Analisis Kesalahan Klasifikasi Hierarkis Segiempat Mahasiswa Menggunakan Diagram Venn

Muchammad Hamdhani; Nur Baiti Nasution

doi:10.30998/jnd8zy48

Authors

Muchammad Hamdhani Universitas Pekalongan Author
Nur Baiti Nasution Universitas Pekalongan Author

DOI:

https://doi.org/10.30998/jnd8zy48

Keywords:

Hierarchical Classification, Venn Diagram, Sankey Chart, Fujita, Quadrilateral

Abstract

Abstract: This study analyzes the difficulties of pre-service mathematics teachers in the hierarchical classification of quadrilaterals using Fujita's categories, which include the Q-P, Q-Rec, and Q-Rh levels. The Q-P level (divided into four sub-levels) indicates the extent of understanding that rectangles, rhombi, and squares are special cases of parallelograms. The Q-Rec level (divided into three sub-levels) evaluates the understanding that squares are special cases of rectangles, while the Q-Rh level (divided into three sub-levels) examines the understanding that squares are special cases of rhombi. The pre-service teachers were assigned an open-ended task to construct Venn diagrams illustrating the inclusion relations among these quadrilaterals. Their visual representations were then analyzed based on the aforementioned leveling categories. The analysis revealed that 95% of the pre-service teachers demonstrated a hierarchical understanding at the Q-P level. However, at the Q-Rec and Q-Rh levels, 70% of the participants exhibited a hierarchical understanding, while 25% showed a prototypical understanding. The findings of this study can serve as an alternative diagnostic tool for educators to rapidly identify students' misconceptions in the hierarchical classification of quadrilaterals.

Abstrak: Penelitian ini menganalisis kesulitan mahasiswa calon guru matematika dalam mengklasifikasikan segiempat secara hierarkis menggunakan kategori Fujita, meliputi level Q-P, level Q-Rec, dan level Q-Rh. Level Q-P (terbagi menjadi 4 sublevel) menunjukkan sejauh mana pemahaman bahwa persegi panjang, belah ketupat, dan persegi merupakan kasus khusus dari jajar genjang. Level Q-Rec (terbagi menjadi 3 sublevel) menunjukkan sejauh mana pemahaman bahwa persegi merupakan kasus khusus dari persegi panjang, dan level Q-Rh (terbagi menjadi 3 sublevel) menunjukkan sejauh mana pemahaman bahwa persegi merupakan kasus khusus dari belah ketupat. Mahasiswa diberikan tugas untuk menggambar diagram Venn mengenai hubungan segiempat-segiempat tersebut. Hasil pekerjaan dianalisis menggunakan kategori pelevelan di atas. Hasil analisis menunjukkan bahwa 95% mahasiswa memiliki pemahaman dengan kategori hierarkis di level Q-P. Sedangkan di level Q-Rec dan Q-Rh, 70% mahasiswa memiliki pemahaman dengan kategori hierarkis, 25% memiliki pemahaman dengan kategori prototipikal. Hasil penelitian ini dapat dijadikan alternatif cara mengidentifikasi kesalahan siswa dalam melakukan klasifikasi hierarkis segiempat secara cepat.

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References

Bharaj, P., & Francis, D. (2020). “A square is not long enough to be a rectangle”: exploring prospective elementary teachers’ conceptions of quadrilaterals. Mathematics Education Across Cultures: Proceedings of the 42nd Meeting of the North American Chapter of the International Group for the Psychology of Mathematics Education. https://doi.org/10.51272/pmena.42.2020-106

Brunheira, L., & da Ponte, J. P. (2019). From the classification of quadrilaterals to the classification of prisms: An experiment with prospective teachers. The Journal of Mathematical Behavior, 53, 65–80.

