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

Year 2020, Volume: 8 Issue: 4, 1361 - 1371, 15.12.2020
https://doi.org/10.17478/jegys.780399

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.

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

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (Third Edit). SAGE Publications, Inc.
  • Moore, K. C. (2014a). Coherence, Quantitative Reasoning, and The Trigonometry of Students.
  • 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
  • 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
  • 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
  • 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
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Profesorado, 23(3), 269–295. https://doi.org/10.30827/profesorado.v23i3.11230
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Yin, R. K. (2011). Qualitative Research from Start to Finish (Second Edi). The Guilford Press: New York, United States of America.
Year 2020, Volume: 8 Issue: 4, 1361 - 1371, 15.12.2020
https://doi.org/10.17478/jegys.780399

Abstract

References

  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative Data Analysis: A Methods Sourcebook (Third Edit). SAGE Publications, Inc.
  • Moore, K. C. (2014a). Coherence, Quantitative Reasoning, and The Trigonometry of Students.
  • 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
  • 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
  • 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
  • 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
  • Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Profesorado, 23(3), 269–295. https://doi.org/10.30827/profesorado.v23i3.11230
  • 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
  • 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
  • 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
  • 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
  • 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
  • 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
  • Yin, R. K. (2011). Qualitative Research from Start to Finish (Second Edi). The Guilford Press: New York, United States of America.
There are 37 citations in total.

Details

Primary Language English
Subjects Other Fields of Education
Journal Section Teacher Education
Authors

Marufi Marufi This is me 0000-0002-1379-3287

Muhammad Ilyas This is me 0000-0002-0016-6380

Salwah Salwah This is me

Rio Pasandaran This is me 0000-0002-1258-4694

Muhammad Ikram 0000-0002-3763-4299

Publication Date December 15, 2020
Published in Issue Year 2020 Volume: 8 Issue: 4

Cite

APA Marufi, M., Ilyas, M., Salwah, S., Pasandaran, R., et al. (2020). Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills. Journal for the Education of Gifted Young Scientists, 8(4), 1361-1371. https://doi.org/10.17478/jegys.780399
AMA Marufi M, Ilyas M, Salwah S, Pasandaran R, Ikram M. Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills. JEGYS. December 2020;8(4):1361-1371. doi:10.17478/jegys.780399
Chicago Marufi, Marufi, Muhammad Ilyas, Salwah Salwah, Rio Pasandaran, and Muhammad Ikram. “Exploration of Pre-Service teachers’ Pedagogical Content Knowledge in Mathematics Learning in Senior High School Based on Gender and Academic Skills”. Journal for the Education of Gifted Young Scientists 8, no. 4 (December 2020): 1361-71. https://doi.org/10.17478/jegys.780399.
EndNote Marufi M, Ilyas M, Salwah S, Pasandaran R, Ikram M (December 1, 2020) Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills. Journal for the Education of Gifted Young Scientists 8 4 1361–1371.
IEEE M. Marufi, M. Ilyas, S. Salwah, R. Pasandaran, and M. Ikram, “Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills”, JEGYS, vol. 8, no. 4, pp. 1361–1371, 2020, doi: 10.17478/jegys.780399.
ISNAD Marufi, Marufi et al. “Exploration of Pre-Service teachers’ Pedagogical Content Knowledge in Mathematics Learning in Senior High School Based on Gender and Academic Skills”. Journal for the Education of Gifted Young Scientists 8/4 (December 2020), 1361-1371. https://doi.org/10.17478/jegys.780399.
JAMA Marufi M, Ilyas M, Salwah S, Pasandaran R, Ikram M. Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills. JEGYS. 2020;8:1361–1371.
MLA Marufi, Marufi et al. “Exploration of Pre-Service teachers’ Pedagogical Content Knowledge in Mathematics Learning in Senior High School Based on Gender and Academic Skills”. Journal for the Education of Gifted Young Scientists, vol. 8, no. 4, 2020, pp. 1361-7, doi:10.17478/jegys.780399.
Vancouver Marufi M, Ilyas M, Salwah S, Pasandaran R, Ikram M. Exploration of pre-service teachers’ pedagogical content knowledge in mathematics learning in senior high school based on gender and academic skills. JEGYS. 2020;8(4):1361-7.
By introducing the concept of the "Gifted Young Scientist," JEGYS has initiated a new research trend at the intersection of science-field education and gifted education.