Unveiling belief and pedagogical content knowledge of prospective secondary mathematics teachers
DOI:
https://doi.org/10.29408/jel.v8i2.5096Keywords:
belief, pedagogical content knowledge, prospective mathematics teacherAbstract
Prospective teachers' beliefs have a beneficial effect on their knowledge and actions. Furthermore, teachers' pedagogical content knowledge is an essential contributor to teachers' impact on students' academic outcomes. However, examining how prospective teachers' beliefs influence their pedagogical content knowledge is still unclear. The current study investigates prospective mathematics teachers' beliefs and pedagogical content knowledge. We recruited three undergraduate students in the mathematics department consisting of one male and two female participants in this study. By assigning two interviews, a test, and observation, we examined three prospective mathematics teachers' pedagogical content knowledge and their beliefs about the nature of mathematics, mathematics learning, and mathematics teaching. Prospective mathematics teachers' test, interview, and observation results were analyzed in three stages: data condensation, presentation, and conclusion drawing and verification. The findings point out that traditional beliefs (instrumentalist and platonist views) are more dominant in prospective teachers' beliefs about the nature of mathematics. Moreover, the more sophisticated prospective teachers' beliefs about the nature of mathematics, mathematics learning, and mathematics teaching are, the higher one's content knowledge and pedagogical content knowledge levels are. Implications of this study, mathematics teacher educators should assist and foster prospective teachers in developing constructivist or problem-solving beliefs.
References
An, S., Kulm, G., & Wu, Z. (2004). The pedagogical content knowledge of middle school, mathematics teachers in China and the U.S. Journal of Mathematics Teacher Education, 7(2), 145–172. https://doi.org/10.1023/B:JMTE.0000021943.35739.1c
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
Beswick, K. (2012). Teachers' beliefs about school mathematics and mathematicians' mathematics and their relationship to practice. Educational Studies in Mathematics, 79(1), 127–147. https://doi.org/10.1007/s10649-011-9333-2
Charalambous, C. Y., & Hill, H. C. (2012). Teacher knowledge, curriculum materials, and quality of instruction: Unpacking a complex relationship. Journal of Curriculum Studies, 44(4), 443–466. https://doi.org/10.1080/00220272.2011.650215
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
Cross, D. I. (2009). Alignment, cohesion, and change: Examining mathematics teachers' belief structures and their influence on instructional practices. Journal of Mathematics Teacher Education, 12(5), 325–346. https://doi.org/10.1007/s10857-009-9120-5
Cross, D. I. (2015). Dispelling the notion of inconsistencies in teachers' mathematics beliefs and practices: A 3-year case study. Journal of Mathematics Teacher Education, 18(2), 173–201. https://doi.org/10.1007/s10857-014-9276-5
Dede, Y. & Uysal, F. (2012). Examining Turkish preservice elementary teachers' beliefs about the nature and the teaching of mathematics. International Journal of Humanities and Social Science, 2(12), 125–135.
Ekawati, R., Lin, F. L., & Yang, K. L. (2015). Primary teachers' knowledge for teaching ratio and proportion in mathematics: The case of Indonesia. Eurasia Journal of Mathematics, Science and Technology Education, 11(3), 513–533. https://doi.org/10.12973/eurasia.2015.1354a
Ernest, P. (1989). The knowledge, beliefs and attitudes of the mathematics teacher: A model. Journal of Education for Teaching:International Research and Pedagogy, 15(1), 13–33. https://doi.org/10.1080/0260747890150102
Felbrich, A., Kaiser, G., & Schmotz, C. (2012). The cultural dimension of beliefs: an investigation of future primary teachers' epistemological beliefs concerning the nature of mathematics in 15 countries. ZDM - International Journal on Mathematics Education, 44(3), 355–366. https://doi.org/10.1007/s11858-012-0418-x
Friesen, M. E. & Kuntze, S. (2020). The role of professional knowledge for teachers' analyzing of classroom situations regarding the use of multiple representations. Research in Mathematics Education, 22(2), 117–134. https://doi.org/10.1080/14794802.2019.1710555
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. https://doi.org/10.5951/jresematheduc.39.4.0372
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
Kersting, N. B., Givvin, K. B., Thompson, B. J., Santagata, R., & Stigler, J. W. (2012). Measuring usable knowledge: Teachers' analyses of mathematics classroom videos predict teaching quality and student learning. American Educational Research Journal, 49(3), 568–589. https://doi.org/10.3102/0002831212437853
Kim, S. (2018). Technological, Pedagogical, and Content Knowledge (TPACK) and beliefs of preservice secondary mathematics teachers: Examining the relationships. EURASIA Journal of Mathematics, Science and Technology Education, 14(10), em1590. https://doi.org/10.29333/ejmste/93179
Lui, A. M. & Bonner, S. M. (2016). Preservice and inservice teachers' knowledge, beliefs, and instructional planning in primary school mathematics. Teaching and Teacher Education, 56, 1–13. https://doi.org/10.1016/j.tate.2016.01.015
Ma’Rufi, Budayasa, I. K., & Juniati, D. (2017). Pedagogical content knowledge: Knowledge of pedagogy novice teachers in mathematics learning on limit algebraic function. AIP Conference Proceedings, 1813. https://doi.org/10.1063/1.4975975
Miles, M. B., Huberman, A. M., & Saldana, J. (2014). Qualitative data analysis: a methods sourcebook (3rd ed.). SAGE Publications, Inc.
