Specialized Content Knowledge Lower Secondary School Teachers on Quadrilaterals

Sadrack Luden Pagiling, Department of Mathematics Education, Universitas Musamus, Indonesia
Khumaeroh Dwi Nur'aini, Department of Mathematics Education, Universitas Musamus, Indonesia

Abstract


The teachers' knowledge of specific content has a positive relationship with the students' mathematics achievement. Mathematics teachers must have an appropriate level to ensure mathematics learning effectively. The quadrilateral is one of the essential contents in geometry.  However, many teachers did not successfully deliver and teach this content in classroom instruction. Therefore, this qualitative study explores the specialized content knowledge of lower secondary teachers in defining and classifying quadrilaterals. Four teachers, two male and two female teachers, were recruited to become participants in this work. All participants have similar teaching experience and do not hold an educator certificate. A test and semi-structured interviews were assigned to obtain specialized content knowledge of the teachers on quadrilaterals. The interview data were analyzed in three stages: data condensation, data presentation, and conclusion drawing. The findings show that only one teacher understands hierarchically in defining and classifying quadrilaterals, two teachers are at the partial prototype level because they cannot see the hierarchical relationship between the quadrilaterals, and another teacher is at the prototype understanding level because it relies on the prototype of quadrilaterals' shape. These findings suggest that lower secondary teachers' special content knowledge of quadrilateral needs to be strengthened through workshops and training professional development.

Keywords


Specialized content knowledge; teacher; quadrilaterals

Full Text:

PDF

References


Aslan-tutak, F., & Adams, T. L. (2015). A Study of Geometry Content Knowledge of Elementary Preservice Teachers. International Electronic Journal of Elementary Education, 7(510), 301–318.

Atay, D., Kaslioglu, O., & Kurt, G. (2010). The pedagogical content knowledge development of prospective teachers through an experiential task. Procedia - Social and Behavioral Sciences, 2(2), 1421–1425. https://doi.org/10.1016/j.sbspro.2010.03.212

Avcu, R. (2022). Pre-service middle school mathematics teachers’ personal concept definitions of special quadrilaterals. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-022-00412-2

Ball, D. L., Thames, M. H., & Phelps, G. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher Education, 59(5), 389–407. https://doi.org/10.1177/0022487108324554

Barut, M. E. O. B., Wijaya, A., & Retnawati, H. (2021). Hubungan pedagogical content knowledge guru matematika dan prestasi belajar siswa sekolah menengah pertama. Pythagoras: Jurnal Pendidikan Matematika, 15(2), 178–189. https://doi.org/10.21831/pg.v15i2.35375

Budiarto, M. T., Fuad, Y., & Sahidin, L. (2021). Teacher’s Specialized Content Knowledge on the Concept of Square: A Vignette Approach. Jurnal Pendidikan Matematika, 15(1), 1–22. https://doi.org/10.22342/jpm.15.1.11653.1-22

Butuner, S. O., & Filiz, M. (2017). Exploring turkish mathematics teachers’ content knowledge of quadrilaterals. International Journal of Research in Education and Science, 3(2), 395–408. https://doi.org/10.21890/ijres.327898

Cansiz Aktaş, M. (2016). Turkish high school students’ definitions for parallelograms: appropriate or inappropriate? International Journal of Mathematical Education in Science and Technology, 47(4), 583–596. https://doi.org/10.1080/0020739X.2015.1124931

Carrillo-Yañez, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, Á., Ribeiro, M., & Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model*. Research in Mathematics Education, 20(3), 236–253. https://doi.org/10.1080/14794802.2018.1479981

Çontay, E. G., & Duatepe-Paksu, A. (2012). Pre-service Mathematics Teachers’ Understandings of The Class Inclusion Between Kite and Square. Procedia - Social and Behavioral Sciences, 55, 782–788. https://doi.org/10.1016/j.sbspro.2012.09.564

Copur-Gencturk, Y., & Lubienski, S. T. (2013). Measuring mathematical knowledge for teaching: A longitudinal study using two measures. Journal of Mathematics Teacher Education, 16(3), 211–236. https://doi.org/10.1007/s10857-012-9233-0

Disnawati, H., Hartono, Y., Ilma, R., & Putri, I. (2012). Eksplorasi Pemahaman Siswa Dalam Pembelajaran Bangun Datar Segi Empat Di Sd Menggunakan Konteks Cak Ingkling. PYTHAGORAS: Jurnal Pendidikan Matematika, 7(2), 65–80.

Duatepe-Paksu, A., Pakmak, G. S., & Iymen, E. (2012). Preservice Elementary Teachers’ Identification of Necessary and Sufficient Conditions for A Rhombus. Procedia - Social and Behavioral Sciences, 46, 3249–3253. https://doi.org/10.1016/j.sbspro.2012.06.045

Ersen, Z. B., & Karakus, F. (2013). Evaluation of Preservice Elementary Teachers’ Concept Images for Quadrilaterals. Turkish Journal of Computer and Mathematics Education (TURCOMAT), 4(2), 124–146. https://doi.org/10.16949/turcomat.21946

Fujita, T. (2012). 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(3), 341–356. https://doi.org/10.1007/s10649-019-09892-9

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. https://doi.org/10.1080/14794800008520167

Haj-Yahya, A., Hershkowitz, R., & Dreyfus, T. (2022). Investigating students’ geometrical proofs through the lens of students’ definitions. Mathematics Education Research Journal, 0123456789. https://doi.org/10.1007/s13394-021-00406-6

Hidayati, A., & Widodo, S. (2015). Proses Penalaran Matematis Siswa Dalam Memecahkan Masalah Matematika Pada Materi Dimensi Tiga Berdasarkan Kemampuan Siswa Di SMA Negeri 5 Kediri. Jurnal Math Educator Nusantara, 01(02), 131–143.

