Skip to main content Skip to main navigation menu Skip to site footer
Beta: Jurnal Tadris Matematika
Articles
DOI: 10.20414/betajtm.v18i2.689
Submitted: 2025-02-10
Published: 2025-11-25

Bridging knowledge and practice: Prospective mathematics teachers’ analysis of student worksheet

Universitas Serambi Mekkah
Universitas Syiah Kuala
Universitas Syiah Kuala
content knowledge pedagogical knowledge PISA prospective mathematics teacher

Galleys

Abstract

[English]: Understanding students' difficulties in solving mathematics problems is crucial for effective teaching. This study aims to determine the ability of prospective mathematics teachers to analyze students' work in solving PISA problems and identify the types of assistance recommended to overcome students' difficulties. Using a descriptive qualitative design within a case study framework, the research subjects consisted of two prospective mathematics teachers from a university in Aceh, who had good knowledge in answering PISA problems. Data was collected through written tests, interview, and documentation of analysis results for student answers. This study was conducted in two stages: (1) the subjects analyzed, assessed, and recommended assistance for students' work, and (2) the researcher evaluated the results of the analysis and the appropriateness of the assistance proposed by the subjects. The findings indicate that varying Pedagogical Content Knowledge (PCK) abilities of teachers can affect the accuracy of the analysis and the effectiveness of the recommended assistance. Subjects with high PCK can analyze students' work and suggest assistance appropriately. In contrast, subjects with low PCK only analyze and provide suggestions to overcome students' difficulties in general. This study emphasizes the importance of integrating content knowledge and pedagogy in preparing prospective teachers.

[Bahasa]: Memahami kesulitan siswa dalam memecahkan masalah matematika sangat penting untuk pengajaran yang efektif. Penelitian ini bertujuan untuk mengetahui kemampuan calon guru matematika dalam menganalisis hasil kerja siswa dalam menyelesaikan soal-soal PISA, dan    mengidentifikasi jenis bantuan yang disarankan untuk mengatasi kesulitan siswa. Dengan menggunakan pendekatan deskriptif kualitatif dengan jenis studi kasus, subjek penelitian ini terdiri dari dua orang calon guru matematika dari salah satu universitas di Aceh, yang memiliki pengetahuan yang baik dalam menjawab soal-soal PISA. Data dikumpulkan melalui tes tertulis, wawancara, dan dokumentasi hasil analisis untuk jawaban siswa. Penelitian ini dilakukan dalam dua tahap: (1) subjek menganalisis, menilai, dan merekomendasikan bantuan untuk hasil kerja siswa; dan (2) peneliti mengevaluasi hasil analisis dan kesesuaian bantuan yang diusulkan subjek. Temuan menunjukkan bahwa kemampuan Pedagogical Content Knowledge (PCK) guru yang bervariasi dapat mempengaruhi ketepatan analisis dan efektivitas bantuan yang direkomendasikan. Subjek dengan PCK yang tinggi dapat menganalisis hasil kerja siswa dan menyarankan bantuan dengan tepat. Sebaliknya, Subjek dengan PCK yang rendah hanya menganalisis dan memberikan saran untuk mengatasi kesulitan siswa secara umum. Studi ini menekankan pentingnya mengintegrasikan pengetahuan konten dan pedagogi dalam mempersiapan calon guru.

Downloads

Download data is not yet available.

