Investigating teachers’ mathematics pedagogical content knowledge on ratio and proportion: Does it exist in teaching?

Rooselyna Ekawati, Universitas Negeri Surabaya, Indonesia
Fou-Lai Lin, National Taiwan Normal University, Taiwan, Province of China
Ahmad Wachidul Kohar, Universitas Negeri Surabaya, Indonesia


There is a widespread agreement that Mathematics Pedagogical Content Knowledge (MPCK) become one of the key resources for teaching mathematics effectively. This qualitative research investigates the existence of primary teachers’ MPCK in mathematics teaching practice on ratio and proportion. Data were collected from the recorded videos of teaching observations of three primary teachers with different levels of Mathematics Content Knowledge (MCK) and MPCK selected from a paper and pencil test. A video observation instrument considering the MPCK factors’ framework for teaching ratio and proportion was used to explore the existence of MPCK in the teachers’ teaching practices. Data were analyzed by employing a whole-to-part approach of video-based data on three components of the teachers’ teaching practices on ratio and proportion, i.e., task level feature, the teaching of problem-solving strategies, and knowledge of students’ conceptual understanding. Results indicate that all the components of teachers’ MPCK can be observed in teaching practice appropriately or inappropriately due to teachers’ different levels of MPCK (Good, Medium, and Low). All MPCK factors were activated by the good teacher in her teaching appropriately differs from Medium and Low teachers. The Medium teacher needs more opportunities to learn about ratio and proportion task level features. The evidence leads to the opportunity to design a learning trajectory for In-service primary teachers that consider the integration of MPCK and MCK in balance.


Mathematics Pedagogical Content Knowledge; Mathematics Teaching; Primary Teacher; Ratio and Proportion

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Abrahamson, D., & Zolkower, B. (2020). Reinventing Realistic Mathematics Education at Berkeley—Emergence and Development of a Course for Pre-service Teachers. In M. Van Den Heuvel-Panhuizen (Ed.), International reflections on the Netherlands Didactics of Mathematics (pp. 255–277). Springer Open.

Adak, B., & Aliustaoğlu, F. (2020). An Investigation of 7th Grade Students’ Misconceptions about Proportion Ratio. Online Journal of Mathematics, Science and Technology Education, 1(1), 55-74.

Anat, K., Einav, K., & Shirley, R. (2019). Development of mathematics trainee teachers’ knowledge while creating a MOOC. International Journal of Mathematical Education in Science and Technology, 51(6), 939–953.

Anderson, J., White, P., Research, P. S.-M. E., & 2005, undefined. (2005). Using a schematic model to represent influences on, and relationships between, teachers’ problem-solving beliefs and practices. Springer, 17(2), 9–38.

Andrews, P., & Xenofontos, C. (2015). Analysing the relationship between the problem-solvingrelated beliefs, competence and teaching of three cypriot primary teachers. Journal of Mathematics Teacher Education, 18(4), 299–325.

Ball, D. L., & Thames, M. H. (2008). Content knowledge for teaching: What makes it special? Journal of Teacher, 59(5), 389–407.

Brodie, K., & Sanni, R. (2014). “We won’t know it since we don’t teach it”: interactions between teachers’ knowledge and practice. African Journal of Research in Mathematics, Science, and Technology, 18(2), 188–197.

Cheang, W. K., Yeo, J. K. K., Chan, E. C. M., & Lim-Teo, S. K. (2007). Development of mathematics pedagogical content knowledge in student teachers. The Mathematics Educator, 10(2), 27–54.

Cochran-Smith, M., & Lytle, S. L. (1999). Relationships of knowledge and practice: Teacher learning in communities. Review of Research in Education, 24, 249–305.

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.

Ekawati, R., Fiangga, S., & Siswono, T. Y. E. (2018). Historical aspect of mathematics on Indonesian mathematics textbook. IOP Conference Series: Materials Science and Engineering, 434(1).


Ekawati, R., Lin, F., & Mathematics, K. Y.-. (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.

Engeln, K., Euler, M., & Maass, K. (2013). Inquiry-based learning in mathematics and science: a comparative baseline study of teachers” beliefs and practices across 12 European countries. Researchgate.Net, 45(6), 823–836.

Erickson, F. (2006). Definition and Analysis of Data from Videotape: Some Research Procedur. In J. Green, J. Camilli, & P. Elmore (Eds.), Handbook of Complementary Methods in Education Research (3rd ed., pp. 177–191). Routledhe.

