Teaching Algebra in Pre-Service Education of Primary Teachers in Spain

Authors

DOI:

https://doi.org/10.35763/aiem30.6885

Keywords:

Algebra, Algebraic meaning, Pre-service education, Primary education

Abstract

In this study, we investigate teaching algebra in the 39 Spanish public universities that offer a bachelor’s degree in Primary Education. Using a descriptive qualitative methodological approach, we analyze 28 teaching guides and the responses to a questionnaire of 35 university teachers. The data show that: (a) 56.4% of universities provide training on algebra and its teaching; and (b) it is mainly carried out in the first two academic years, combining pedagogical and disciplinary knowledge, using content instruction as a training method and with the support of manipulatives and technological resources. We conclude that it is necessary to identify and address the causes of the limited presence of teaching algebra, as well as to describe updated disciplinary and pedagogical knowledge that enables the development of more integrated training.

References

Aké, L. (2013). Evaluación y desarrollo del razonamiento algebraico elemental en maestros en formación [Tesis Doctoral sin publicar]. Universidad de Granada.

Alsina, Á. y García-Alonso, I. (2023). La estadística y la probabilidad y su didáctica en la formación inicial de maestros en España. Matemáticas, Educación y Sociedad, 6(2), 11–27.

Alsina, Á., Pincheira, N. y Franco, J. (2025). Mathematics teachers’ professional development: A systematic review of training methods. Eurasia Journal of Mathematics, Science and Technology Education, 21(3), em2595. https://doi.org/10.29333/ejmste/16041

Alsina, Á., Vásquez, C., García-Alonso, I. y Berciano, A. (2024). Educación estadística y probabilística para futuros docentes españoles de infantil y primaria: Características, enfoque y metodología. RELIME, 27(1), 73–104. https://doi.org/10.12802/relime.24.2713

Ampaipipatkul, W. (2004). A study of content and training methods for a five-day trainer course [Tesis de maestría sin publicar]. Mahidol University.

Artigue, M. (2017). ¿Qué es la educación matemática basada en la indagación? La Gaceta de la RSME, 20(3), 593–609.

Ayala-Altamirano, C., Molina, M. y Ambrose, R. (2022). Fourth graders expression of the general case. ZDM–Mathematics Education, 54(6), 1377–1392. https://doi.org/10.1007/s11858-022-01398-8

Bergmann, J. y Sams, A. (2012). Flip your classroom. Reach every student in every class every day. International Society for Technology in Education (ISTE).

Blanton, M. L., Levi, L., Crites, T. y Dougherty, B. (Eds.). (2011). Developing essential understanding of algebraic thinking for teaching mathematics in grades 3–5. National Council of Teachers of Mathematics.

Blanton, M., Stephens, A., Knuth, E., Gardiner, A. M., Isler, I. y Kim, J.-S. (2015). The development of children’s algebraic thinking: The impact of a comprehensive early algebra intervention in third grade. Journal for Research in Mathematics Education, 46(1), 39–87. https://doi.org/10.5951/jresematheduc.46.1.0039

Cai, J., Ng, S. F. y Moyer, J. C. (2011). Developing students’ algebraic thinking in earlier grades: Lessons from China and Singapore. En J. Cai y E. Knuth (Eds.), Early algebraization: A global dialogue from multiple perspectives (pp. 25–41). Springer. https://doi.org/10.1007/978-3-642-17735-4_3

Cañadas, M. C. (2023). Una panorámica de las investigaciones sobre pensamiento numérico y pensamiento algebraico. En C. Jiménez-Gestal, Á. A. Magreñán, E. Badillo y P. Ivars (Eds.), Investigación en Educación Matemática XXVI (pp. 3–9). SEIEM.

Cañadas, M. C., Moreno, A. y Torres, M. D. (2024). First encounter with constructing graphs in the functional thinking approach to school algebra in 3rd and 4th grades. ZDM–Mathematics Education, 56, 1059–1078. https://doi.org/10.1007/s11858-024-01627-2

Cohen, L., Manion, L. y Morrison, L. (2017). Research methods in education (8ª edition). Routledge. https://doi.org/10.4324/9781315456539

Ellis, A. B. (2011). Generalizing-promoting actions: How classroom collaborations can support students’ mathematical generalizations. Journal for Research in Mathematics Education, 42(4), 308–345. https://doi.org/10.5951/jresematheduc.42.4.0308

Esteve, O. y Alsina, Á. (2024). ¿Cómo hay que plantear el binomio “teoría-práctica”? En O. Esteve & Á. Alsina (Eds.), Hacia una formación transformadora de docentes. Estrategias eficaces para formadores (pp. 37–52). Narcea.

Hidalgo-Moncada, D. y Cañadas, M. C. (2020). Intervenciones en el trabajo con una tarea de generalización que involucra las formas directa e inversa de una función en sexto de primaria. PNA, 14(3), 204–225. https://doi.org/10.30827/pna.v14i3.11378

Heyd-Metzuyanim, E., Tabach, M. y Nachlieli, T. (2016). Opportunities for learning given to prospective mathematics teachers: Between ritual and explorative instruction. Journal of Mathematics Teacher Education, 19, 547–574. https://doi.org/10.1007/s10857-015-9311-1

Hohensee, C. (2015). Preparing elementary prospective teachers to teach early algebra. Journal of Mathematics Teacher Education, 20, 231–257. https://doi.org/10.1007/s10857-015-9324-9

Isoda, M., Stephens, M., Ohara, Y. y Miyakawa, T. (Eds.). (2007). Japanese lesson study in mathematics: Its impact, diversity and potential for educational improvement. World Scientific. https://doi.org/10.1142/6339

Kaput, J. J. (2000). Transforming algebra from an engine of inequity to an engine of mathematical power by “algebrafying” the K-12 curriculum. National Center for Improving Student Learning and Achievement in Mathematics and Science.