References

  1. Akkoc, H., & Yesildere, S. (2010). Investigation development of pre-service elementary mathematics teachers' pedagogical content knowledge through a school practicum course. Procedia Social and Behavioral Sciences, 2(2) 1410–1415. Doi: https://doi.org/10.1016/j.sbspro.2010.03.210
  2. Anggraeny, E., & Khongput, S. (2022). Teachers’ perceptions and practices of critical thinking instruction in indonesian senior high schools: a case study. TEFLIN Journal, 33(1), 1–26. https://doi.org/10.15639/teflinjournal.v33i1/1-26
  3. Baker, M., & Chick, H. (2006). Pedagogical content knowledge for teaching primary mathematics: A case study of two teachers. In P. Grootenboer, R. Zevenbergen & M. Chinnappan (Eds.), Identities, Cultures, and Learning Spaces: Proceedings of the 29th Annual Conference of The Mathematics Education Research Group of Australasia (MERGA), Canberra, Vol. 1, 60-67. https://udmathteaching.wordpress.com/wp-content/uploads/2013/08/pck-for-teaching-primary-mathematics.pdf
  4. Ball, D.L., & Bass, H. (2000). Interweaving content and pedagogy in teaching and learning to teach: Knowing and using mathematics. In J. Boaler (Ed.), Multiples perspectives on the teaching and learning of mathematics (pp. 83-104). Westport, Conn.: Ablex Publishing.
  5. 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. Doi: https://doi.org/10.1177/0022487108324554
  6. Brunner, K., Obersteiner, A. & Leuders, T. (2024). How pedagogical content knowledge sharpens prospective teachers’ focus when judging mathematical tasks: an eye-tracking study. Educ Stud Math 115, 177–196. https://doi.org/10.1007/s10649-023-10281-6
  7. Cochran, K.F., DeRuiter, J.A., & King, R.A. (1993). Pedagogical content knowledge: An integrative model for teacher education. Journal of Teacher Education, 44, 263–272. Doi: https://doi.org/10.1177/0022487193044004004
  8. Creswell, J.W., & Poth, C.N. (2018). Qualitative inquiry and research design: Choosing among five approaches. Sage Publications.
  9. Christodoulou, P., & Papanikolaou, A. (2023). Examining pre-service teachers’ critical thinking competences within the framework of education for sustainable development: A qualitative analysis. Education Sciences, 13(12), 1187. https://doi.org/10.3390/educsci13121187
  10. Darling-Hammond, L., & Bransford, J. (Eds.). (2005). Preparing teachers for a changing world: What teachers should learn and be able to do. USA: Jossey-Bass.
  11. Darling-Hammond, L. (2010). Teacher education and the American future. Journal of Teacher Education, 61(1-2), 35-47. Doi: https://doi.org/10.1177/0022487109348024
  12. Depaepe, F., Verschaffel, L., & Kelchtermans, G. (2013). Pedagogical content knowledge: A systematic review of the way in which the concept has pervaded mathematics education research. Teaching and Teacher Education, 34, 12-25. Doi: https://doi.org/10.1016/j.tate.2013.03.001
  13. Grigaliūnienė, M., Lehtinen, E., Verschaffel, L. et al. (2025). Systematic review of research on pedagogical content knowledge in mathematics: Insights from a topic-specific approach. ZDM Mathematics Education 57, 777–794. https://doi.org/10.1007/s11858-025-01684-1
  14. Hattie, J. (2008). Visible learning: A synthesis of over 800 meta-analyses relating to achievement. London: Routledge.
  15. Hill, H., & Ball, D.L. (2004). Learning mathematics for teaching: Results from California's mathematics professional development institutes. Journal for Research in Mathematics Education, 35(5), 330-351. Doi: https://doi.org/10.2307/30034819
  16. 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. Doi: https://psycnet.apa.org/doi/10.3102/00028312042002371
  17. Isiksal, M., & Cakiroglu, E. (2010). The nature of prospective mathematics teachers' pedagogical content knowledge: The case of multiplication of fractions. Journal of Mathematics Teacher Education, 14, 213-230. Doi: https://doi.org/10.1007/s10857-010-9160-x
  18. Kanmaz, A. (2022). Middle school teachers' critical thinking skills and awareness towards teaching critical thinking skills. International Online Journal of Education and Teaching, 9(4), 1648-1671.
  19. Kholid, M.M., Rofi’ah, F., Ishartono, N., Waluyo, M., Maharani, S., Swastika, A., Faiziyah, N., & Sari, C.K. (2022). What are students’ difficulties in implementing mathematical literacy skills for solving PISA-like problem? Journal of Higher Education Theory and Practice, 22(2), 181 – 200. Doi: https://doi.org/10.33423/jhetp.v22i2.5057
  20. Koehler, M.J., Mishra, P., & Cain, W. (2017). What is technological pedagogical content knowledge (TPACK)? Journal of Education, 193(3), 13-19. Doi: https://doi.org/10.1177/002205741319300303
  21. Koehler, M.J., Mishra, P., Kereluik, K., Shin, T.S., & Graham, C.R. (2014). The technological pedagogical content knowledge framework. In Spector, J., Merrill, M., Elen, J., Bishop, M. (Eds.) Handbook of Research on Educational Communications and Technology. New York: Springer. Doi: https://doi.org/10.1007/978-1-4614-3185-5_9
