UNDERSTANDING MORE MATHEMATICS PEDAGOGICAL CONTENT KNOWLEDGE
Keywords:
teacher competence, mathematics pedagogical content knowledge, MPCK, systematic review
Abstract
The effectiveness of mathematics learning activities in the classroom is influenced by many factors such as the psychology of student learning, the level of material being taught, the classroom atmosphere, and the knowledge of the mathematics teacher. A mathematics teacher must at least have in-depth knowledge of mathematics content, strong pedagogical knowledge, and sophisticated technology knowledge. The integration of mathematics content knowledge and pedagogic knowledge makes mathematics pedagogical content knowledge (MPCK) unique as teachers must understand science, philosophy, and dimensions of mathematics, and then integrate it into learning activities so that learning objectives are achieved. A systematic review approach was carried out in this study by reviewing 29 out of 221 articles based on the results of analysis from searches with various keywords. The results showed that MPCK has specifications in terms of definition, aspects, linkages with various aspects of learning, methods of assessment and evaluation, improving method, teacher characteristics, and the impact on a mathematics lesson. This research supports mathematics teachers' efforts to implement effective mathematics learning by understanding more MPCK and optimizing MPCK.
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References
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Ekawati, R., Lin, F.-L., & Yang, K. (2018). The enactment of mathematics content knowledge and mathematics pedagogical content knowledge in teaching practice of ratio and proportion: A case of two primary. IOP Conference Series: Materials Science and Engineering, 288(1), 012122. https://doi.org/10.1088/1757-899X/288/1/012122
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Gall, M. D., Gall, J. P., & Borg, W. R. (2003). Educational Research: An Introduction (7th ed.). Allyn & Bacon.
Gasteiger, H., Bruns, J., Benz, C., Brunner, E., & Sprenger, P. (2019). Mathematical pedagogical content knowledge of early childhood teachers: a standardized situation‑related measurement approach. ZDM - Mathematics Education, 55(2), 193–205. https://doi.org/10.1007/s11858-019-01103-2
Hoth, J., Kaiser, G., Busse, A., Döhrmann, M., König, J., & Blömeke, S. (2017). Professional competences of teachers for fostering creativity and supporting high-achieving students. ZDM - Mathematics education, 49(1), 107–120. https://doi.org/10.1007/s11858-016-0817-5
Hsieh, F.-J. (2013). Strengthening the conceptualization of mathematics pedagogical content knowledge for international studies: A Taiwanese perspective. International Journal of Science and Mathematics, 11(4), 923–947. https://doi.org/10.1007/s10763-013-9425-9
Indonesia, P. (2005). Undang-Undang Republik Indonesia Nomor 14 Tahun 2005 Tentang Guru dan Dosen. Sekretariat Negara.
