Proportionality problem posing in secundary school teacher training

Authors

  • Jorhan José Chaverri Hernández Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica. Costa Rica
  • María Burgos Departamento de Didáctica de la Matemática, Universidad de Granada, Granada, España. Spain
  • Luis Fabián Gutiérrez-Fallas Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica. Costa Rica

DOI:

https://doi.org/10.24310/mar.6.2.2025.18994

Keywords:

problem posing, proportionality, teacher training, didactic-mathematical knowledge
Agencies: Investigación realizada como parte del proyecto de investigación PID2022-139748NB-I00 financiado por MCIN/AEI/ 10.13039/501100011033 y FEDER (una forma de hacer Europa).

Abstract

The creation of mathematical problems for educational purposes requires diverse knowledge and specific competencies in teachers, making it a goal of teacher training programs. This paper describes the results of a formative intervention with future secondary education teachers in Costa Rica, aiming to develop the competency of creating proportionality problems in various contexts. It is a descriptive-qualitative study, supported by the theoretical and methodological tools of the Ontosemiotic Approach. The results reveal the difficulties participants face in creating relevant problems that meet a certain level of complexity, as well as in identifying the challenges a given problem may pose to students and how to modify it to overcome them. Better outcomes are observed in the creation of arithmetic problems compared to geometric and probabilistic contexts. The need for further research and the design of formative actions on problem creation is concluded as a means through which teachers can assist their students in learning mathematics.

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Author Biographies

Jorhan José Chaverri Hernández, Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica.

Profesor de la Escuela de Matemática de la Universidad de Costa Rica. Licenciado en la Enseñanza de la Matemática (Universidad de Costa Rica). Máster en Didáctica de la Matemática (Universidad de Granada).

María Burgos, Departamento de Didáctica de la Matemática, Universidad de Granada, Granada, España.

Profesora de la Universidad de Granada (España) Doctora en Matemáticas y Doctora en Didáctica de las Matemáticas.

Luis Fabián Gutiérrez-Fallas, Escuela de Matemática, Universidad de Costa Rica, San José, Costa Rica.

Profesor de la Escuela de Matemática de la Universidad de Costa Rica.

References

Balderas, R. G., Block, D. y Guerra, M. T. (2014). “Sé cómo se hace, pero no por qué”: Fortalezas y debilidades de los saberes sobre la proporcionalidad de maestros de secundaria. Educación Matemática, 26(2), 7–32. https://bit.ly/48edyhE

Batanero, C., Gómez, E., Contreras, J. M. y Díaz, C. (2015). Conocimiento matemático de profesores de primaria en formación para la enseñanza de la probabilidad: Un estudio exploratorio. Práxis Educativa, 10(1), 11–34. https://doi.org/10.5212/PraxEduc.v.10i1.0001

Bayazit, I. y Kirnap-Donmez, S. M. (2017). Prospective teachers’ proficiencies at problem posing in the context of proportional reasoning. Turkish Journal of Computer and Mathematics Education, 8(1), 130–160. https://bit.ly/49fgWtO

Ben-Chaim, D., Keret, Y. e Ilany, B. S. (2012). Ratio and proportion: Research and teaching in mathematics teachers’ education. Sense Publisher. https://doi.org/10.1007/978-94-6091-784-4

Bryant, P. y Nunes, T. (2012). Children’s understanding of probability: A literature review (full report). The Nuffield Foundation. https://bit.ly/4bxPKbl

Buforn, A., Llinares, S., Fernández, C., Coles, A. y Brown, L. (2020). Pre-service teachers’ knowledge of the unitizing process in recognizing students’ reasoning to propose teaching decisions. International Journal of Mathematics Education in Science and Technology, 1–9. https://doi.org/10.1080/0020739X.2020.1777333

Buforn, A. y Fernández, C. (2014). Conocimiento de matemáticas especializado de los estudiantes para maestro de primaria en relación al razonamiento proporcional. BOLEMA, 28(48), 21–41. https://doi.org/10.1590/1980-4415v28n48a02

Burgos, M., Beltrán-Pellicer, P., Giacomone, B. y Godino, J. D. (2018). Conocimientos y competencia de futuros profesores de matemáticas en tareas de proporcionalidad. Educação e Pesquisa, 44, 1–22. https://doi.org/10.1590/s1678-4634201844182013

Burgos, M. y Chaverri, J. (2022). Knowledge and Competencies of Prospective Teachers for the Creation of Proportionality Problems. Acta Scientiae, 24(6), 270–306. https://doi.org/10.17648/acta.scientiae.7061

Burgos, M. y Chaverri, J. (2023). Creación de problemas de proporcionalidad en la formación de docentes de primaria. Uniciencia, 33(1), 1–24. https://doi.org/10.15359/ru.37-1.14

