Teachers’ specialized knowledge through problem posing in pre-school education





Professional knowledge, problem posing, early childhood education, MTSK


Problem posing, as a genuinely mathematical activity, provides an inexhaustible source of alternatives in a classroom. Many authors, as well as institutions such as the National Council of Teachers of Mathematics, highlight the importance of this mathematical practice. With this case study, we intend to demonstrate the characteristics of the type of knowledge used by a teacher when implementing this type of session in 4-year-olds, with an emphasis on the knowledge used for planning and putting the session into practice. We used fragments of the session’s recording, as well as a subsequent interview with the informant, in order to corroborate the information identified during the data analysis. The specific mathematical nature of this activity leads us to use the MTSK model (Mathematics Teachers’ Specialized Knowledge) as a reference to analyze the specialized knowledge that a pre-school teacher uses during a classroom practice. This practice is comprised of two tasks, both created and designed by the informant teacher. Results show aspects of knowledge related to MK (Mathematical Knowledge), but, above all, PCK (Pedagogical Content Knowledge) predominance, evidencing the importance of this type of knowledge in early childhood education to implement a problem posing session.


Ball, D., Thames, M. H. & G. 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

Barlow, A. T. & Cates, J. M. (2006). The impact of problem posing on elementary teachers’ beliefs about mathematics and mathematics teaching. School Science and Mathematics, 106(2), 64–73. https://doi.org/10.1111/j.1949-8594.2006.tb18136.x

Baroody, A. J. (1994). El pensamiento matemático de los niños. Visor: Madrid.

Bassey, M. (1999). Case study research in educational settings. Open University Press: Buckingham.

Björklund, C., Van den Heuvel-Panhuizen, M. & Kullberg, A. (2020). Research on early childhood mathematics teaching and learning. ZDM Mathematics Education, 52, 607–619. https://doi.org/10.1007/s11858-020-01177-3

Brown, S. I. & Walter, I. M. (2004). The art of problem posing (3rd edition). London: Lawrence Erlbaum Associates Publishers.

Buschman, J. E. (2003). Dismantling the public sphere: situating and sustaining librarianship in the age of the new public philosophy. Westport, CT: Libraries Unlimited.

Cai, J. & Cifarelli, V. (2005). Exploring mathematical exploration: how do two college students formulate and solve their own mathematical problems? Focus on Learning Problems in Mathematics, 27(3), 43-72.

Cai, J. & Howson, A. G. (2013). Toward an international mathematics curriculum. In M. A. Clements, A. Bishop, C. Keitel, J. Kilpatrick, & K. S. F. Leung (Eds.), Third international handbook of mathematics education research (pp. 949–974). Springer: Nueva York. https://doi.org/10.1007/978-1-4614-4684-2_29

Cai, J. & Hwang, S. (2021). Teachers as redesigners of curriculum to teach mathematics through problem posing: conceptualization and initial findings of a problem‑posing project. ZDM Mathematics Education. https://doi.org/10.1007/s11858-021-01252-3

Cai, J., Hwang, S., Jiang, C. & Silber, S. (2015). Problem-posing research in mathematics education: Some answered and unanswered questions. In F. M. Singer, N. Ellerton, & J. Cai (Eds.), Mathematical problem posing: From research to efective practice (pp. 3–34). Springer. https://doi.org/10.1007/978-1-4614-6258-3_1

Cankoy, O. & Darbaz, S. (2010). Effect of a problem posing based problem solving instruction on understanding problem. Hacettepe University Journal Of Education, 38, 11-24.

Carrillo J., Climent N., Contreras L. C., Montes M. Á. (2019) Mathematics Teachers’ Specialised Knowledge in Managing Problem-Solving Classroom Tasks. In: Felmer P., Liljedahl P., Koichu B. (eds) Problem Solving in Mathematics Instruction and Teacher Professional Development. Research in Mathematics Education. Springer, Cham. https://doi.org/10.1007/978-3-030-29215-7_16

Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ávila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, A., Ribeiro, M. & Muñoz-Catalán, M. C. (2018). The Mathematics Teacher’s Specialised Knowledge (MTSK) model. Research in Mathematics Education, 20, 236-253. https://doi.org/10.1080/14794802.2018.1479981

Carpenter, T. P. & Romberg, T. A. (2004). Powerful practices in mathematics & science: Research-based practices for teaching and learning. Madison: University of Wisconsin.

Chang, N. (2007). Responsibilities of a Teacher in a Harmonic Cycle of Problem Solving and Problem Posing. Early Childhood Education Journal 34(4), 265–271. https://doi.org/10.1007/s10643-006-0117-8

Doerr, H. M. & English, L. D. (2003). A modeling perspective on students’ mathematical reasoning about data. Journal for Research in Mathematics Education, 34(2), 110-136. https://doi.org/10.2307/30034902

Einstein. A. & Infeld, L. (1938). The evolution of physics. New York, NY: Simon & Schuster.

