Browsing by Author "Font, Vicenc"

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La complejidad de los objetos matemáticos en la formación inicial de docentes
(Universidad de los Lagos, 2022) Font, Vicenc
The objective is the development of competence in the analysis of didactic suitability, corresponding to the representative sample component of the complexity of the mathematical object, in training programs for mathematics teachers in Ecuador. It is a qualitative research that describes the competent use of said component and, on the other hand, it has a development component when developing didactic resources to achieve it. Tasks were designed and the productions of the participants were analyzed from a priori categories (the different meanings of the mathematical object involved) through a content analysis to infer the partial meaning used. The main result is that participants assume the importance of considering the multiple meaning of mathematical objects in the instructional process; nevertheless, they have difficulty designing tasks that involve the use of a variety of meanings.
Partial meanings of the Pythagorean theorem used by teachers in the creation of tasks within the framework of a continuing education program
(2023) Calle Palomeque, Carmen Eulalia
[Objective] This article presents the results of research on the teaching and learning of the criterion “implement a representative sample of the complexity of the mathematical object to be taught,” which was carried out with high school mathematics teachers from Ecuador in a master’s degree program in continuing education. [Methodology] After a discussion of the instructional process which was used when teaching this criterion, a qualitative analysis of the responses to one of the tasks proposed for the students in this master’s degree program is presented: creating tasks for whose resolution the students had to apply a certain partial meaning of the Pythagorean theorem (geometric or arithmetic-algebraic), as a demonstration of the learning that they had achieved. [Results] The results show that some students in the master’s degree program proposed tasks to work on the Pythagorean theorem, but did not specify or justify whether the tasks they designed were related to arithmetic-algebraic meaning, to geometric meaning or to both; other students did not propose any task to work on arithmetic-algebraic meaning; and one participant in the master’s program did not propose any task to work on geometric meaning. It was also observed that some students created tasks that did not correspond to either of these meanings. [Conclusions] It was concluded that teachers have difficulties in creating a task and indicating the type of meaning of the Pythagorean theorem that should be used to solve it, and that geometric meaning was most related to the tasks that they proposed.
Reflection on the complexity of mathematical objects in the initial training of teachers
(2021) Font, Vicenc
This work aims to know the perception of future mathematics teachers about the complexity of mathematical objects and their possible application in teaching practice, in order to improve the teaching and learning of mathematics in Basic General Education (GBS) and the Unified General Baccalaureate (BGU). For this, 19 future professors were asked about the different meanings of some mathematical objects, and they were proposed to raise contextualized problems in which a certain meaning had to be applied in their resolution. The results show that encouraging reflection on the complexity of mathematical objects in the initial training of teachers and their relationship with the design of contextualized problems affects their way of understanding mathematical competence.