Burgos, M. y Godino, J. D. (2020). Prospective primary school teachers’ competence for analysing the difficulties in solving proportionality problem. Mathematics Education Research Journal. https://doi.org/10.1007/s13394-020-00344-9

Burgos, M. y Godino J. D. (2022). Assessing the Epistemic Analysis Competence of Prospective Primary School Teachers on Proportionality Tasks. International Journal of Science and Mathematics Education, 20, 367–389. https://doi.org/10.1007/s10763-020-10143-0

Cohen, L., Manion, L. y Morrison, K. (2018). Research methods in education (8va ed.). Routledge. https://doi.org/10.4324/9781315456539

Copur-Gencturk, Y., Baek, C. y Doleck, T. (2023) Closer Look at Teachers’ Proportional Reasoning. International Journal of Science and Mathematics Education, 21, 113–129. https://doi.org/10.1007/s10763-022-10249-7

Ellerton, N. F. (2013). Engaging pre-service middle-school teacher-education students in mathematical problem posing: development of an active learning framework. Educational Studies in Mathematics, 83(1), 87–101. https://doi.org/10.1007/s10649-012-9449-z

Fernández, M. y Carrillo, J. (2020). Un acercamiento a la forma en que los estudiantes de primaria formulan problemas. Revista de Educação Matemática, 17, 1–19. https://doi.org/10.37001/remat25269062v17id257

Godino, J. D., Beltrán-Pellicer, P., Burgos, M. y Giacomone, B. (2017). Significados pragmáticos y configuraciones ontosemióticas en el estudio de la proporcionalidad. En J. M. Contreras, P. Arteaga, G. R. Cañadas, M. M. Gea, B. Giacomone y M. M. López-Martín (Eds.), Actas del Segundo CIVEOS. https://bit.ly/49jmDak

Godino, J. D., Batanero, C. y Font, V. (2007). The onto-semiotic approach to research in mathematics education. ZDM. The International Journal on Mathematics Education, 39(1-2), 127–135. https://doi.org/10.1007/s11858-006-0004-1

Godino, J. D., Giacomone, B., Batanero, C. y Font, V. (2017). Enfoque Ontosemiótico de los Conocimientos y Competencias del Profesor de Matemáticas. Bolema, 31(57), 90–113. https://doi.org/10.1590/1980-4415v31n57a05

Godino, J., Font, V., Wilhelmi, M. y Lurduy, O. (2009). Sistemas de prácticas y configuraciones de objetos y procesos como herramientas para el análisis semiótico en educación matemática. XIII Simposio de la SEIEM. https://bit.ly/42F0voj

Grundmeier, T. A. (2015). Developing the Problem-Posing Abilities of Prospective Elementary and Middle School Teachers. En F.M. Singer et al. (Eds.), Mathematical Problem Posing, Research in Mathematics Education (pp. 411–431). https://doi.org/10.1007/978-1-4614-6258-3_20

Isik, A., Isik, C. y Kar, T. (2011). Analysis of the problems related to verbal and visual representations posed by pre-service mathematics teachers. Pamukkale University Journal of Education, 30(1), 39–49. https://bit.ly/49b9eB2

Kar, T. (2016). Prospective middle school mathematics teachers’ knowledge of linear graphs in context of problem-posing. International Electronic Journal of Elementary Education, 8(4), 643-658. https://bit.ly/3SU382b

Kılıç, Ç. (2017). A new problem-posing approach based on problem-solving strategy: Analyzing pre-service primary school teachers’ performance. Educational Sciences: Theory & Practice, 17, 771–789. https://doi.org/10.12738/estp.2017.3.0017

Koichu, B. y Kontorovich, I. (2013). Dissecting success stories on mathematical problem posing: A case of the Billiard Task. Educational Studies in Mathematics, 83(1), 71–86. https://doi.org/10.1007/s10649-012-9431-9

Lamon, S. (2007). Rational number and proportional reasoning. Toward a theoretical framework for research. En F. K. Lester (Ed.), Second handbook of research on mathematics teaching and learning (pp. 629–667). Information Age Pub Inc. https://bit.ly/4bCZYad

Leavy, A. y Hourigan, M. (2020). Posing mathematically worthwhile problems: developing the problem‑posing skills of prospective teachers. Journal of Mathematics Teacher Education, 23, 341–361. https://doi.org/10.1007/s10857-018-09425-w

Llinares, S. (2003). Fracciones, decimales y razón. Desde la relación parte-todo al razonamiento proporcional. En M. C. Chamorro (Coord.), Didáctica de las matemáticas para Primaria (pp. 187-220). Pearson Prentice Hall. https://bit.ly/3HZsc1y

Malaspina, U. (2016). Creación de problemas: sus potencialidades en la enseñanza y aprendizaje de las Matemáticas. En A. Ruiz (Ed.), Cuadernos de Investigación y Formación en Educación Matemática (pp. 321–331). Universidad de Costa Rica. https://bit.ly/3UyYLLa

