Mathematical processes for the development of algebraic reasoning in geometrical situations with in-service secondary school teachers
Rosa Cecilia Gaita 1 * , Miguel R. Wilhelmi 2 , Francisco Javier Ugarte 1 , Cintya Sherley Gonzales 1 2
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1 Research Institute on the Teaching of Mathematics, Pontifical Catholic University of Peru, PERU2 Public University of Navarre, Pamplona-Iruña, SPAIN* Corresponding Author

Abstract

This paper starts from the hypothesis that algebraic reasoning can be used as an axis between different mathematical domains at school. This is relevant given the importance attributed to mathematical connections for curriculum development and the algebraic reasoning makes it possible to articulate it in a coherent manner. A definition of generalized algebraic reasoning is proposed, based on the notion of elementary algebraic reasoning of the onto-semiotic approach, and it is used to highlight the presence of typical algebraic processes in problem solving in geometrical contexts. To develop these ideas, a training course is designed and implemented with in-service secondary school teachers. Based on design-based research, the results obtained are contrasted with the expected answers. In this way, relevant information is obtained on how teachers mobilize different typically algebraic processes, that is, particularization-generalization, representation-signification, decomposition-reification and modelling. Actually, it is clear to affirm that teachers need specific training to improve their skills about how algebraic reasoning can help them to develop mathematical connections with their students.

License

This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 20, Issue 12, December 2024, Article No: em2553

https://doi.org/10.29333/ejmste/15709

Publication date: 11 Dec 2024

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Article Downloads: 140

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