La práctica de la enseñanza de las matemáticas a través de las situaciones de contingencia

Abstract

This thesis is a study in the field of mathematics education, which follows the line of investigation about the analysis of teaching practice of mathematics teachers. It is a line of investigation that is relevant these days. The doctoral thesis has as objective the analysis of the teaching practice through the contingency situations. These situations are defined by Rowland (2005) as those unplanned teaching situations which are caused by the student´s ideas, the teacher´s ideas or by the lack of necessary tools. The theoretical framework performs a synthesis between the frameworks of Rowland (Knowledge Quartet, KQ), (2005, 2009, 2011) and of Ball (Mathematical knowledge of teaching, MKT) (2008), following also the studies of Turner (2012). This frames are some of the main theoretical constructs for the study of mathematics teaching practice and follow the works initiated by Shulman (1986) and also other recent works about the analysis of practice through episodes (Schoenfeld, 2011). The methodology used is qualitative and forms part of a high number of data picked up by the frame of the EDU project 2009-07298. In particular, 69 recordings of full classes of 6th grade and of 1st ESO have been analyzed. From this data only the most relevant contingency episodes have been selected (12 in total, corresponding to four different teachers) which have been the subject of analysis on various dimensions: triggers of contingency (Rowland, 2011), management of the episodes by the teachers, ways of solving contingency for mathematical knowledge and for teaching (according with the of the MKT model of Ball, 2008) mobilized in the management. The results of the investigation have allowed characterizing each one of the analyzed dimensions. It also has determined the influence of the different types of knowledge that the teacher has to manage and solve contingency. Regarding the triggers, Rowland´s statements have been confirmed in the sense that the ideas of the students (spontaneous interventions, questions and answers to the demands of the teacher, either correct or incorrect) are the most frequent, relevant and have contributed with significant data about the mobilized knowledge by the teachers in the management and solving of contingency. In summary, the analysis of practice performed in this investigation is based on the idea that teaching is given through details. Particularly, in the interaction of the students with their teachers about particular ideas in specific circumstances.

Date of Award	4 Mar 2015
Original language	Spanish
Supervisor	Jordi Deulofeu Piquet (Director) & Lourdes Figueiras Ocaña (Director)