Malaspina, U. y Vallejo, E. (2014). Creación de problemas en la docencia e investigación. En U. Malaspina (Ed.), Reflexiones y Propuestas en Educación Matemática (pp. 7–54). Editorial Moshera S.R.L. https://bit.ly/48aaW4g

Malaspina, U., Torres, C. y Rubio, N. (2019). How to stimulate in-service teachers’ didactic analysis competence by means of problem posing. En P. Liljedahl, y L. Santos-Trigo (Eds.), Mathematical Problem Solving (pp. 133–151). Springer. https://doi.org/10.1007/978-3-030-10472-6_7

Mallart, A., Font, V. y Diez, J. (2018). Case Study on Mathematics Pre-service Teachers’ Difficulties in Problem Posing. Eurasia Journal of Mathematics, Science and Technology Education, 14(4), 1465–1481. https://doi.org/10.29333/ejmste/83682

Mallart, A., Font, V. y Malaspina, U. (2016). Reflexión sobre el significado de qué es un buen problema de en la formación inicial de maestros. Perfiles educativos, 38(152), 14–30. https://doi.org/10.22201/iisue.24486167e.2016.152.57585

Ministerio de Educación Pública (MEP) (2012). Programas de estudio de Matemáticas. San José, Costa Rica. https://bit.ly/4bANz6D

National Council Teacher Mathematics (NCTM) (2000). Principles and Standards for School Mathematics. Reston.

Norton, S. J. (2005). The construction of proportional reasoning. En H. L. Chick y J. L. Vincent (Eds.), Proceedings of the 29th Conference of the International Group for the Psychology of Mathematics Education (pp. 17–24). Melbourne, Australia: PME. https://bit.ly/4bxIzzR

OECD (2004). Marcos teóricos de PISA 2003: Conocimientos y destrezas en Matemáticas, Lectura, Ciencias y Solución de problemas. Madrid: Ministerio de Educación y Ciencia, Instituto Nacional de Evaluación y Calidad del Sistema Educativo. https://doi.org/10.1787/9789264065963-es

OECD (2013). PISA 2012 Assessment and analytical framework. Mathematics, Reading, Science, Problem Solving and Financial Literacy. OECD Publishing. http://dx.doi.org/10.1787/9789264190511-en

Pelczer, I. y Gamboa, F. (2009). Problem posing: Comparison between experts and novices. En M. Tzekaki, M. Kaldrimidou, y H. Sakonidis (Eds.), Proceedings of the 33th Conference of the International Group for the Psychology of Mathematics Education (pp. 353–360). International Group for the Psychology of Mathematics Education.

Piñeiro, J. L., Castro-Rodríguez, E. y Castro, E. (2019). Componentes de conocimiento del profesor para la enseñanza de la resolución de problemas en educación primaria. PNA 13(2), 104–129. https://doi.org/10.30827/pna.v13i2.7876

Santillana (2014). Matemática 7. Costa Rica. Santillana.

Şengül, S. y Katranci, Y. (2015). The analysis of the problems posed by prospective mathematics teachers about ‘ratio and proportion’ subject. Procedia. Social and Behavioral Sciences, 174, 1364–1370. https://doi.org/10.1016/j.sbspro.2015.01.760

Silver, E. A. (1994). On mathematical problem posing. For the Learning of Mathematics, 14(1), 19–28. https://www.jstor.org/stable/40248099?origin=JSTOR-pdf

Singer, F. y Voica, C. (2013). A problem-solving conceptual framework and its implications in designing problem-posing tasks. Educational studies in mathematics, 83(1), 9–26. https://doi.org/10.1007/s10649-012-9422-x

Supply, A. S., Vanluydt, E., Van Dooren, W. y Onghena, P. (2023). Out of proportion or out of context? Comparing 8- to 9-year-olds’ proportional reasoning abilities across fair-sharing, mixtures, and probability contexts. Educ. Stud. Math. 113, 371–388. https://doi.org/10.1007/s10649-023-10212-5

Tichá, M. y Hošpesová, A. (2013). Developing teachers’ subject didactic competence through problem posing. Educational Studies in Mathematics, 83(1), 133–143. https://doi.org/10.1007/s10649-012-9455-1

Weiland, T., Orrill, C.H., Nagar, G.G., Brown, R. y Burke, J. (2020). Framing a robust understanding of proportional reasoning for teachers. Journal of Mathematics Teacher Education, 24(2), 179–202. https://doi.org/10.1007/s10857-019-09453-0

Published

2025-07-31

How to Cite

Chaverri Hernández, J. J., Burgos, M., & Gutiérrez-Fallas, L. F. (2025). Proportionality problem posing in secundary school teacher training. Márgenes, Revista De Educación De La Universidad De Málaga, 6(2), 160–182. https://doi.org/10.24310/mar.6.2.2025.18994

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Section

RESEARCHES