Hill, H. C., Ball, D. L., & Schilling, S. G. (2008). Unpacking pedagogical content knowledge: Conceptualizing and measuring teachers’ topic-specific knowledge of students. Journal for Research in Mathematics Education, 39(4), 372–400.

Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Ball, D. L. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Cognition and Instruction, 26(4), 430–511. https://doi.org/10.1080/07370000802177235

Hill, H. C., Rowan, B., & Ball, D. L. (2005). Effects of teachers’ mathematical knowledge for teaching on student achievement. American Educational Research Journal, 42(2), 371–406. https://doi.org/10.3102/00028312042002371

Marbán, J. M., & Sintema, E. J. (2020). Pre-service secondary teachers’ knowledge of the function concept: A cluster analysis approach. JRAMathEdu (Journal of Research and Advances in Mathematics Education), 5(1), 38–53. https://doi.org/10.23917/jramathedu.v5i1.9703

Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: a methods sourcebook (3rd ed.). SAGE Publications, Inc.

Miller, S. M. (2018). An analysis of the form and content of quadrilateral definitions composed by novice pre-service teachers. Journal of Mathematical Behavior, 50(February), 142–154. https://doi.org/10.1016/j.jmathb.2018.02.006

Nur’aini, K. D., & Pagiling, S. L. (2020). Analisis pedagogical content knowledge guru matematika sekolah menengah pertama ditinjau dari segi gender [Analysis of lower secondary mathematics teachers’ pedagogical content knowledge viewed from gender]. AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(4), 1036. https://doi.org/10.24127/ajpm.v9i4.3171

Okazaki, M., & Fujita, T. (2007). Prototype Phenomena and Common Cognitive Paths in the Understanding of the Inclusion Relations. Proceedings of the 31st Conference of the International Group for the Psychology of Mathematics Education, 4(January), 41–48.

Pagiling, S. L., & Munfarikhatin, A. (2020). Bagaimana Konsepsi Guru Sekolah Menengah Pertama Tentang Representasi Dalam Pembelajaran Matematika? AKSIOMA: Jurnal Program Studi Pendidikan Matematika, 9(4), 1005. https://doi.org/10.24127/ajpm.v9i4.3199

Pagiling, S. L., & Taufik, A. R. (2022). Unveiling belief and pedagogical content knowledge of prospective secondary mathematics teachers. Jurnal Elemen, 8(2), 411–426. https://doi.org/10.29408/jel.v8i2.5159

Rothbaeur, P. M. (2008). Triangulation. In L. M. Given (Ed.), The SAGE Encyclopedia of Qualitative Research Methods (pp. 892–894). SAGE Publications, Inc.

Saleh, S., Uwamahoro, J., Joachim, N., & Orodho, J. A. (2021). Assessing the Level of Secondary Mathematics Teachers ’ Pedagogical Content Knowledge. Eurasia Journal of Mathematics, Science and Technology Education, 17(6), 1–11. https://doi.org/10.29333/ejmste/10883

Setyaningrum, W., Mahmudi, A., & Murdanu. (2018). Pedagogical Content Knowledge of Mathematics Pre-service Teachers: Do they know their students? Journal of Physics: Conference Series, 1097(1). https://doi.org/10.1088/1742-6596/1097/1/012098

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. http://www.jstor.org/stable/1175860

Türnüklü, E., Akkaş, E. N., & Gündoğdu-Alaylı, F. (2013). Mathematics Teachers’ Perceptions of Quadrilaterals and Understanding the Inclusion Relations. In B. Ubuz, C. Haser, & M. A. Mariotti (Eds.), Proceedings of 8th Congress of the European Society for Research in Mathematics Education (pp. 705–714). http://cerme8.metu.edu.tr/wgpapers/WG4/WG4_Akkas.pdf

Türnüklü, E., Gündoǧdu Alayli, F., & Akkaş, E. N. (2013). Investigation of prospective primary mathematics teachers’ perceptions and images for quadrilaterals. Educational Sciences: Theory & Practice, 13(2), 1225–1232.

Villiers, M. De. (1994). The Role and Function of Hierarchical Classification of Quadrilaterals. For the Learning of Mathematics, 14(1), 11–18.

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.

Zandieh, M., & Rasmussen, C. (2010). Defining as a mathematical activity: A framework for characterizing progress from informal to more formal ways of reasoning. Journal of Mathematical Behavior, 29(2), 57–75. https://doi.org/10.1016/j.jmathb.2010.01.001

Zaslavsky, O., & Shir, K. (2005). Students’ conceptions of a mathematical definition. Journal for Research in Mathematics Education, 36(4), 317–346. https://doi.org/10.2307/27646367

Zazkis, R., & Leikin, R. (2008). Exemplifying definitions: A case of a square. Educational Studies in Mathematics, 69(2), 131–148. https://doi.org/10.1007/s10649-008-9131-7

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

Žilková, K. (2015). Misconceptions in Pre-service Primary Education Teachers about Quadrilaterals Misconceptions in Pre-service Primary Education Teachers about Quadrilaterals. Journal of Education, Psychology and Social Sciences, 3(1), 30–37.




DOI: https://doi.org/10.21831/pythagoras.v17i1.42446

Refbacks

  • There are currently no refbacks.


PYTHAGORAS: Jurnal Matematika dan Pendidikan Matematika indexed by:


Creative Commons License Pythagoras is licensed under a Creative Commons Attribution 4.0 International License.
Based on a work at http://journal.uny.ac.id/index.php/pythagoras.

All rights reserved p-ISSN: 1978-4538 | e-ISSN: 2527-421X

Visitor Number:

View Pythagoras Stats