Cansiz, M. (2012). Eighth Grade Students’ Understanding and Hierarchical Classification of Quadrilaterals *. https://consensus.app/papers/eighth-grade-students-understanding-and-hierarchical-cansiz/171bf6af8b605cbd8441c2da04ac99de/

Civak, R. A., Baktemur, G., & Bostan, M. I. (2021). Pre-service Middle School Mathematics Teachers’ (Mis)conceptions of Definitions, Classifications, and Inclusion Relations of Quadrilaterals. European Journal of Science and Mathematics Education. https://doi.org/10.30935/scimath/11206

Craine, T., & Rubenstein, R. (1993). A Quadrilateral Hierarchy to Facilitate Learning in Geometry. Mathematics Teacher: Learning and Teaching PK–12, 86, 30–36. https://doi.org/10.5951/mt.86.1.0030

Cybulski, F. C., Oliveira, H., & Cyrino, M. (2024). Quadrilaterals hierarchical classification and properties of the diagonals: A study with pre-service mathematics teachers. Eurasia Journal of Mathematics, Science and Technology Education. https://doi.org/10.29333/ejmste/14916

Ekawati, R., Kohar, A. W., Siswono, T. Y. E., Lukito, A., Yang, K.-L., & Nisa, K. (2023). Mathematics teacher educators’ noticing of pedagogical content knowledge on hierarchical classification of quadrilateral. Infinity Journal, 12(2), 261–274.

Erdogan, E. O., & Dur, Z. (2014). Preservice mathematics teachers’ personal figural concepts and classifications about quadrilaterals. Australian Journal of Teacher Education (Online), 39(6), 107–133.

Fujita, T. (2008a). Learners’ understanding of the hierarchical classification of quadrilaterals. Proceedings of the British Society for Research into Learning Mathematics, 28(2), 31–36.

Fujita, T. (2008b). Learners’ understanding of the hierarchical classification of quadrilaterals. Proceedings of the British Society for Research into Learning Mathematics, 28(2), 31–36.

Fujita, T. (2012a). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. The Journal of Mathematical Behavior, 31(1), 60–72.

Fujita, T. (2012b). Learners’ level of understanding of the inclusion relations of quadrilaterals and prototype phenomenon. Journal of Mathematical Behavior, 31(1), 60–72. https://doi.org/10.1016/j.jmathb.2011.08.003

Fujita, T., Doney, J., & Wegerif, R. (2019). Students’ collaborative decision-making processes in defining and classifying quadrilaterals: a semiotic/dialogic approach. Educational Studies in Mathematics, 101, 341–356.

Fujita, T., & Jones, K. (2007). LEARNERS’UNDERSTANDING OF THE DEFINITIONS AND HIERARCHICAL CLASSIFICATION OF QUADRILATERALS: TOWARDS A THEORETICAL FRAMING. Research in Mathematics Education, 9(1), 3–20.

Ili, L. (2022). Analysis of Students’ Misconceptions in Solving Mathematics Problems on Flat Construction Materials. Eduvest - Journal Of Universal Studies. https://doi.org/10.36418/edv.v2i3.388

Kabaca, T. (2017). Understanding the hierarchical classification of quadrilaterals through the ordered relation according to diagonal properties. International Journal of Mathematical Education in Science and Technology, 48(8), 1240–1248.

Pangadongan, F. V. (2019). Konsepsi Mahasiswa Calon Guru Sekolah Dasar Terhadap Segiempat. DWIJA CENDEKIA: Jurnal Riset Pedagogik, 3(2), 142–155.

Risnawati, R., Andrian, D., Azmi, M. P., Amir, Z., & Nurdin, E. (2019). Development of a Definition Maps-Based Plane Geometry Module to Improve the Student Teachers’ Mathematical Reasoning Ability. International Journal of Instruction. https://doi.org/10.29333/iji.2019.12333a

Sahidin, L., & Ikman, I. (2020). Investigasi Pemahaman Konseptual Calon Guru Terhadap Segiempat. Pedagogy: Jurnal Pendidikan Matematika, 5(1), 58–77.

Tandililing, P., Sirampun, E., Kho, R., & Ruamba, M. Y. (2025). Geometric Thinking Levels in Learning Quadrilaterals: A Van Hiele-Based Case Study in a Papuan Junior High School. Edumatica : Jurnal Pendidikan Matematika. https://doi.org/10.22437/edumatica.v15i2.43719

Villiers, M. (1994). The Role and Function of a Hierarchical Classification of Quadrilaterals. For the Learning of Mathematics, 14, 11–18. https://consensus.app/papers/the-role-and-function-of-a-hierarchical-classification-of-villiers/ad6c57b16f45518b988ef20bfb498024/