Las Escuelas Normales y la renovación de la enseñanza de las matemáticas (1909-1936)

Laburpena

Teacher training colleges and the renewal of mathematics teaching (1909-1936) Abstract During the first third of the 20th Century, a great many education reforms were planned, projected and implemented in Spain. These innovations had as a reference point international education movements, especially the new school movement. Within this context, innovations in the field of the study of mathematics both in teaching training colleges as well as in primary schools are of special interest. The following research problems are formulated: How did teaching training college professors contribute to the educational renewal process, in terms of teachers' methodological training in mathematics? What were the characteristics of their innovative proposals in mathematics? Which of them are specific to mathematics? What were their proposals for innovation in mathematics education in primary school? The present research focuses on the History of Mathematics Education. Consequently, methods of historical research, and more specifically, those features related to the History of Education, are taken into account. However, mathematical content is also analyzed using theoretical tools developed in Mathematics Teaching. The choice of these tools is linked to the research programme to which we subscribe, the Epistemological Research Programme in Mathematics Teaching, which considers mathematical activity itself as a primary object of study. The Anthopological Theory of Didactics (ATD) is adopted. This theoretical framework focuses on the mathematical and instructional organizations which emerge in the study of mathematics within an institution. The ATD provides valuable research tools for examining the History of Mathematics Education. These tools have so far been underused in the field so that their full potential is still unknown. As a result, further research problems still to be addressed include: Which analysis of the processes of mathematical study developed in the past allows the application of the ATD tools? How do available sources influence this research? What relationship is there between the pedagogical, epistemological and teaching models in mathematics? These questions are broken down into more specific issues which are discussed in different chapters. The analysis of the training of future teachers in both mathematics and the teaching of mathematics involves making reference to disciplinary subjects such as arithmetic or geometry, which form part of Mathematics, and to another subject, Mathematics Methodology or Mathematics Didactics, which at that time, was still in the process of becoming a discipline. These processes take place within the educational system, in confluence or confrontation with other disciplines similarly affected by educational policies and changes in the curriculum and closely related to the professionalization of their teachers. Thus, along with the praxeological analysis, that provides a method for analyzing the institutional practices that allow for the description and study of the conditions of implementation (praxeologies or mathematical and didactic organizations), an ecological analysis considers the setting and the conceptual environment of an object of knowledge, as well as the role of this object in the system it interacts with. The conditions and mutual restrictions between the mathematical organizations studied in institutional teacher training colleges -and primary schools- and the corresponding didactic organizations are analyzed, in order to determine how the influence of the levels of didactic co-determination beyond Discipline or Pedagogy, such as School and the Society, determine the above mentioned study.