Kaarstein, H. (2014). Norwegian mathematics teachers’ and educational researchers’ perception of MPCK items used in the TEDS-M study. Nordic Studies in Mathematics Education, 19(3), 57–82. ncm.gu.se/wp-content/uploads/2020/06/19_3-4_057082_kaarstein.pdf
Kaiser, G., Blömeke, S., Busse, A., Döhrmann, M., & König, J. (2016). Professional knowledge of (prospective) Mathematics teachers – Its structure and development. Cuadernos de Investigación y Formación en Educación Matemática, 83–89. https://revistas.ucr.ac.cr/index.php/cifem/article/view/23941
Kow, J. Y. K. (2008). Teaching area and perimeter: Mathematics pedagogical content knowledge in action. https://repository.nie.edu.sg/bitstream/10497/14397/1/MERGA-2008-621-YeoKK_a.pdf
Kwong, C. W., Joseph, Y. K. K., Eric, C. C. M., & Khoh, L.-T. S. (2007). Development of mathematics pedagogical content knowledge in student teachers. The Mathematics Educator, 10(2), 27–54. http://hdl.handle.net/10497/102
Laschke, C. (2013). Effects of future mathematics teachers’ affective, cognitive and socio-demographic characteristics on their knowledge at the end of the teacher education in Germany and Taiwan. International Journal of Science and Mathematics Education, 11(4), 895–921. https://doi.org/10.1007/s10763-013-9423-y
Lerman, S. (1989). Constructivism, mathematics and mathematics education. Educational studies in mathematics, 20(2), 211–223. https://doi.org/10.1007/BF00579463
Lin, Y.-H., & Lee, Y.-S. (2016). Clustering analysis on teachers’ perceptions of mathematics pedagogical content knowledge. American Journal of Applied Psychology, 5(2), 6–11. https://doi.org/10.11648/j.ajap.20160502.11
Luna, C. A., & Aclan, E. G. (2015). The Influence of Teachers’ Mathematics Pedagogy Content Knowledge Training on Pupils’ Mathematics Achievement. American Journal of Educational Research, 3(10), 1311–1314. https://doi.org/10.12691/education-3-10-16
Moh’d, S. 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
Msimango, M. N., Fonseca, K., & Petersen, N. F. (2020). Mentoring and preparing primary school mathematics teacher. Perspective in Education, 38(2), 272–284. https://doi.org/10.18820/2519593X/pie.v38.i2.18
Norton, S. J. (2017). Primary mathematics trainee teacher confidence and its relationship to mathematical knowledge. Australian Journal of Teacher Education, 42(2), 47–61. https://doi.org/10.14221/ajte.2017v42n2.4
Novikasari, I. (2020). Pre-service teacher’s mathematical knowledge for teaching in problem-based learning. JRAMathEdu, 5(2), 160–174. https://doi.org/10.23917/jramathedu.v5i2.10556
Qian, H., & Youngs, P. (2015). The effect of teacher education programs on future elementary mathematics teachers’ knowledge: a five country analysis using TEDS-M data. Journal of Mathematics Teacher Education, 19(4), 371–396. https://doi.org/10.1007/s10857-014-9297-0
Senk, S. L., Tatto, M. T., Reckase, M., Peck, R., Rowley, G., & Bankov, K. (2012). Knowledge of future primary teachers for teaching mathematics: an international comparative study. ZDM - Mathematics Education, 44, 307–324. https://doi.org/10.1007/s11858-012-0400-7
Shahbari, J. A. (2017). Mathematical and pedagogical knowledge amongst first- and second-grade in-service and pre-service mathematics teachers. International Journal for Mathematics Teaching and Learning, 18(1), 41–65.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard educational review, 57(1), 1–23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Sintema, E. J., & Marbán, J. M. (2020). Pre-service secondary teachers’ mathematical pedagogical content knowledge self-concept related to their content knowledge of functions and students. International Electronic Journal of Mathematics Education, 15(3), em0598. https://doi.org/10.29333/iejme/8327
Triana, D., Anggraito, Y. U., & Ridlo, S. (2020). No TitleEffectiveness of environmental change learning tools based on STEM-PjBL towards 4C skills of students. Journal of Innovative Science Education, 9(2), 180–187. https://doi.org/10.15294/jise.v8i3.34048
Walshaw, M. (2012). Teacher knowledge as fundamental to effective teaching practice. Journal of mathematics teacher education, 15, 181–185. https://doi.org/10.1007/s10857-012-9217-0
Yang, X., Kaiser, G., König, J., & Blömeke, S. (2020). Relationship between pre‑service mathematics teachers’ knowledge, beliefs and instructional practices in China. ZDM - Mathematics Education, 52, 281–294. https://doi.org/10.1007/s11858-020-01145-x
