transformation geometry at a university in Indonesia. The results found in this study indicated epistemological obstacles at each level of geometric thinking in van Hiele’s model.

Keywords

epistemological obstacles
transformation geometry
van Hiele’s model

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, 2022, Volume 18, Issue 4, Article No: em2096

https://doi.org/10.29333/ejmste/11914

Publication date: 23 Mar 2022

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Article Downloads: 993

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Disclosure

Declaration of Conflict of Interest: No conflict of interest is declared by author(s).

Data sharing statement: Data supporting the findings and conclusions are available upon request from the corresponding author(s).

References

Abdullah, A. H., & Zakaria, E. (2013). The effect 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. (2012). 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, 2(1), 16-22. https://doi.org/10.11591/ijere.v2i2.1935
Albert, M., Mylopoulos, M., & Laberge, S. (2018). Examining grounded theory through the lens of rationalist epistemology. Refllections, 24, 827-837. https://doi.org/10.1007/s10459-018-9849-7
Alex, J. K., & Mammen, K. J. (2016). Lessons learnt from employing van Hiele theory based instruction in senior secondary school geometry classrooms. Eurasia Journal of Mathematics, Science & Technology Education, 12(8), 2223-2236. https://doi.org/10.12973/eurasia.2016.1228a
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), em1694. https://doi.org/10.29333/ejmste/103562
Artigue, M., Haspekian, M., & Corblin-Lenfant, A. (2014). Introduction to the theory of didactical situations (TDS). In: A. Bikner-Ahsbahs, & S. Prediger (Eds.), Networking of theories as a research practice in mathematics education. Advances in mathematics education. Springer, Cham. https://doi.org/10.1007/978-3-319-05389-9_4
Clements, D. H., & Sarama, J. (2011). Early childhood teacher education: The case of geometry. Journal of Mathematics Teacher Education, 14, 133-148. https://doi.org/10.1007/s10857-011-9173-0
Darawsheh, W. (2014). Reflexivity in research: Promoting rigour, reliability and validity in qualitative research. International Journal of Therapy and Rehabilitation, 21(12), 560-568. https://doi.org/10.12968/ijtr.2014.21.12.560
Dwyer, C. (2018). 12 common biases that affect how we make everyday decisions. Psychology Today. [Online]. https://ssh.expoplanner.com/files/12/SpeakerFiles/27241_Handout_12_Common_Biases_That_Affect_How_We_Make_Everyday_Decisions.pdf
Hegedus, S. J., & Moreno-Armella, L. (2011). The emergence of mathematical structures. Educational Studies in Mathematics, 77, 369-388. https://doi.org/10.1007/s10649-010-9297-7
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, 6(3), 338-365. https://doi.org/10.16949/turcomat.31338
Kutluca, T. (2013). The effect of geometry instruction with dynamic geometry software; GeoGebra on van Hiele geometry understanding levels of students. Educational Research and Reviews, 8(17), 1509-1518. https://eric.ed.gov/?id=EJ1017439
Mol, L. D., & Primiero, G. (2014). Facing computing as technique: Towards a history and philosophy of computing. Philosophy & Technology, 27, 321-326. https://doi.org/10.1007/s13347-014-0169-4
Moss, J., Hawes, Z., Naqvi, S., & Caswell, B. (2015). Adapting Japanese lesson study to enhance the teaching and learning of geometry and spatial reasoning in early years classrooms: A case study. ZDM Mathematics Education, 47, 377-390. https://doi.org/10.1007/s11858-015-0679-2
Noto, M. S., Priatna, N., & Dahlan, J. A. (2019). Mathematical proof: The learning obstacles of pre-service mathematics teachers on transformation geometry. Journal on Mathematics Education, 10(1), 117-126. https://doi.org/10.22342/jme.10.1.5379.117-126
Pelligrini, E. F., Nesso, A. C., Zaccaro, A. M. S., Berenguel, D. C. C., Campos, E. J., & Rodrigues, L. S. A. (2020). Between the frontier of learning and school failure in attention deficit hyperactivity disorder. International Journal of Humanities Social Sciences and Education, 7(12), 1-14. https://doi.org/10.20431/2349-0381.0712001
Phillips-Pula, L., Strunk, J., & Pickler, R. H. (2011). Understanding phenomenological approaches to data analysis. Journal of Pediatric Health Care, 25(1), 76-71.https://doi.org/10.1016/j.pedhc.2010.09.004
Rivas, R., & Gibson-Light, M. (2016). Exploring culture through in-depth interviews: Is it useful to ask people about what they think, mean, and do? Cinta de Moebio, 57, 316-329. https://doi.org/10.4067/S0717-554X2016000300007
Rønning, F. (2021). Opportunities for language enhancement in a learning environment designed on the basis of the theory of didactical situations. ZDM Mathematics Education 53, 305-316. https://doi.org/10.1007/s11858-020-01199-x
Saldana, J. (2016). The coding manual for qualitative researchers. SAGE. https://emotrab.ufba.br/wp-content/uploads/2020/09/Saldana-2013-TheCodingManualforQualitativeResearchers.pdf
Sleep, L. (2012). The work of steering instruction toward the mathematical point: A decomposition of teaching practice. American Educational Research Journal, 49(5), 935-970. https://doi.org/10.3102/0002831212448095
Subroto, T., & Suryadi, D. (2018). Epistemological obstacles in mathematical abstraction on abstract algebra. IOP Journal of Physics: Conference Series, 1132, 1-6. https://doi.org/10.1088/1742-6596/1132/1/012032
Sunariah, L. & Mulyana, E. (2019). The didactical and epistemological obstacles on the topic of geometry transformation. IOP Journal of Physics: Conference Series, 1521, 032089. https://doi.org/10.1088/1742-6596/1521/3/032089
Trouche, L. (2016). Didactics of mathematics: Concepts, roots, interactions and dynamics from France. In Tools and mathematics: Instruments for learning. Springer, Cham. https://doi.org/10.1007/978-3-319-02396-0_10
Turk, Y., & Arslan, S. (2012). Examining creative drama based mathematics course with respect to theory of didactical situations in mathematics. Procedia-Social and Behavioral Sciences, 46, 4782-4785. https://doi.org/10.1016/j.sbspro.2012.06.334
Wijeratne, C., & Zazkis, R. (2015). On painter’s paradox: Contextual and mathematical approaches to infinity. International Journal of Research in Undergraduate Mathematics Education, 1, 163-186. https://doi.org/10.1007/s40753-015-0004-z
Yilmaz, G. K., & Koparan, T. (2016). The effect of designed geometry teaching lesson to the candidate teachers’ van Hiele geometric thinking level. Journal of Education and Training Studies, 4(1), 129-141. https://doi.org/10.11114/jets.v4i1.1067
Zhang, Q.-P., & Hong, N. Y. (2021). The learning trajectories of similarity in mathematics curriculum: An epistemological analysis of Hong Kong secondary mathematics textbooks in the past half century. Mathematics, 9, 2310. https://doi.org/10.3390/math9182310
Zorin, B. (2011). Geometric transformations in middle school mathematics textbooks [Graduate theses and dissertations, The University of South Florida].

