Conocimiento especializado en geometría en un aula de 5º de primaria

Abstract

The first intention of this paper —within the framework of the project Characterization of Specialised Knowledge of the Mathematics Teacher (EDU2013-44047P), financed by the Ministry of Economy and Competitiveness of Spain—- was to characterize the specialised knowledge of a teacher when teaching Geometry in its Fifth grade classroom. However, influenced by my academic training, my theoretical sensitivity and my work as a researcher in Didactics of Mathematics and teacher of prospective teachers, when I came into the classroom for the very first time and started the observations, reality invited me to understand what was happening in the classroom from another perspective. . This paper aims to show the concerns that led us, as researchers, to go beyond the evidences and indications of specialised knowledge about Geometry that we could observe in the practice of a Fifth grade primary school teacher and the consequences that this had on our work. These concerns caused our initial perspective to be modified and become a potential vision, understood as the one with which the researcher interprets the knowledge that is mobilized in the classroom. Knowledge opportunities are seen as the methodological element that has allowed us,- as researchers, to identify the knowledge evoked by situations generated in the classroom: caused by the interventions of the students, by the use of materials (structured or not) or by the teacher’s interventions on her own. The following situation is an example: one of the first days of observation, when the teacher asked the straight lines and their relative positions to find out the previous knowledge of her students, a girl exemplified with her fingers two segments that were cut in a point. Then, she separated them vertically and got two segments that intersect, but were not cut, making explicit the space context. This simple gesture revealed what neither the textbook nor the class had reflected on: what was the context of the relative positions of the lines being studied? The focus, then, should be on what allows us to learn from observation and analyze the specialized knowledge that emerges in the classroom, which includes both the teacher’s observed knowledge and those that evoke the interventions of students and other agents present, such as the textbook and other resources. We started with the transcriptions of direct observation (videotaped) of the practice of a teacher when she taught Geomfetry in a Fifth grade classroom. The Mathematics Teachers’ Specialised Knowledge (MTSK) model, whose domains, subdomains, categories and indicators have enabled us to study the different situations, have also allowed us to characterize this knowledge. The analysis was done initially in chronological order, that is to say, starting from the transcription and taking apart its content based on the mentioned model. Subsequently, both the evidence and signs observed in the teacher's knowledge and the opportunities evoked in the classroom have been gathered from MTSK. In our conclusion, we can say that a case that, initially, was instrumental, became with this vision of opportunities in an intrinsic case and that the MTSK emerging from such opportunities has sometimes become a knowledge for the teacher trainee. Finally, and more importantly, we consider that a systematic analysis of different situations such as the one observed, emphasizing both signs and evidences as well as opportunities of knowledge, could have an instrumental character that would enrich our perception of the specialised knowledge that teaching and learning management which is required in Primary Education.