Pre-service secondary teachers’ knowledge of the function concept: A cluster analysis approach

José María Marbán(1*), Edgar John Sintema(2)

(1) Department of Experimental,Social and Mathematical Sciences Teaching, University of Valladolid
(2) PhD candidate, School of Doctoral Studies, University of Valladolid
(*) Corresponding Author


Teacher training is a key aspect for the success of any educational system and it is a prior challenge to facein-depth in Zambia. This study explores some dimensions of prospective secondary mathematics teachers’ subject-matter knowledge and pedagogical content knowledge restricted to the topic of the function concept. Data were collected by means of a questionnaire that was administered to a sample of 150 prospective teachers enrolled attwo public universities inCopperbelt, Zambia. A two-step cluster analysis was used to reveal natural grouping within the datasetobtained. As a result, a two-cluster solution was revealedas the solution that best profiled the data, with participants within both clusters scoringlow in the knowledge domains under consideration. To further understand the results a one-way between-subjects multivariate analysis of variance (MANOVA) and a follow-up discriminant function analysis (DFA) were also conducted. Common content knowledge was shown to be the most important factor in discriminating between prospective teachers in Cluster 1 and those in Cluster 2. The knowledge inadequacies identified are certainly worrisome and are likely to be transferred to young learners at secondary schools. Consequently, it is necessary to address with some urgency certain reforms in educational policies for teacher training programs in Zambia.


Function concept, mathematics, pedagogical content knowledge, secondary teacher education, subject-matter knowledge

Full Text:



Aksu, Z., & Kul, U. (2016). Exploring mathematics teachers’ pedagogical content knowledge in the context of knowledge of students. Journal of Education and Practice, 7(30), 35–42. Retrieved from

Aziz, T. A., & Kurniasih, M. D. (2019). External Representation Flexibility of Domain and Range of Function. Journal on Mathematics Education, 10(1), 143–156.

Aziz, T. A., Pramudiani, P., & Purnomo, Y. W. (2018). Differences between quadratic equations and functions: Indonesian pre-service secondary mathematics teachers’ views. Journal of Physics: Conference Series, 948(1), 012043.

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.

Creswell, J. W. (2014). Research design: Qualitative, quantitative and mixed methods approaches. Thousand Oaks, CA: Sage

Even, R. (1990). Subject-matter knowledge for teaching and the case of functions. Education Studies in Mathematics Education, 21(6), 521–544.

Even, R. (1993). Subject-matter knowledge and pedagogical content knowledge: Prospective secondary teachers and the function concept. Journal for Research in Mathematics Education, 24(2), 94–116.

Hatisaru, V., & Erbas, A. K. (2017). Mathematical knowledge for teaching the function concept and student learning outcomes. Journal of Science and Mathematics Education, 15(4), 703–722.

Malambo, P. (2016). Exploring Zambian mathematics student teachers’ content knowledge of functions and trigonometry for secondary schools (University of Pretoria). Retrieved from

Malambo, P., Van Putten, S., Botha, J. J., & Stols, G. H. (2019). Dysfunctional functions: the case of Zambian mathematics education students. Eurasia Journal of Mathematics, Science and Technology Education, 15(1), em 1651.

McCulloch, A., Lovett, J., & Edgington, C. (2019). Designing to Provoke Disorienting Dilemmas: Transforming Preservice Teachers’ Understanding of Function Using a Vending Machine Applet. Contemporary Issues in Technology and Teacher Education, 19(1), 4–22. Retrieved from

Nyikahadzoyi, M. R. (2015). Teachers’ knowledge of the concept of a function: A theoretical framework. International Journal of Science and Mathematics Education, 13, 261–283.

Paoletti, T., Stevens, I. ., Hobson, N. ., Moore, K. ., & LaForest, K. R. (2018). Inverse function: Pre-service teachers’ techniques and meanings. Educational Studies in Mathematics, 97(1), 93–109.

Ribeiro, A. J., & da Ponte, J. P. (2019). Professional learning opportunities in a practice- based teacher education programme about the concept of function. Acta Scientiae, 21(2), 49–74.

Sajka, M. (2003). A secondary school student’s understanding of the concept of function-A case study. Educational Studies in Mathematics, 53(3), 229–254.

Shulman, L. . (1986). Those who understand; Knowledge growth in teaching. Educational Researcher, 15(2), 4–14. Retrieved from

Sintema, E.J., Phiri, P.A., & Marbán, J.M. (2018). Zambian mathematics pre-service secondary teachers’ knowledge of the function concept: Theoretical framework and a literature review with implications for Zambia. Journal of Global Research in Education and Social Science, 12(3), 133-147 Retrieved from

Steele, M. D., Hillen, A. F., & Smith, M. S. (2013). Developing mathematical knowledge for teaching in a methods course: the case of function. Journal of Mathematics Teacher Education, 16(6), 451–482.

Taşdan, B. T. (2019). Mathematics Teachers’ Use of Mathematical Descriptions, Explanations and Justifications While Teaching Function Concept: The Case of Samet. Journal of Theoretical Educational Science/KuramsalEğitimbilim Dergisi, 12(4).

Taşdan, B. T., & Koyunkaya, M. Y. (2017). Examination of pre-service mathematics teachers’ knowledge of teaching function concept. Acta Didactica Napocensia, 4(3), 1–17. Retrieved from

Thames, M. H., & Ball, D. L. (2010). What Maths Knowledge Does Teaching Require? Teaching Children Mathematics, 17(4), 220–229.

Ubah, I. J. A., & Bansilal, S. (2018). Pre-service mathematics teachers’ knowledge of mathematics for teaching: quadratic functions. Problems of Education in the 21st Century, 76(6), 847–863.

Watson, A., Ayalon, M., & Lerman, S. (2018). Comparison of students’ understanding of functions in classes following English and Israel national curricula. Education Studies in Mathematics, 97(3), 255–272. 9798-8

You, Z. (2010). Preservice teachers’ knowledge of linear functions within multiple representation modes (Texas A & M University). Retrieved from

Article Metrics

Abstract view(s): 452 time(s)
PDF: 180 time(s)


  • There are currently no refbacks.