The impact of sending letters in improving teaching-learning process of natural number of pre-service teachers

Mónica Arnal-Palacián, Nuria Begué, Cristina Blanco


The first contact that a pre-service teacher has with didactics of mathematics is the notion of natural number, being still in the university classroom and not having started working a real classroom. Therefore, the main objective of this work is to relate the knowledge of a trainee teacher to the different difficulties developed by the children and to evaluate the learning processes in a real environment. The participants were 20 future teachers and 40 (9-year-old) children. During the experience, six letters closely related to the contents of the university subject were exchanged; as well as two socialisation letters; and four videos, including two presentation and two farewell videos. Among the results obtained, we highlight that the participating university students have been able to reinforce the knowledge learned in class through the analysis of the children's resolutions, specifically the following: a) counting, b) resolution of additive-concrete situations, c) resolution of multiplicative-concrete situations, d) resolution of a monetary problem, and e) being aware of the manipulation of Cuisenaire's rods.


Natural Number; Pre-Service Teachers; Problem-Solving; Teaching-Learning

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Alghamdi, A., Jitendra, A. K., & Lein, A. E. (2020). Teaching students with mathematics disabilities to solve multiplication and division word problems: The role of schema-based instruction. ZDM, 52(1), 125-137.

Alsina, A. (2006). Cómo desarrollar el pensamiento matemático de 0 a 6 años [How to develop mathematical thinking from 0 to 6 years old]. Octaedro.

Alsina, A. (2019). Itinerarios didácticos para la enseñanza de las matemáticas (6-12 años) [Didactic itineraries for the teaching of mathematics (6-12 years old)]. GRAÓ.

Ball, D. L., & Cohen, D. K. (1999). Developing practice, developing practitioners: Toward a practice-based theory of professional education. In L. Darling-Hammond & G. Sykes (Eds.), Teaching as the learning profession: Handbook of policy and practice (pp. 3-32). Jossey-Bass.

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.

Bracho, R., Maz, A., Jiménez-Fanjul, N., & García, T. (2011). Formación del profesorado en el uso de materiales manipulativos para el desarrollo del sentido numérico [Teacher training in the use of manipulative materials for the development of number sense]. Unión: Revista Iberoamericana de Educación Matemática, 28, 41-60.

Cañadas, M. C., Molina, M., & del Río, A. (2018). Meanings given to algebraic symbolism in problem-posing. Educational Studies in Mathematics, 98(1), 19-37.

Carrillo, J., Climent, N., Montes, M., Contreras, L. C., Flores-Medrano, E., Escudero-Ãvila, D., Vasco, D., Rojas, N., Flores, P., Aguilar-González, M., Ribeiro, M. & Muñoz-Catalán, M. C. (2018). The mathematics teacher’s specialised knowledge (MTSK) model. Research in Mathematics Education, 20(3), 236-253.

Chapman, O. (2011). Supporting the development of mathematical thinking. In B. Ubuz (Ed.). Proceedings of the 35th International Conference for the Psychology of Mathematics Education, 1, pp. 69-75. IGPME.

Chorney, S., & Bakos, S. (2021). Investigating the positioning of pre-service teachers in relation to incorporating First Peoples’ worldviews into mathematics teaching. Canadian Journal of Science, Mathematics and Technology Education, 21, 714–739.

Elliot, R., & Timulak, L. (2005). Descriptive and interpretive approaches to qualitative research. In: J. Miles, & P. Gilbert (Eds.). A handbook of research methods for clinical and health psychology. Oxford University Press.

English, L. D. (2020). Teaching and learning through mathematical problem posing: Commentary. International Journal of Educational Research, 102, 101451.

Goos, M. (2014). Researcher–teacher relationships and models for teaching development in mathematics education. ZDM Mathematics Education, 46, 189-200.

Ma, L. (1999). Knowing and teaching elementary mathematics teachers’ understanding of fundamental mathematics in China and the United States. Lawence Erlbaum.

McMillan, J. H., & Schumacher, S. (2005). Investigación educativa (5.a edicion) [Educational research (5th edition)]. Pearson Education.

Niss, M. (2020) Functions learning and teaching. Encyclopedia of Mathematics Education, 303-306.

Polotskaia, E., & Savard, A. (2018). Using the relational paradigm: Effects on pupils’ reasoning in solving additive word problems. Research in Mathematics Education, 20(1), 70-90.

Polotskaia, E., & Savard, A. (2021). Some multiplicative structures in elementary education: A view from relational paradigm. Educational Studies in Mathematics, 106(3), 447-469.

Póveda, B., Barceló, M. L., Rodríguez Gómez, I., & López-Gómez, E. (2021). Percepciones y creencias del estudiantado universitario sobre el aprendizaje en la universidad y en el prácticum: Un estudio cualitativo [Perceptions and beliefs of university students about learning at university and in the practicum: A qualitative study]. Revista Complutense de Educación, 32(1), 41-53.

Riley, M. S., & Greeno, J. G. (1988). Developmental analysis of understanding language about quantities and of solving problems. Cognition and Instruction, 5(1), 49-101.

Riley, N. S., Greeno, J., & Heller, J. I. (1983). Development of children's problem solving ability in arithmetic. In H. P. Ginsburg (Ed.), The development of mathematical thinking (pp. 153–196). Academic Press.

Shulman, L. S. (1986). Those who understand: Knowledge growth in teaching. Educational Researcher, 15(2), 4-14.

Treffers, A. (2008). Kindergarten 1 and 2. Growing number sense. In M. Van den Heuvel-Panhuzen (Ed.), Children Learn Mathematics. A Learning-Teaching Trajectory with Intermediate Attainment Targets for Calculation with Whole Numbers in Primary School (pp. 31-42). Sense Publishers.

Valle, J. M., & Manso, J. (2018). El practicum en la formación inicial: Aportaciones del modelo 9:20 de competencias docentes [The practicum in initial training: Contributions of the 9:20 model of teaching competencies]. Cuadernos de Pedagogía, 489, 33-40.



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Journal of Honai Math
Universitas Papua
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