Mitchell, R., Charalambous, C. Y., & Hill, H. C. (2014). Examining the task and knowledge demands needed to teach with representations. Journal of Mathematics Teacher Education, 17(1), 37–60. https://doi.org/10.1007/s10857-013-9253-4
Muhtarom, Happy, N., Nursyahidah, F., & Casanova, A. (2019). Pre-service teacher's beliefs and knowledge about mathematics. Al-Jabar: Jurnal Pendidikan Matematika, 10(1), 101–110. https://doi.org/10.24042/ajpm.v10i1.3617
Muhtarom, Juniati, D., & Siswono, T. Y. E. (2017). Exploring beliefs in a problem-solving process of prospective teachers' with high mathematical ability. Global Journal of Engineering Education, 19(2), 130–136.
Muhtarom, Juniati, D., & Siswono, T. Y. E. (2019). Examining prospective teachers' belief and pedagogical content knowledge towards teaching practice in mathematics class: A case study. Journal on Mathematics Education, 10(2), 185–202. https://doi.org/10.22342/jme.10.2.7326.185-202
Muhtarom, M. (2020). Pengetahuan pedagogi mahasiswa calon guru dalam perencanaan pengajaran matematika dan hubungannya dengan keyakinan [Prospective teachers’ pedagogical knowledge in planning of mathematics teaching and relationship with belief]. Jurnal Elemen, 6(2), 262–276. https://doi.org/10.29408/jel.v6i2.2094
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
Philipp, R. A. (2007). Mathematics teachers' beliefs and affect. In F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 257–315). Information Age Publishing.
Rothbaeur, P. M. (2008). Triangulation. In L. M. Given (Ed.), The SAGE Encyclopedia of Qualitative Research Methods (pp. 892–894). SAGE Publications, Inc.
Safrudiannur, Labulan, P. M., Suriaty, & Rott, B. (2021). Beliefs about school mathematics vs. university mathematics and beliefs about teaching and learning in different contexts of students' achievement. Beta Jurnal Tadris Matematika, 14(1), 1–14. https://doi.org/10.20414/betajtm.v14i1.439
Safrudiannur & Rott, B. (2020). Offering an approach to measure beliefs quantitatively: Capturing the influence of students' abilities on teachers' beliefs. International Journal of Science and Mathematics Education, 19, 419-441. https://doi.org/10.1007/s10763-020-10063-z
Safrudiannur, S. & Rott, B. (2019). Measuring teachers' beliefs: A comparison of three different approaches. EURASIA Journal of Mathematics, Science and Technology Education, 16(1), 1–16. https://doi.org/10.29333/ejmste/110058
Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
Siswono, T. Y. E., Kohar, A. W., & Hartono, S. (2017). Secondary teachers' mathematics-related beliefs and knowledge about mathematical problem-solving. Journal of Physics: Conference Series, 812. https://doi.org/10.1088/1742-6596/755/1/011001
Smith, R. C., Kim, S., & McIntyre, L. (2016). Relationships between prospective middle grades mathematics teachers' beliefs and TPACK. Canadian Journal of Science, Mathematics and Technology Education, 16(4), 359–373. https://doi.org/10.1080/14926156.2016.1189624
Stipek, D. J., Givvin, K. B., Salmon, J. M., & MacGyvers, V. L. (2001). Teachers' beliefs and practices related to mathematics instruction. Teaching and Teacher Education, 17(2), 213–226. https://doi.org/10.1016/S0742-051X(00)00052-4
Wilkins, J. L. M. (2008). The relationship among elementary teachers' content knowledge, attitudes, beliefs, and practices. Journal of Mathematics Teacher Education, 11(2), 139–164. https://doi.org/10.1007/s10857-007-9068-2
Zhang, Q. (2022). Understanding Chinese mathematics teaching: how secondary mathematics teachers' beliefs and knowledge influence their teaching in mainland China. ZDM - Mathematics Education. https://doi.org/10.1007/s11858-022-01336-8
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