Caracterización del conocimiento especializado sobre el área de figuras planas en estudiantes para maestro

Abstract

The aim of the present doctoral thesis is to characterize the specialized knowledge put into play by preservice teachers when faced with a set of professional tasks involving the area of flat figures. For this purpose, the Mathematics Teacher’s Specialized Knowledge model is used. In order to respond to the objective, the study is positioned in an interpretative paradigm and adopts a qualitative methodology. A semi-structured open-ended questionnaire is designed to be answered by 147 preservice teachers of the third year of the Primary Education Degree at the Autonomous University of Barcelona, during the school period 2020/21. A content analysis is carried out to identify the categories of specialized knowledge that preservice teachers mobilize in their resolutions and to elaborate indicators of specialized knowledge on the area of flat figures. The results of this research show that when preservice teachers use geometric representations and procedures related to the decomposition and reorganization of figures, their resolutions and justifications are more robust. This is because these representations and procedures allow them to explain how and why they solve the tasks in a certain way. Likewise, it is observed that the use of geometric representations and the associated procedures promote the joint mobilization of different properties. Thus, it is possible that these properties allow preservice teachers to expand their repertoire of strategies when solving area tasks, giving support to alternative procedures to the use of formulas. The results also show that the coordination between different registers of representation, geometric-symbolic, allows preservice teachers to improve their performance in solving area tasks. This, because the use of such registers of representation allows the coordination of procedures based on calculations, decompositions and reconfigurations of geometric figures, in addition to the joint mobilization of properties. It is also evident that the joint use of different procedures was a key aspect for preservice teachers to be able to interpret students’ answers and promote teaching strategies to correct students’ errors. Finally, the results show that the constructed indicators of specialized knowledge were useful to characterize the mathematical and pedagogical knowledge of preservice teachers in relation to the area of flat figures.