  22. Koirala, H.P., Davis, M., & Johnson, P. (2008). Development of a performance assessment task and rubric to measure prospective secondary school mthematics teachers' pedagogical content knowledge and skill. Journal of Mathematics Teacher Education, 11, 127-138. Doi: https://doi.org/10.1007/s10857-007-9067-3
  23. Krauss, S., Brunner, M., Kunter, M., Baumert, J., Blum, W., Neubrand, M., & Jordan, A. (2008). Pedagogical content knowledge and content knowledge of secondary mathematics teachers. Journal of Educational Psychology, 100(3), 716-725. Doi: https://psycnet.apa.org/doi/10.1037/0022-0663.100.3.716
  24. Lestari, N.D.S., Najih, M., Putri, I.W.S., Murtafiah, W., Yahya, F.H., & Suwarno. (2025). PISA content quantity-standardized test: Exploring vocational student’s mathematical communication skills. TEM Journal, 14(1), 848-860. Doi: 10.18421/TEM141-75
  25. Taber, K.S. (2014). Understanding and developing science teachers’ pedagogical content knowledge. Teacher Development, 18(3), 441-444. Doi: https://doi.org/10.1080/13664530.2014.938464
  26. Merriam, S.B., & Tisdell, E.J. (2016). Qualitative research: A guide to design and implementation. USA: Jossey-Bass.
  27. Miles, M.B., Huberman, A.M., & Saldana, J. (2014). Qualitative data analysis: A methods sourcebook, 3rd Edition. USA: Sage Publications.
  28. Munkebye, E., & Gericke, N. (2022). Primary school teachers’ understanding of critical thinking in the context of education for sustainable development. In B. Puig & M. P. Jiménez-Aleixandre (Eds.) Critical thinking in biology and environmental education: Facing challenges in a post-truth world (pp. 249–266). Cham: Springer International Publishing. https://doi.org/10.1007/978-3-030-92006-7_14
  29. OECD. (2012). PISA 2012 results in focus: What 15-year-olds know and what they can do with what they know.
  30. https://www.oecd.org/content/dam/oecd/en/about/programmes/edu/pisa/publications/national-reports/pisa-2012/pisa-2012-in-focus/pisa-2012-results-overview.pdf
  31. Schmidt, W.H., Wang, H.C., & McKnight, C.C. (2005). Curriculum coherence: An examination of US mathematics and science content standards from an international perspective. Journal of Curriculum Studies, 37(5), 525–559. Doi: https://doi.org/10.1080/0022027042000294682
  32. Shulman, L.S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14. Doi: http://dx.doi.org/10.3102/0013189X015002004
  33. Shulman, L.S. (1987). Knowledge and teaching: Foundation of the new reform. Harvard Educational Review, 57(1). Doi: http://dx.doi.org/10.17763/haer.57.1.j463w79r56455411
  34. Sorto, M.A., Marshall, J.H., Luschei, T.F., & Camoy, M. (2009). Teacher knowledge and teaching in Panama and Costa Rica: A comparative study in primary and secondary education. Revista Latinoamericana de Investigación en Matemática Educativa, 12(2), 251-290. Retrieved from https://www.researchgate.net/publication/28316427_Teacher_knowledge_and_teaching_in_Panama_and_Costa_Rica_A_comparative_study_in_Primary_and_Secondary_education
  35. Silver, E.A., Stein, M.K., Smith, M.S., & Henningsen M. (2000). Implementing standards-based mathematics instruction: A casebook for professional development. New York: Teachers College Press.
  36. Staberg, R. L., Munkebye, E., Scheie, E., Berglund, T., & Fredagsvik, M. S. (2026). Primary school teachers’ perceptions of critical thinking in general and in their teaching. Thinking Skills and Creativity, 59, 101942. https://doi.org/https://doi.org/10.1016/j.tsc.2025.101942
  37. Sulastri, R., Johar, R., & Munzir, S. (2019). Developing assessment rubrics in pedagogical content knowledge for mathematical problems. Proceedings of the 1st Workshop on Multidisciplinary and Its Applications Part 1, Aceh – Indonesia. Doi: https://doi.org/10.4108/eai.20-1-2018.2282086
  38. Van de Walle, J.A., Karp, K.S., & Bay-Williams, J.M. (2020). Elementary and middle school mathematics: Teaching developmentally (9th ed.). London: Pearson Education.
  39. Yuan, R., & Stapleton, P. (2020). Student teachers’ perceptions of critical thinking and its teaching. ELT journal, 74(1), 40-48.
  40. Yuan, R., Liao, W., Wang, Z., Kong, J., & Zhang, Y. (2022). How do English-as-a-foreign-language (EFL) teachers perceive and engage with critical thinking: A systematic review from 2010 to 2020. Thinking skills and creativity, 43, 101002.

How to Cite

Sulastri , R., Johar, R. ., & Munzir, S. (2025). Bridging knowledge and practice: Prospective mathematics teachers’ analysis of student worksheet. Beta: Jurnal Tadris Matematika, 18(2), 1–15. https://doi.org/10.20414/betajtm.v18i2.689

License

Copyright (c) 2025 Rini Sulastri , Rahmah Johar, Said Munzir

Creative Commons License

This work is licensed under a Creative Commons Attribution-NonCommercial-ShareAlike 4.0 International License.