Yang, X., Kaiser, G., König, J., & Blömeke, S. (2021). Relationship between Chinese mathematics teachers’ knowledge and their professional noticing. International Journal of Science and Mathematics Education, 19, 815–837. https://doi.org/10.1007/s10763-020-10089-3
Zakiah, N. E., & Fajriadi, D. (2020). Management of authentic assessment in mathematics lessons to develop 4C skills. Journal of Physics: Conference Series, 1613(1), 012050. https://doi.org/10.1088/1742-6596/1613/1/012050
Alfaro, H., & Joutsenlahti, J. (2020). What skills and knowledge do university mathematics teacher education programs give future teachers in Costa Rica? European Journal of Science and Mathematics, 8(3), 145–162. https://doi.org/10.30935/scimath/9553
Ariyanti, M. (2015). Pengaruh kompetensi pedagogik guru terhadap prestasi belajar matematika siswa kelas XI SMA. Seminar Nasional Matematika dan Pendidikan Matematika UNY 2015, 169–174. seminar.uny.ac.id/semnasmatematika/sites/seminar.uny.ac.id.semnasmatematika/files/banner/PM-25.pdf
Astuti, T. A., & Jailani. (2020). Kontribusi kompetensi guru matematika SMP terhadap prestasi belajar siswa. Jurnal riset pendidikan matematika, 7(2), 241–253. https://doi.org/10.21831/jrpm.v7i2.16453
Baki, M., & Arslan, S. (2017). Effects of mathematics content knowledge on mathematics pedagogical content knowledge. Journal of Teacher Education and Educators, 6(1), 53–68. https://dergipark.org.tr/en/pub/jtee/issue/43270/525677
Bandura, A. (1977). Social learning theory. Prentice-Hall.
Baumert, J., & Kunter, M. (2013). The COACTIV model of teachers’ professional competence. In Kunter, M., Baumert, J., Blum, W., Klusmann, U., Krauss, S., Neubrand, M. (eds), Cognitive activation in the mathematics classroom and professional competence of teachers (hal. 25–48). Springer. https://doi.org/10.1007/978-1-4614-5149-5_2
Blömeke, S., Buchholtz, N., Suhl, U., & Kaiser, G. (2014). Resolving the chicken-or-egg causality dilemma: The longitudinal interplay of teacher knowledge and teacher beliefs. Teaching and Teacher Education, 37, 130–139. https://doi.org/10.1016/j.tate.2013.10.007
Blömeke, S., Suhl, U., & Kaiser, G. (2011). Teacher education effectiveness: quality and equity of future primary teachers’ mathematics and mathematics pedagogical content knowledge. Journal of Teacher Education, 62(2), 154–171. https://doi.org/10.1177/0022487110386798
Buchholtz, N. F. (2017). The acquisition of mathematics pedagogical content knowledge in university mathematics education courses: results of a mixed methods study on the effectiveness of teacher education in Germany. ZDM - Mathematics Education, 49(2), 249–264. https://doi.org/10.1007/s11858-017-0849-5
Buchholtz, N. F., & Kaiser, G. (2013). Improving mathematics teacher education in Germany: Empirical results from a longitudinal evaluation of innovative programs. International Journal of Science and Mathematics Education, 11(4), 949–977. https://doi.org/10.1007/s10763-013-9427-7
Christou, C., Eliophotou-Menon, M., & Philippou, G. (2004). Teachers’ concerns regarding the adoption of a new mathematics curriculum: An application of CBAM. Educational studies in mathematics, 57(2), 157–176. https://doi.org/10.1023/B:EDUC.0000049271.01649.dd
Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation. Journal of teacher education, 44(3), 263–272. https://doi.org/10.1177/002248719304400400
Döhrmann, M., Kaiser, G., & Blömeke, S. (2012). The conceptualisation of Mathematics competencies in the international teacher education study TEDS-M. International perspectives on teacher knowledge, beliefs and opportunities to learn, 431–456. https://doi.org/110.1007/978-94-007-6437-8_20
Ekawati, R., Lin, F.-L., & Kohar, A. W. (2022). Investigating teachers’ mathematics pedagogical content knowledge on ratio and proportion: Does it exist in teaching? Jurnal Cakrawala Pendidikan, 41(3), 830–847. https://doi.org/10.21831/cp.v41i3.39457
Ekawati, R., Lin, F.-L., & Yang, K. (2018). The enactment of mathematics content knowledge and mathematics pedagogical content knowledge in teaching practice of ratio and proportion: A case of two primary. IOP Conference Series: Materials Science and Engineering, 288(1), 012122. https://doi.org/10.1088/1757-899X/288/1/012122
Ernest, P. (2004). Postmodernity and social research in mathematics education. In Valero, P., Zevenbergen, R. (eds), Researching the socio-political dimensions of mathematics education (hal. 65–84). Springer. https://doi.org/doi.org/10.1007/1-4020-7914-1_7
Gall, M. D., Gall, J. P., & Borg, W. R. (2003). Educational Research: An Introduction (7th ed.). Allyn & Bacon.
