The distance between students’ concept image and quadrilateral object definition based on students’ mathematical ability

Idris Fadillah, Kusnandi Kusnandi, Dadang Juandi, Suparman Suparman


Students learn mathematics through practical applications without applying it. Consequently, the concept images and definitions that students offer do not match. This study examines the gap in mathematical ability between the concept images of professionals in mathematics education and students' concept images of content, including quadrilaterals. This study employed a qualitative approach with a hermeneutic phenomenology method. Sixty-two seventh-grade students were involved in conducting this study. Some instruments, such as quadrilateral-related tests and semi-structured interview questions, were used to collect the data. The results of quadrilateral-related tests and interviews revealed that most students with high mathematical ability, some with medium mathematical ability, and a small number with low mathematical ability have a concept image that matches the definition but cannot produce proof of the properties of a quadrilateral. In addition, a small number of students with high mathematical talents, some with medium mathematical abilities, and a large number of students with low mathematical abilities were unable to completely explain each rectangle's formal definition and properties. This indicates that there are some students whose concept image is low. So, several alternatives and effective mathematics learning should be implemented to facilitate students in enhancing students concept image. 


Concept Image, Hermeneutic Phenomenology, Mathematical Ability, Quadrilateral

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Cohen, L., Manion, L., & Morrison, K. (2018). Research methods in education (8 th). Routledge.

Creswell, J. W. (2014). Research design: Qualitative, quantitative, and mixed methods approaches (4 th). SAGE Publications, Inc.

Dahl, B. (2016). First-year non-STEM majors ’ use of definitions to solve calculus tasks : benefits of using concept image over concept definition ?. International Journal of Science and Mathematics Education, 15(7).

Erdogan, E. O., & Dur, Z. (2014). Preservice mathematics teachers' figural concepts and classifications about quadrilaterals. Australian Journal of Teacher Education, 39(6).

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

Glaeser, G. (2020). Geometry and its applications in arts, nature and technology second edition. In Geometry and Its Applications (Second Edi). Springer.

Hwang, W. Y., Purba, S. W. D., Liu, Y. F., Zhang, Y. Y., & Chen, N. S. (2019). An investigation of the effects of measuring authentic contexts on geometry learning achievement. IEEE Transactions on Learning Technologies, 12(3), 291–302.

Jaya, I., & Ardat. (2013). Penerapan statistik untuk pendidikan (I. R. Karo-karo (ed.)). Citapustaka Media Perintis.

Musla Mustika, A., Budiyono, B., & Riyadi, R. (2018). Learning obstacle analysis of indonesian primary students on rectangular concept and its altenative solutions. Jurnal Pendidikan Progresif, 8(1), 18–28.

Novitasari, D., Nasrullah, A., Wahyu Triutami, T., Ayu Apsari, R., & Silviana, D. (2021). High level of visual-spatial intelligence’s students in solving PISA geometry problems. Journal of Physics: Conference Series, 1778(1).

Rab Dangal, M., & Joshi, R. (2020). Hermeneutic phenomenology: Essence in educational research. Open Journal for Studies in Philosophy, 4(1), 25–42.

Ramsook, L. (2018). A methodological approach to hermeneutic phenomenology. International Journal of Humanities and Social Sciences, 10(1), 14–24.

Seah, R. (2015). Understanding geometric ideas: Pre-service primary teachers ’ knowledge as a basis for teaching. (Proceedings of the 38th Annual Conference of the Mathematics Education Research Group of Australasia), 571–578.

Sugiyono. (2015). Metode penelitian pendidikan pendekatan kuantitatif, kualitatif dan R&D.. Alfabeta.

Tall, D. (1988). Concept image and concept definitio. Senior Secondary Mathematics Education, 37–81.

Tall, D. (2013). How humans learn to think matematically. Cambridge University Press.

Tsamir, P., Tirosh, D., Levenson, E., Barkai, R., & Tabach, M. (2015). Early years teachers’ concept images and concept definitions. ZDM Mathematics Education, 47, 497–509.

Ulku, A., Nazan, G., & Figen, B. (2017). Understanding of prospective mathematics teachers of the concept of diagonal. Journal on Mathematics Education, 8(2), 165–184.

Vinner, S. (1983). Concept definition, concept image and the notion of function. International Journal of Mathematical Education in Science and Technology, 14(3), 293–305.

Yavuzsoy-Köse, N., Y. Yilmaz, T., Yeşil, D., & Yildirim, D. (2019). Middle school students’ interpretation of definitions of the parallelogram family: Which definition for which parallelogram? International Journal of Research in Education and Science, 5(1), 157–175.


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Al-Jabar : Jurnal Pendidikan Matematika is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.