El Conocimiento Profesional del Profesor de Matemáticas en Formación Inicial: Variabilidad Estadística

Abstract

This research addresses how the professional knowledge of the mathematics teacher in initial training can be evidenced through teaching planning processes in the teaching practice, taking into account a training model that constitutes a key axis to identify the conceptual assumptions to adequately perform a teaching task. The professional development processes are in correspondence with the initial teacher training activities and these, in turn, have as a fundamental objective the elaboration of professional knowledge. Also, the study of the school content "statistical variability", understood here as a fundamental stochastic idea, which is present as an underlying element to multiple concepts of statistics and probability, acquires a relevant role. In order to delimit its study, the following sources of variability are chosen: data variability, sample variability and random variability. The general purpose of this research was to analyze the components of professional knowledge on statistical variability of mathematics teachers in initial training in basic and secondary education in Colombia. The research was carried out from the interpretative paradigm in the qualitative approach, using the collective case study method through written questionnaires and focus groups in four groups of teaching practice of a bachelor's degree program in mathematics. The categories of analysis with which the professional knowledge of the mathematics teacher in initial training was studied, are in the theoretical framework of "Didactic Analysis" proposed by Rico et al. (2013), however, an emerging category was found: pedagogy is communication in teaching practice. In this regard, they indicated that the experience in teaching practice allowed them to develop the ability to communicate with their students in the different moments of the class. In conclusion, it could be seen that mathematics teachers in initial training identified the absence of the teaching of variability as a fundamental stochastic idea in the development of random thinking in the school curriculum and stated that they did not know this content; however, when they worked on the components of the didactic analysis, they were able to identify the conceptual foci, the systems of representation and senses and modes of use of statistical variability, and according to the levels of understanding of variability proposed by Watson et al (2003), future teachers show that they have a better performance in situations of random variability. However, in data and sampling variability, some difficulties in their understanding were identified. In addition, it is interpreted that the didactic analysis provides guidance to teachers in initial training, in the processes of teaching planning in an organized manner and they manage to articulate the knowledge of content and didactic knowledge, through the conceptual foci, representations, meanings and modes of use, the sequencing of tasks, the organization of classroom work and the materials and resources that they synthesized in the lesson plans. This will help them face situations in their future teaching work. Nevertheless, the teachers in training evidenced few conditions to anticipate their learning, which translates into attending to the difficulties and errors of the students, aspects that should be attended to in the teaching practice of the future mathematics teacher.