Gasteiger, H., Bruns, J., Benz, C., Brunner, E., & Sprenger, P. (2019). Mathematical pedagogical content knowledge of early childhood teachers: a standardized situation‑related measurement approach. ZDM - Mathematics Education, 55(2), 193–205. https://doi.org/10.1007/s11858-019-01103-2
Hoth, J., Kaiser, G., Busse, A., Döhrmann, M., König, J., & Blömeke, S. (2017). Professional competences of teachers for fostering creativity and supporting high-achieving students. ZDM - Mathematics education, 49(1), 107–120. https://doi.org/10.1007/s11858-016-0817-5
Hsieh, F.-J. (2013). Strengthening the conceptualization of mathematics pedagogical content knowledge for international studies: A Taiwanese perspective. International Journal of Science and Mathematics, 11(4), 923–947. https://doi.org/10.1007/s10763-013-9425-9
Indonesia, P. (2005). Undang-Undang Republik Indonesia Nomor 14 Tahun 2005 Tentang Guru dan Dosen. Sekretariat Negara.
Kaarstein, H. (2014). Norwegian mathematics teachers’ and educational researchers’ perception of MPCK items used in the TEDS-M study. Nordic Studies in Mathematics Education, 19(3), 57–82. ncm.gu.se/wp-content/uploads/2020/06/19_3-4_057082_kaarstein.pdf
Kaiser, G., Blömeke, S., Busse, A., Döhrmann, M., & König, J. (2016). Professional knowledge of (prospective) Mathematics teachers – Its structure and development. Cuadernos de Investigación y Formación en Educación Matemática, 83–89. https://revistas.ucr.ac.cr/index.php/cifem/article/view/23941
Kow, J. Y. K. (2008). Teaching area and perimeter: Mathematics pedagogical content knowledge in action. https://repository.nie.edu.sg/bitstream/10497/14397/1/MERGA-2008-621-YeoKK_a.pdf
Kwong, C. W., Joseph, Y. K. K., Eric, C. C. M., & Khoh, L.-T. S. (2007). Development of mathematics pedagogical content knowledge in student teachers. The Mathematics Educator, 10(2), 27–54. http://hdl.handle.net/10497/102
Laschke, C. (2013). Effects of future mathematics teachers’ affective, cognitive and socio-demographic characteristics on their knowledge at the end of the teacher education in Germany and Taiwan. International Journal of Science and Mathematics Education, 11(4), 895–921. https://doi.org/10.1007/s10763-013-9423-y
Lerman, S. (1989). Constructivism, mathematics and mathematics education. Educational studies in mathematics, 20(2), 211–223. https://doi.org/10.1007/BF00579463
Lin, Y.-H., & Lee, Y.-S. (2016). Clustering analysis on teachers’ perceptions of mathematics pedagogical content knowledge. American Journal of Applied Psychology, 5(2), 6–11. https://doi.org/10.11648/j.ajap.20160502.11
Luna, C. A., & Aclan, E. G. (2015). The Influence of Teachers’ Mathematics Pedagogy Content Knowledge Training on Pupils’ Mathematics Achievement. American Journal of Educational Research, 3(10), 1311–1314. https://doi.org/10.12691/education-3-10-16
Moh’d, S. 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
Msimango, M. N., Fonseca, K., & Petersen, N. F. (2020). Mentoring and preparing primary school mathematics teacher. Perspective in Education, 38(2), 272–284. https://doi.org/10.18820/2519593X/pie.v38.i2.18