English, L. D. (1998). Children's problem posing within formal and informal contexts. Journal for Research in Mathematics Education, 29(1), 83–106. https://doi.org/10.2307/749719

Felmer, P., Pehkonen, E. & Kilpatrick, J. (2016). Posing and solving mathematical problems. Suiza: Springer. https://doi.org/10.1007/978-3-319-28023-3

Flick, U. (2007). Introducción a la investigación cualitativa. Morata.

Gasteiger, H. & Benz, C. (2018). Enhancing and analyzing kindergarten teachers’ professional knowledge for early mathematics education. The Journal of Mathematical Behavior, 51, 109-117. https://doi.org/10.1016/j.jmathb.2018.01.002

Kilpatrick, J. (1987). Problem formulating: Where do good problems come from? In A.H. Schoenfeld (Ed.), Cognitive science and mathematics education (pp. 123-147). Hillsdale, NJ: Lawrence Erlbaum. https://doi.org/10.4135/9781071878781

Kojima, K., Miwa, K. & Matsui, T. (2015). Experimental study of learning support through examples mathematical problem posing. Research and Practice in Technology Enhanced Learning. doi: 10.1007/s41039-015-0001-5

Krippendorf, K. (2018). Content analysis: An introduction to its methodology. Sage.

Leikin, R. & Elgrably, H. (2019). Problem posing through investigations for the development and evaluation of proof-related skills and creativity skills of prospective high school mathematics teachers. International Journal of Educational Research, 102, 101424. https://doi.org/10.1016/j.ijer.2019.04.002

Martín-Díaz, J. P., Montes, M., Codes, M. & Carrillo, J. (2020). Characterisers of Teaching in a Mathematics Problem Posing Lesson in Preschool Education. Sustainability, 12(15), 6148. doi:10.3390/su12156148

Montes, M. A., Contreras, L. C. & Carrillo, J. (2013). Conocimiento del profesor de matemáticas: Enfoques del MKT y del MTSK. En A. Berciano, G. Gutiérrez, A. Estepa & N. Climent (Eds.), Investigación en Educación Matemática XVII (403-410). Bilbao: SEIEM.

Muñoz-Catalán, M. C., Liñán, M. M. & Ribeiro, M. (2017). Conocimiento especializado para enseñar la operación de resta en Educación Infantil. Cadernos de Pesquisa, 24, 4-19. 10.18764/2178-2229.v24nespecialp4-19

National Council of Teachers of Mathematics. (2000). Principios y estándares para la educación. Matemática. Reston: VA.

Pólya, G. (1954). How to solve it. Princeton: Princeton University Press.

Sengul, S. & Katranci, Y. (2012). Problem solving and problem posing skills of prospective mathematics teachers about the sets subject. Procedia-Social and Behavioral Sciences, 69, 1650-1655. https://doi.org/10.1016/j.sbspro.2012.12.111

Schwab, J. J. (1978). Science, curriculum and liberal education. Chicago: University of Chicago Press.

Shulman, L. S. (1986). Those who understand: knowledge growth in teaching. Educational Researcher, 15(2), 4-14. https://doi.org/10.3102/0013189X015002004

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19-28.

Silver, E. A. (1997). Fostering creativity through instruction rich in mathematical problem solving and problem posing. ZDM, 29(3), 75–80. https://doi.org/10.1007/s11858-997-0003-x

Singer, F. M., Ellerton, N. F. & Cai, J. (2013). Problem posing research in mathematics education: New questions and directions. Educational Studies in Mathematics: An International Journal, 82(3). https://doi.org/10.1007/s10649-013-9478-2

Singer, F. M., Ellerton, N. F. & Cai, J. (2015). Mathematical Problem Posing. Suiza: Springer. https://doi.org/10.1007/978-1-4614-6258-3

Stake, R. E. (2006). Multiple case study analysis. Nueva York: The Guilford Press.

Van Harpen, X. Y. & Presmeg, N. C. (2013). An investigation of relationships between students’ mathematical problem-posing abilities and their mathematical content knowledge. Educational Studies in Mathematics., 83(1), 117–132. https://doi.org/10.1007/s10649-012-9456-0



How to Cite

Teachers’ specialized knowledge through problem posing in pre-school education. (2022). Uniciencia, 36(1), 1-19. https://doi.org/10.15359/ru.36-1.37



Original scientific papers (evaluated by academic peers)

How to Cite

Teachers’ specialized knowledge through problem posing in pre-school education. (2022). Uniciencia, 36(1), 1-19. https://doi.org/10.15359/ru.36-1.37

Comentarios (ver términos de uso)

Most read articles by the same author(s)