An Examination of Middle School Mathematics Teachers' Pedagogical Content Knowledge Regarding Prime Numbers

Year 2026, Issue: Advanced Online Publication, 35 - 56

Nurşen Cenikli , Adem Şahin , Mukaddes İnan Tutkun

https://doi.org/10.17275/per.26.03.13.1

Abstract

This study examines middle school mathematics teachers’ pedagogical content knowledge (PCK) regarding prime numbers. The study focuses on three subcomponents of PCK: Subject matter knowledge, knowledge of students’ understanding, and knowledge of instructional strategies. A case study method, one of the qualitative research approaches, was employed. The participants consisted of 12 middle school mathematics teachers. Data were collected through the Prime Numbers Knowledge Test (PNKT) and semi-structured interviews developed by the researchers. The data were analyzed using content analysis. The findings revealed that mathematics teachers demonstrated limited PCK, particularly in the components of subject matter knowledge and knowledge of instructional strategies. Specifically, it was observed that teachers provided definitions and responded to questions related to prime numbers without including negative integers, indicating gaps in their subject matter knowledge. Regarding the knowledge of students’ understanding component, participants showed satisfactory competence and performed better than in the other two components. Findings revealed that the teachers had a high level of awareness regarding students' learning difficulties, errors, and misconceptions, and they were able to correctly answer the questions posed by the researchers in this regard. Despite this relative strength, teachers’ knowledge of instructional strategies was notably weak. Although teachers confused the concepts of strategy, method, and technique, they still applied these in their teaching practices. The presentation teaching strategy, the discovery-based teaching strategy, and the question-and-answer technique were identified as the most frequently implemented by the participants.

Keywords

middle school mathematics teachers , pedagogical content knowledge , prime numbers

Ethical Statement

This research was approved by the Ethics Commission of the researcher’s institution (Approval Date: 27.12.2022; Decision No: E-34659092-605.01-66908793).

Thanks

The authors would like to thank all the participants for their valuable contributions to this study.