Norton, S. J. (2017). Primary mathematics trainee teacher confidence and its relationship to mathematical knowledge. Australian Journal of Teacher Education, 42(2), 47–61. https://doi.org/10.14221/ajte.2017v42n2.4
Novikasari, I. (2020). Pre-service teacher’s mathematical knowledge for teaching in problem-based learning. JRAMathEdu, 5(2), 160–174. https://doi.org/10.23917/jramathedu.v5i2.10556
Qian, H., & Youngs, P. (2015). The effect of teacher education programs on future elementary mathematics teachers’ knowledge: a five country analysis using TEDS-M data. Journal of Mathematics Teacher Education, 19(4), 371–396. https://doi.org/10.1007/s10857-014-9297-0
Senk, S. L., Tatto, M. T., Reckase, M., Peck, R., Rowley, G., & Bankov, K. (2012). Knowledge of future primary teachers for teaching mathematics: an international comparative study. ZDM - Mathematics Education, 44, 307–324. https://doi.org/10.1007/s11858-012-0400-7
Shahbari, J. A. (2017). Mathematical and pedagogical knowledge amongst first- and second-grade in-service and pre-service mathematics teachers. International Journal for Mathematics Teaching and Learning, 18(1), 41–65.
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
Shulman, L. S. (1987). Knowledge and teaching: Foundations of the new reform. Harvard educational review, 57(1), 1–23. https://doi.org/10.17763/haer.57.1.j463w79r56455411
Sintema, E. J., & Marbán, J. M. (2020). Pre-service secondary teachers’ mathematical pedagogical content knowledge self-concept related to their content knowledge of functions and students. International Electronic Journal of Mathematics Education, 15(3), em0598. https://doi.org/10.29333/iejme/8327
Triana, D., Anggraito, Y. U., & Ridlo, S. (2020). No TitleEffectiveness of environmental change learning tools based on STEM-PjBL towards 4C skills of students. Journal of Innovative Science Education, 9(2), 180–187. https://doi.org/10.15294/jise.v8i3.34048
Walshaw, M. (2012). Teacher knowledge as fundamental to effective teaching practice. Journal of mathematics teacher education, 15, 181–185. https://doi.org/10.1007/s10857-012-9217-0
Yang, X., Kaiser, G., König, J., & Blömeke, S. (2020). Relationship between pre‑service mathematics teachers’ knowledge, beliefs and instructional practices in China. ZDM - Mathematics Education, 52, 281–294. https://doi.org/10.1007/s11858-020-01145-x
Yang, X., Kaiser, G., König, J., & Blömeke, S. (2021). Relationship between Chinese mathematics teachers’ knowledge and their professional noticing. International Journal of Science and Mathematics Education, 19, 815–837. https://doi.org/10.1007/s10763-020-10089-3
Zakiah, N. E., & Fajriadi, D. (2020). Management of authentic assessment in mathematics lessons to develop 4C skills. Journal of Physics: Conference Series, 1613(1), 012050. https://doi.org/10.1088/1742-6596/1613/1/012050
Published
13-11-2023
How to Cite
Radite, R., & Sulistyawati, E. (2023). UNDERSTANDING MORE MATHEMATICS PEDAGOGICAL CONTENT KNOWLEDGE. Pedagogy: Jurnal Pendidikan Matematika, 8(2), 341-357. https://doi.org/10.30605/pedagogy.v8i2.3111
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