Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills

Abstract

In Indonesia, pre-service mathematics teacher education is strictly supervised so that Pedagogical Content Knowledge (PCK) becomes an important aspect to build the quality of learning. This study aimed to explore pre-service mathematics teachers’ PCK based on gender and academic skills. To obtain rich and in-depth data, a qualitative approach was used. A total of 70 subjects aged between 19 – 21 years old participated in this study. There were two subjects selected based on their academic skills and gender. Using a grounded theory approach, we conducted a preliminary analysis, open coding, axial coding to obtain the three PCK components, namely Knowledge of Subject Matter (KSM), Knowledge of Pedagogy (KP), and Knowledge of Student (KS). Research findings revealed that the pre-service teachers’ pedagogical content knowledge in terms of knowledge of subject matter was categorized as good in mathematics learning. As for their knowledge of pedagogy, the male subjects presented the concepts by employing the expository strategy, the female subjects with high skills used the guided discovery, and the female subjects with average skill also employed the strategy of expository. In the aspect of knowledge of students, the subjects with average skills overcame students’ misconception by explaining the procedures and using the strategy of asking, but the subjects with high academic skills did not only implement the two previous strategies but also used their reasoning behind every procedure of problem-solving that they carried out. These findings can be used as recommendations for the development of mathematics learning.

Keywords

• content knowledge
• pedagogy
• knowledge of students
• gender
• academic skills

Thanks

The research team would like to thank the Directorate of Research and Community Service at the Ministry of Research, Technology and Higher Education for financing this mono-year research (grant no. 115/SP2H/LT/DPRM/2019).

References

1. Ball, D., 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
2. Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., & Tsai, Y. M. (2010). Teachers’ mathematical knowledge, cognitive activation in the classroom, and student progress. American Educational Research Journal, 47(1), 133–180. https://doi.org/10.3102/0002831209345157
3. Campbell, P.F. Nishio, M., Smith, T.M., Clark, L.M., Conant, D.L., Rust, A.H., DePiper, J.N., Frank, T.J., Griffin, M.J., & Choi, Y. (2014). The Relationship Between Teachers’ Mathematical Content and Pedagogical Knowledge, Teachers’ Perceptions, and Student Achievement. Journal for Research in Mathematics Education, 45(4), 419. https://doi.org/10.5951/jresematheduc.45.4.0419
4. 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-
5. 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
6. Csíkos, C., & Szitányi, J. (2020). Teachers’ pedagogical content knowledge in teaching word problem solving strategies. ZDM - Mathematics Education, 52(1), 165–178. https://doi.org/10.1007/s11858-019-01115-y
7. Cueto, S., León, J., Sorto, M. A., & Miranda, A. (2017). Teachers’ pedagogical content knowledge and mathematics achievement of students in Peru. Educational Studies in Mathematics, 94(3), 329–345. https://doi.org/10.1007/s10649-016-9735-2
8. Depaepe, F., Van Roy, P., Torbeyns, J., Kleickmann, T., Van Dooren, W., & Verschaffel, L. (2018). Stimulating pre-service teachers’ content and pedagogical content knowledge on rational numbers. Educational Studies in Mathematics, 99(2), 197–216. https://doi.org/10.1007/s10649-018-9822-7

9. Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics educational research. Teaching and Teacher Education, 34, 12–25. https://doi.org/10.1016/j.tate.2013.03.001
10. Fiallo, J., & Gutiérrez, A. (2017). Analysis of the cognitive unity or rupture between conjecture and proof when learning to prove on a grade 10 trigonometry course. Educational Studies in Mathematics, 96(2), 145–167. https://doi.org/10.1007/s10649-017-9755-6
11. Gasteiger, H., & Benz, C. (2018). Enhancing and analyzing kindergarten teachers’ professional knowledge for early mathematics education. Journal of Mathematical Behavior, 51(December 2016), 109–117. https://doi.org/10.1016/j.jmathb.2018.01.002
12. Gasteiger, H., Bruns, J., Benz, C., Brunner, E., & Sprenger, P. (2020). Mathematical pedagogical content knowledge of early childhood teachers: a standardized situation-related measurement approach. ZDM - Mathematics Education, 52(2), 193–205. https://doi.org/10.1007/s11858-019-01103-2
13. Goldin, G. A. (2000). A scientific perpsective on structured, task-based interviews in mathematics education research. In Handbook of Research Design in Mathematics and Science Education (Issue January 2000). https://doi.org/10.4324/9781410602725
14. Haciomeroglu, E. S., & Chicken, E. (2012). Visual thinking and gender differences in high school calculus. International Journal of Mathematical Education in Science and Technology, 43(3), 303–313. https://doi.org/10.1080/0020739X.2011.618550
15. Ikram, M., Purwanto, Parta, I. N., & Susanto, H. (2020). Relationship between reversible reasoning and conceptual knowledge in composition of function. Journal of Physics: Conference Series, 1521(3). https://doi.org/10.1088/1742-6596/1521/3/032004
16. Ikram, M., Purwanto, Parta, I. N., & Susanto, H. (2020). Exploring the potential role of reversible reasoning: Cognitive research on inverse function problems in mathematics. Journal for the Education of Gifted Young Scientists, 8(1), 591–611. https://doi.org/10.17478/jegys.665836
17. Ilyas, M., Ma’Rufi, & Basir, F. (2019). Students metacognitive skill in learning mathematics through cooperative based emotional intelligence. Journal of Physics: Conference Series, 1397(1). https://doi.org/10.1088/1742-6596/1397/1/012089
18. Kamber, D., & Takaci, D. (2018). On problematic aspects in learning trigonometry. International Journal of Mathematical Education in Science and Technology, 49(2), 161–175. https://doi.org/10.1080/0020739X.2017.1357846
19. Loewenberg Ball, D., 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
20. Ma’rufi, Ilyas, M., & Pasandaran, R. F. (2020). Higher order thinking skills (HOTS) first middle school of class viii students in completing the problem of polyhedron. Journal of Physics: Conference Series, 1470(1). https://doi.org/10.1088/1742-6596/1470/1/012073
21. Ma’rufi, Ilyas, M., Pasandaran, R. F., & Salwah. (2019). Exploration of teachers’ “knowledge of students” in study-based teaching on polyhedron material. Journal of Physics: Conference Series, 1397(1). https://doi.org/10.1088/1742-6596/1397/1/012088
22. Ma’rufi, Ilyas, M., Salwah, & Syamsuddin, A. (2020). ADD-CoRE Model Development : Mathematics Teachers Mentoring Based on Pedagogical Content Knowledge and Lesson Study. 8(10), 4580–4590. https://doi.org/10.13189/ujer.2020.081026
23. Mesa, V., & Herbst, P. (2011). Designing representations of trigonometry instruction to study the rationality of community college teaching. ZDM - International Journal on Mathematics Education, 43(1), 41–52. https://doi.org/10.1007/s11858-010-0300-7
24. Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (Third Edit). SAGE Publications, Inc.
25. Moore, K. C. (2014a). Coherence, Quantitative Reasoning, and The Trigonometry of Students.
26. Moore, K. C. (2014b). Quantitative Reasoning and the Sine Function: The Case of Zac. Journal for Research in Mathematics Education, 45(1), 102–138. https://doi.org/10.5951/jresematheduc.45.1.0102
27. Moore, K. C., Paoletti, T., & Musgrave, S. (2013). Covariational reasoning and invariance among coordinate systems. Journal of Mathematical Behavior, 32(3), 461–473. https://doi.org/10.1016/j.jmathb.2013.05.002
28. Norton, S. (2019). The relationship between mathematical content knowledge and mathematical pedagogical content knowledge of prospective primary teachers. Journal of Mathematics Teacher Education, 22(5), 489–514. https://doi.org/10.1007/s10857-018-9401-y
29. Orhun, N. (2010). the Gap Between Real Numbers and Trigonometric Relations. Dipmat.Math.Unipa.It. http://dipmat.math.unipa.it/~grim/QRDM_Orhun_20_2010.pdf
30. Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Profesorado, 23(3), 269–295. https://doi.org/10.30827/profesorado.v23i3.11230
31. Siyepu, S. W. (2013). An exploration of students ’ errors in derivatives in a university of technology. Journal of Mathematical Behavior, 32(3), 577–592. https://doi.org/10.1016/j.jmathb.2013.05.001
32. Siyepu, S. W. (2015). Analysis of errors in derivatives of trigonometric functions. International Journal of STEM Education, 2(1), 16. https://doi.org/10.1186/s40594-015-0029-5
33. Tallman, M. A., & Frank, K. M. (2020). Angle measure, quantitative reasoning, and instructional coherence: an examination of the role of mathematical ways of thinking as a component of teachers’ knowledge base. Journal of Mathematics Teacher Education, 23(1), 69–95. https://doi.org/10.1007/s10857-018-9409-3
34. Torbeyns, J., Verbruggen, S., & Depaepe, F. (2020). Pedagogical content knowledge in preservice preschool teachers and its association with opportunities to learn during teacher training. ZDM - Mathematics Education, 52(2), 269–280. https://doi.org/10.1007/s11858-019-01088-y
35. Verschaffel, L., van Dooren, W., Greer, B., & Mukhopadhyay, S. (2010). Die Rekonzeptualisierung von Textaufgaben als Übungen in mathematischer Modellierung. Journal Fur Mathematik-Didaktik, 31(1), 9–29. https://doi.org/10.1007/s13138-010-0007-x
36. Von Glasersfeld, E. (1995). Radical Constructivism: A Way of Knowing and Learning. In Studies in Mathematics Education Series (Issue 9). https://doi.org/10.4324/9780203454220
37. Yin, R. K. (2011). Qualitative Research from Start to Finish (Second Edi). The Guilford Press: New York, United States of America.