Fawns, R., & Nance, D. (1993). Teacher Knowledge, Education Studies and Advanced Skills Credentials. Australian Journal of Education, 37(3), 248–258.

Fenstermacher, G. D. (1989). Philosophy of research on teaching: Three aspects. Handbook of Research on Teaching, 3(4), 37–49.

Forsythe, M. E., Criswell, B. A., Arias, A. M., Ellis, J. A., Escalada, L., Johnson, H. J., Palmeri, A. B., Riccio, J., & Parker, M. E. (2022). The Framework for Analyzing Video in Science Teacher Education (FAVSTE). Taylor & Francis, 33(6), 621–640.

Gamayao, M., & Binas, J. (2021). Teaching competence and pedagogical content knowledge of science teachers in the First District of Capiz, Philippines: Basis for a sustainable instructional. European Journal of Humanities and Educational Advancement, 2(1).

Graham, L. J., White, S. L., Cologon, K., & Pianta, R. C. (2020). Do teachers’ years of experience make a difference in the quality of teaching?. Teaching and teacher education, 96, 103190.

Glassmeyer, D., Brakoniecki, A., & Amador, J. (2021). Identifying and supporting teachers’ robust understanding of proportional reasoning. The Journal of Mathematical Behaviour, 62, 100873.

Hill, H. C., Blunk, M. L., Charalambous, C. Y., Lewis, J. M., Phelps, G. C., Sleep, L., & Loewenberg Ball, D. (2008). Mathematical knowledge for teaching and the mathematical quality of instruction: An exploratory study. Taylor & Francis, 26(4), 430–511.

Im, S., & Jitendra, A. (2020). Analysis of proportional reasoning and misconceptions among students with mathematical learning disabilities. The Journal of Mathematical Behaviour, 57, 100753.

Izsák, A., & Jacobson, E. (2017). Preservice teachers’ reasoning about relationships that are and are not proportional: A knowledge-in-pieces account. Journal for Research in Mathematics Education, 48(3), 300–339.

Khalil, I. (2021). Mathematics textbooks content development at the primary stage: a proposed vision. Journal for the Mathematics Education and Teaching Practices, 2(2), 47-53.

Jacobs, J., Hollingsworth, H., Methods, K. G.-F., & 2007, undefined. (2007). Video-based research made “easy”: Methodological lessons learned from the TIMSS video studies. Journals.Sagepub.Com, 19(3), 284–299.

Jaworski, B. (2002). Investigating mathematics teaching: A constructivist enquiry. Falmer Press.

Jitendra, A. K., Harwell, M. R., Dupuis, D. N., Jitendra, A. K., Harwell, M. R., Dupuis, D. N., & Karl, S. R. (2015). A randomized trial of the effects of schema-based instruction on proportional problem-solving for students with mathematics problem-solving difficulties. Journal of Learning Disabilities, 50(3), 322–336.

Jordan, A., Klusmann, U., Krauss, S., Neubrand, M., Tsai, Y.-M., Baumert, J., Kunter, M., Blum, W., Brunner, M., Voss, T., Jordan, A., Klussmann, 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), 180.

Kahan, J., Cooper, D., & Bethea, K. (2003). The role of mathematics teachers’ content knowledge in their teaching: A framework for research applied to a study of student teachers. Journal of Mathematics Teacher Education, 6(3), 223–252.

Leavy, A. (2015). Looking at practice: revealing the knowledge demands of teaching data handling in the primary classroom. Mathematics Education Research Journal, 27(3), 283–309.

Lepik, M., Grevholm, B., & Viholainen, A. (2015). Using textbooks in the mathematics classroom–the teachers’ view. Nordic Studies in Mathematics Education, 20(3-4), 129-156.

Mewborn, D. (2003). Teaching, teachers’ knowledge, and their professional... - Google Scholar. In J. Kilpatrick, W. G. Martin, & D. Schifter (Eds.), A Research Companion to Principles and Standards for School Mathematics (pp. 45–52). NCTM.’+knowledge%2C+and+their+professional+development.+In+J.+Kilpatrick%2C+W.+G.+Martin%2C+%26+D.+Schifter+%28Eds.%29%2C+A+Research+Companion+to+Principles+and+Standards+for+School+Mathematics+&btnG=

Moliner, L., & Alegre, F. (2022). Attitudes, beliefs and knowledge of mathematics teachers regarding peer tutoring. European Journal of Teacher, 45(1), 93–112.