How to cite this article

APA

Kandaga, T., Rosjanuardi, R., & Juandi, D. (2022). Epistemological Obstacle in Transformation Geometry Based on van Hiele’s Level. Eurasia Journal of Mathematics, Science and Technology Education, 18(4), em2096. https://doi.org/10.29333/ejmste/11914

Vancouver

Kandaga T, Rosjanuardi R, Juandi D. Epistemological Obstacle in Transformation Geometry Based on van Hiele’s Level. EURASIA J Math Sci Tech Ed. 2022;18(4):em2096. https://doi.org/10.29333/ejmste/11914

AMA

Kandaga T, Rosjanuardi R, Juandi D. Epistemological Obstacle in Transformation Geometry Based on van Hiele’s Level. EURASIA J Math Sci Tech Ed. 2022;18(4), em2096. https://doi.org/10.29333/ejmste/11914

Chicago

Kandaga, Thesa, Rizky Rosjanuardi, and Dadang Juandi. "Epistemological Obstacle in Transformation Geometry Based on van Hiele’s Level". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 4 (2022): em2096. https://doi.org/10.29333/ejmste/11914

Harvard

Kandaga, T., Rosjanuardi, R., and Juandi, D. (2022). Epistemological Obstacle in Transformation Geometry Based on van Hiele’s Level. Eurasia Journal of Mathematics, Science and Technology Education, 18(4), em2096. https://doi.org/10.29333/ejmste/11914

MLA

Kandaga, Thesa et al. "Epistemological Obstacle in Transformation Geometry Based on van Hiele’s Level". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 4, 2022, em2096. https://doi.org/10.29333/ejmste/11914