The impact of sending letters in improving teaching-learning process of natural number of pre-service teachers
DOI:
https://doi.org/10.30862/jhm.v5i1.240Keywords:
Natural Number, Pre-Service Teachers, Problem-Solving, Teaching-LearningAbstract
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.References
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. https://doi.org/10.1007/s11858-019-01078-0
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. https://doi.org/10.1177/0022487108324554
Bracho, R., Maz, A., Jiménez-Fanjul, N., & GarcÃa, 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 RÃo, A. (2018). Meanings given to algebraic symbolism in problem-posing. Educational Studies in Mathematics, 98(1), 19-37. https://doi.org/10.1007/s10649-017-9797-9
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. https://doi.org/10.1080/14794802.2018.1479981
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. https://doi.org/10.1007/s42330-021-00180-4
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. https://doi.org/10.1016/j.ijer.2019.06.014
Goos, M. (2014). Researcher–teacher relationships and models for teaching development in mathematics education. ZDM Mathematics Education, 46, 189-200. https://doi.org/10.1007/s11858-013-0556-9
Ma, L. (1999). Knowing and teaching elementary mathematics teachers’ understanding of fundamental mathematics in China and the United States. Lawence Erlbaum. https://doi.org/10.4324/9781410602589
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. https://doi.org/10.1007/978-3-030-15789-0_96
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. https://doi.org/10.1080/14794802.2018.1442740
Polotskaia, E., & Savard, A. (2021). Some multiplicative structures in elementary education: A view from relational paradigm. Educational Studies in Mathematics, 106(3), 447-469. https://doi.org/10.1007/s10649-020-09979-8
Póveda, B., Barceló, M. L., RodrÃguez 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. https://doi.org/10.5209/rced.67953
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. https://doi.org/10.1207/s1532690xci0501_2
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. https://doi.org/10.3102/0013189X015002004
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. https://doi.org/10.1163/9789087903954_006
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 PedagogÃa, 489, 33-40. http://hdl.handle.net/10486/685215
Downloads
Published
How to Cite
Issue
Section
License
License and Copyright Agreement
In submitting the manuscript to the journal, the authors certify that:
- They are authorized by their co-authors to enter into these arrangements.
- The work described has not been formally published before, except in the form of an abstract or as part of a published lecture, review, thesis, or overlay journal. Please also carefully read Journal of Honai Math Posting Your Article Policy at http://journalfkipunipa.org/index.php/jhm/about
- That it is not under consideration for publication elsewhere,
- That its publication has been approved by all the author(s) and by the responsible authorities – tacitly or explicitly – of the institutes where the work has been carried out.
- They secure the right to reproduce any material that has already been published or copyrighted elsewhere.
- They agree to the following license and copyright agreement.
Copyright
Authors who publish with Journal of Honai Math agree to the following terms:
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License (CC BY-NC-SA 4.0) that allows others to share the work with an acknowledgment of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgment of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work.
