El conocimiento especializado del profesor de matemáticas acerca de la proporcionalidadun estudio de casos

Abstract

This work is the result of various efforts through which we seek to show the importance of understanding the teaching of proportionality as a key concept in the construction of mathematical thinking. The specialized knowledge of the teacher was chosen as the object of study, for which the interpretive paradigm and the case study were used as contributing tools to answer the research question: What specialized knowledge does a secondary school teacher mobilize when teaching proportionality? To answer this question, we chose to use the bottom-up, top-down methodology, which seeks to establish an ascending and descending relationship between the data collected and the theory on the object of study. In this sense, four class sessions were initially recorded and systematized in which this concept was taught in the facilities of a public school in the city of Bogotá. The MTSK model was used as an analysis tool, created within the framework of the Research Seminar in Mathematical Didactics (SIDM) of the University of Huelva and previously used in several doctoral theses that also inquire about the specialized knowledge of the mathematics teacher. Once the data was collected through the recording of the classes, taking notes in the field diary and holding interviews with the informant teacher, a chronological analysis is carried out that seeks to establish each of the twenty episodes studied and the subdomains present in each of these episodes. Thanks to the acquisition of a theoretical sensitivity, it was also possible to establish new relationships between these subdomains by investigating the opportunities and indications observed. Subsequently, for the discussion of data analysis, a reflection is made in two directions; how the present investigation contributes to, or debates, previous investigations on the teacher's knowledge about proportionality and how the relationships between the data can contribute to the understanding of the different subdomains of the MTSK model. The conclusions revolve around the theoretical and methodological contributions offered by the MTSK model and possible impacts that this research may have, among which are the preparation of proposals for teacher training, the creation of new academic spaces for reflection on knowledge teacher training, identifying the training needs of mathematics teachers, designing proportionality teaching sequences, and understanding and overcoming proportionality learning difficulties. Finally, the limitations and future projections of the present investigation are presented, thus showing the investigative processes as cyclical constructions that can leave questions and situations open for subsequent inquiries about the teacher's specialized knowledge.