Kaput, J. J. (2008). What is algebra? What is algebraic reasoning? En J. J. Kaput, D. W. Carraher y M. L. Blanton (Eds.), Algebra in the early grades (1.ª ed., pp. 5–18). Routledge. https://doi.org/10.4324/9781315097435-2

Kim, D. W. y Kim, Y. (2022). Interview study on preservice teachers’ knowledge for teaching early algebra. Journal of Educational Research in Mathematics, 32(3), 287–308. https://doi.org/10.29275/jerm.2022.32.3.287

Krippendorff, K. (2013). Content analysis. An introduction to its methodology. Sage.

Malara, N. A. y Navarra, G. (2009). The analysis of classroom-based processes as a key task in teacher training for the approach to early algebra. En B. Clarke, B. Grevholm y R. Millman (Eds.), Tasks in primary mathematics teacher education: Purpose, use and exemplars (pp. 235–261). Springer. https://doi.org/10.1007/978-0-387-09669-8

Margolinas, C. (Ed.). (2013). Task design in mathematics education: Proceedings of ICMI Study 22. University of Oxford.

Martin, B. O., Kolomitro, K. y Lam, T. C. M. (2014). Training methods: A review and analysis. Human Resource Development Review, 13(1), 11–35. https://doi.org/10.1177/1534484313497947

Morales, R., Cañadas, M. C., Brizuela, B. M. y Gómez, P. (2018). Relaciones funcionales y estrategias de alumnos de primero de educación primaria en un contexto funcional. Enseñanza de las Ciencias, 36(3), 59–78. https://doi.org/10.5565/rev/ensciencias.2472

Narváez, R. y Cañadas, M. C. (2023). Mediaciones realizadas a estudiantes de segundo de primaria en una tarea de generalización. PNA, 17(3), 239–264. https://doi.org/10.30827/pna.v17i3.24153

National Council of Teachers of Mathematics [NCTM]. (2000). Principles and standards for school mathematics.

Nolla, A., Muñoz, R., Cerisola, A. y Fernández, B. (2021). La formación inicial de los maestros en matemáticas y su didáctica. Revista Interuniversitaria de Formación del Profesorado, 96(36.1), 185–208. https://doi.org/10.47553/rifop.v96i35.1.85882

Orden ECI/385760/2007, de 27 de diciembre, por la que se establecen los requisitos para la verificación de los títulos universitarios oficiales que habiliten para el ejercicio de la profesión de Maestro en Educación Primaria. Boletín Oficial del Estado, 312, 53747–53750. https://www.boe.es/eli/es/o/2007/12/27/eci3857/dof/spa/pdf

Pang, J. y Sunwoo, J. (2022). Design of a pattern and correspondence unit to foster functional thinking in an elementary mathematics textbook. ZDM–Mathematics Education, 54(6), 1315–1331. https://doi.org/10.1007/s11858-022-01411-0

Pincheira, N. y Alsina, Á. (2021a). Hacia una caracterización del álgebra temprana a partir del análisis de los currículos contemporáneos de educación infantil y primaria. Revista Educación Matemática, 33(1), 153–180. https://doi.org/0.24844/EM3301.06

Pincheira, N. y Alsina, Á. (2021b). Teachers’ mathematics knowledge for teaching early algebra: A systematic review from the MKT perspective. Mathematics, 9, 2590. https://doi.org/10.3390/math9202590

Pincheira, N. y Alsina, Á. (2022). Mathematical knowledge of pre-service early childhood and primary education teachers: An approach based on the design of tasks involving patterns. Australian Journal of Teacher Education, 47(8), 50–69. https://doi.org/10.14221/ajte.2022v47n8.4

Real Decreto 822/2021, de 28 de septiembre, por el que se establece la organización de las enseñanzas universitarias y del procedimiento de aseguramiento de su calidad. Boletín Oficial del Estado, 233, 119537–119578. https://www.boe.es/eli/es/rd/2021/09/28/822/con

Real Decreto 157/2022, de 1 de marzo, por el que se establecen la ordenación y las enseñanzas mínimas de la educación primaria. Boletín Oficial del Estado, 52, 24386–24504. https://www.boe.es/eli/es/rd/2022/03/01/157

Rico, L., Gómez, P. y Cañadas, M. C. (2014). Formación inicial en educación matemática de los maestros de Primaria en España, 1991–2010. Revista de Educación, 363, 35–59.

Stephens, A., Blanton, M., Knuth, E., Isler, I. y Gardiner, A. M. (2015). Just say yes to early algebra! Teaching Children Mathematics, 22(2), 92–101. https://doi.org/10.5951/teacchilmath.22.2.0092

Stylianou, D. A., Stroud, R., Cassidy, M., Knuth, E., Stephens, A., Gardiner, A. y Demers, L. (2019). Putting early algebra in the hands of elementary school teachers: Examining fidelity of implementation and its relation to student performance. Journal for the Study of Education and Development, 42(3), 523–569. https://doi.org/10.1080/02103702.2019.1604021

Warren, E. y Cooper, T. (2005). Introducing functional thinking in Year 2: A case study of early algebra teaching. Contemporary Issues in Early Childhood, 6(2), 150–162. https://doi.org/10.2304/ciec.2005.6.2.5

Downloads

Published

2026-11-02

Issue

Section

Artículos

How to Cite

Pincheira, N., Alsina, Ángel, Acosta, Y., & Cañadas, M. C. (2026). Teaching Algebra in Pre-Service Education of Primary Teachers in Spain. Advances of Research in Mathematics Education, 30, 11-32. https://doi.org/10.35763/aiem30.6885

Most read articles by the same author(s)