References

• Akkan, Y., & Öztürk, M. (2019). Çarpanlar ve katlar [Multiples and factors]. In E. Ertekin & M. Ünlü (Eds.), Kuramdan uygulamaya etkinlik örnekleriyle sayıların öğretimi [Teaching numbers with examples of activities from theory to practice] (pp. 131–173). Ankara: Pegem Akademi Publishing.
• Akkaş, E. N. (2014). Ortaokul 5. ve 7. sınıf matematik öğretmenlerinin geometri öğretim süreçlerinin ve geometrik-pedagojik alan bilgilerinin incelenmesi [An investigation of 5th and 7th grade mathematics teachers' geometry teaching processes and geometric - pedagogical content knowledge]. (Unpublished doctoral dissertation). Dokuz Eylül University, İzmir.
• Baştan, R. (2019). Asal sayılar üzerine [On prime numbers]. (Unpublished master’s thesis). Giresun University, Giresun.
• Baştürk Şahin, B. N., Şahin, G., & Tapan Broutin, M. S. (2017). Teaching the concept of prime numbers in the light of the theory of didactic states: An action research. Necatibey Faculty of Education Electronic Journal of Science and Mathematics Education, 11(2), 156-171. https://doi.org/10.17522/balikesirnef.373146
• Büyüköztürk, Ş., Çakmak, E., Akgün, Ö. K., Karadeniz, Ş., & Demirel, F. (2014). Bilimsel araştırma yöntemleri [Scientific research methods] (17th ed.). Ankara: Pegem Akademi Publishing.
• Ceylan Oral, S. (2021). An alternative material for teaching prime numbers: Prime factors chart. Journal of Inquiry Based Activities, 11(2), 92-110.
• Cochran, K. F., DeRuiter, J. A., & King, R. A. (1993). Pedagogical content knowing: An integrative model for teacher preparation. Journal of Teacher Education, 44(4), 263–272. https://doi.org/10.1177/0022487193044004004
• Crilly, T. (2011). Cambridge: The rise and fall of the mathematical tripos. In J. Fauvel & J. van Maanen (Eds.), Mathematics in Victorian Britain (pp. 17–32). Oxford: Oxford University Press.
• Doğruel, A. B. (2019). Ortaokul matematik öğretmenlerinin oran ve orantı konusuna ilişkin pedagojik alan bilgilerinin incelenmesi [An examination of elementary school mathematics teachers' pedagogical content knowledge on ratio and proportion]. (Unpublished master’s thesis). Afyon Kocatepe University, Afyonkarahisar.
• Ercire, Y. E. (2022). İlköğretim matematik öğretmen adaylarının sayılar ve işlemler öğrenme alanına ilişkin alan ve pedagojik alan bilgilerinin incelenmesi [An examination of preservice primary school mathematics teachers' content and pedagogical content knowledge related to numbers and operations learning domain]. (Unpublished doctoral dissertation). Dokuz Eylül University, İzmir.
• Fennema, E., & Franke, M. L. (1992). Teachers’ knowledge and its impact. In D. A. Grouws (Ed.), Handbook of research on mathematics teaching and learning (pp. 147–164). New York: Macmillan.
• Gardner, M. (1984). The sixth book of mathematical games from "Scientific American". Chicago: University of Chicago Press.
• Gökbulut, Y. (2010). Sınıf öğretmeni adaylarının geometrik cisimler konusundaki pedagojik alan bilgileri [Prospective primary teachers’ pedagogical content knowledge about geometric shapes. (Unpublished doctoral dissertation). Gazi University, Ankara.
• Gökkurt, B. (2014). Ortaokul matematik öğretmenlerinin geometrik cisimler konusuna ilişkin pedagojik alan bilgilerinin incelenmesi [An examination of secondary school mathematics teachers' pedagogical content knowledge on geometric shapes]. (Unpublished doctoral dissertation). Atatürk University, Erzurum.
• Grossman, P. L. (1990). The making of a teacher: Teacher knowledge and teacher education. New York: Teachers College Press.
• Gürefe, N., & Aktaş, G. S. (2020). The concept of prime number and the strategies used in explaining prime numbers. South African Journal of Education, 40(3), 1–9. https://doi.org/10.15700/saje.v40n3a1741
• Huang, H. M. E., Hoth, J., Chang, W. S., Heinze, A., & Ruwisch, S. (2025). Exploring teachers’ pedagogical content knowledge for teaching length estimation. In C. Cornejo, P. Felmer, D. M. Gómez, P. Dartnell, P. Araya, A. Peri, & V. Randolph, (Eds.) Proceedings of the 48th conference of the international group for the psychology of mathematics education: Research reports (pp. 403-410). Santiago: PME.
• Li, X., Maas, C., & Oppenzato, C. (2025). Investigating preschool teachers’ pedagogical content knowledge of number comparison. Early Education and Development, 36(2), 249-264. https://doi.org/10.1080/10409289.2024.2389362
• Marks, R. (1990). Pedagogical content knowledge: From a mathematical case to a modified conception. Journal of Teacher Education, 41(3), 3–11. https://doi.org/10.1177/002248719004100302
• McMillan, J. H., & Schumacher, S. (2010). Research in education: Evidence-based inquiry (7th ed.). Boston: Pearson.
• Ministry of National Education [MoNE]. (2018). Mathematics curriculum (Grades 5-8). Board of Education and Discipline.
• Özçelik, U. (2023). Ortaokul ve imam hatip ortaokul 6. sınıf matematik ders kitabı [Middle school and imam hatip middle school 6th-grade mathematics textbook]. Ankara: Ata Publishing.
• Özdeş, H. (2013). 9. sınıf öğrencilerinin doğal sayılar konusundaki kavram yanılgıları [Misconceptions of 9th class students regarding to natural numbers]. (Unpublished master’s thesis). Adnan Menderes University, Aydın.
• Putnam, R. T., Heaton, R. M., Prawat, R. S., & Remillard, J. T. (1992). Teaching mathematics for understanding: Discussing case studies of four fifth-grade teachers. The Elementary School Journal, 93(2), 213–228. https://doi.org/10.1086/461723
• Satan, N., Aksakal, K., Bağdat, A., & Altay, M. K. (2024). Preschool teachers’ pedagogical content knowledge regarding the concept of numbers. Cukurova University Faculty of Education Journal, 53(2), 652-680. https://doi.org/10.14812/cuefd.1326946
• Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. https://doi.org/10.3102/0013189X015002004
• Tossavainen, A. (2025). Pedagogical content knowledge in prospective elementary teachers’ descriptions of teaching and learning of fractions. Scandinavian Journal of Educational Research, 69(5), 958-972. https://doi.org/10.1080/00313831.2024.2362928
• Watson, J., & Callingham, R. (2013). PCK and average. In V. Steinle, L. Ball, & C. Bardini (Eds.), Mathematics education: Yesterday, today and tomorrow (pp. 642-649). Melbourne, VIC: MERGA.
• Yağmur, B. E. (2020). A game-based activity related to prime numbers. Journal of Inquiry Based Activities, 10(1), 18-30.
• Yurtyapan, M. İ. (2018). Ortaokul matematik öğretmenlerinin üçgenler ve dörtgenler konusuna ilişkin pedagojik alan bilgilerinin incelenmesi [Examination of secondary school mathematics teachers' pedagogical content knowledge about triangles and quadrilaterals]. (Unpublished master’s thesis). Bülent Ecevit University, Zonguldak.
• Zazkis, R. (2005). Representing numbers: Prime and irrational. International Journal of Mathematical Education in Science and Technology, 36(2–3), 207–217.
• Zazkis, R., & Campbell, S. (1996). Prime decomposition: Understanding uniqueness. Journal for Mathematical Behavior, 15(2), 207–218.
• Zazkis, R., & Liljedahl, P. (2004). Understanding primes: The role of representation. Journal for Research in Mathematics Education, 35(3), 164–186. https://doi.org/10.2307/30034911