Munter, C., & Wilhelm, A. (2021). Mathematics teachers’ knowledge, networks, practice, and change in instructional visions. Journal of Teacher Education, 72(3), 342–354.

Özdemir, B. G., & Soylu, Y. (2017). Examination of The Pedagogical Content Knowledge of Mathematics Teachers. International Online Journal of Primary Education, 6(1), 26–39.

Pansell, A., & Bjorklund Boistrup, L. (2018). Mathematics teachers’ teaching practices in relation to textbooks: Exploring praxeologies. The Mathematics Enthusiast, 15(3), 541-562.

Patton, M. (2002). Qualitative research and evaluation methods (3rd ed.). Sage Publications.

Podolsky, A., Kini, T., & Darling-Hammond, L. (2019). Does teaching experience increase teacher effectiveness? A review of US research. Journal of Professional Capital and Community, 4(4), 286-308

Porter, A. C. (2002). Measuring the Content of Instruction: Uses in Research and Practice. Educational Researcher, 31(7), 3–14.

Riehl, S., & Steinthorsdottir, O. (2019). Missing-value proportion problems: The effects of number structure characteristics. Investigations in Mathematics Learning, 11(1), 56–68.

Ross, J., McDougall, D., Hogaboam-Gray, A., & LeSage, A. (2003). A survey measuring elementary teachers’ implementation of standards-based mathematics teaching. Journal for Research in Mathematics Education, 34(4), 344–363.

Sarama, J., Clements, D. H., Wolfe, C. B., & Spitler, M. E. (2016). Professional development in early mathematics: Effects of an intervention based on learning trajectories on teachers’ practices. Nordic Studies in Mathematics Education, 21(4), 29-55.

Shulman, L. S. (1986). Those Who Understand: Knowledge Growth in Teaching. Educational Researcher, 15(2), 4–14.

Skilling, K., & Stylianides, G.-. (2020). Using vignettes in educational research: a framework for vignette construction. Journal of Research & Method in Education, 43(5), 541–556.

Steele, M. D., & Rogers, K. C. (2012). Relationships Between Mathematical Knowledge for Teaching and Teaching Practice: The Case of Proof. Journal of Mathematics Teacher Education, 15(2), 159–180.

Sztajn, P., & Wilson, P. H. (2019). Learning trajectories and professional development. Learning trajectories for teachers: Designing effective professional development formath instruction, 1-14.

Tchoshanov, M. A. (2011). Relationship between teacher knowledge of concepts and connections, teaching practice, and student achievement in middle grades mathematics. Educational Studies in Mathematics, 76(2), 141–164.

Van Den Ham, A. K., & Heinze, A. (2018). Does the textbook matter? Longitudinal effects of textbook choice on primary school students’ achievement in mathematics. Studies in Educational Evaluation, 59, 133-140

Van Zanten, M., & van den Heuvel-Panhuizen, M. (2018). Opportunity to learn problem solving in Dutch primary school mathematics textbooks. ZDM, 50(5), 827-838.

Walshaw, M. (2012). Teacher knowledge as fundamental to effective teaching practice. Journal of Mathematics Teacher Education, 15(3), 181–185.

Weiland, T., Orrill, C. H., Nagar, G. G., Brown, R. E., & Burke, J. (2021). Framing a robust understanding of proportional reasoning for teachers. Journal of Mathematics Teacher Education, 24(2), 179–202.

Wilson, P. H., Sztajn, P., Edgington, C., & Confrey, J. (2014). Teachers’ use of their mathematical knowledge for teaching in learning a mathematics learning trajectory. Journal of Mathematics Teacher Education, 17(2), 149-175.

Xie, M., Talin, R., & Sharif, S. (2014). The Relationship between Teachers’ Knowledge, Attitude and Belief with the Implementation of Inquiry-Based Learning in Zhengzhou, China. International Journal of Learning, Teaching, and Educational Research, 8(1), 149–161.

Yang, X., Kaiser, G., König, J., & Blömeke, S. (2020). Relationship between pre-service mathematics teachers’ knowledge, beliefs and instructional practices in China. Zdm, 52(2), 281-294.

Zulkardi, Z., Putri, R., & Wijaya, A. (2020). Two decades of realistic mathematics education in Indonesia. In M. van den Heuvel-Panhuizen (Ed.), International reflections on on the Netherlands Didactics of Mathematics (pp. 325–340). Springer Open.



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