Estudio sobre la actuación docente y la interacción en la creación y aprovechamiento de oportunidades de aprendizaje en el aula de matemáticas

Abstract

This doctoral thesis asks the following research question: How is teaching activity capable of promoting students’ mathematical learning when managing classroom discussions on similarity tasks? To answer this question, two objectives were defined:_x000D_ 1. To characterize the teaching activity of secondary school teachers when they manage classroom discussions on similarity tasks that can create mathematical learning opportunities._x000D_ 2. To analyse the effect of classroom discussions on the students’ ability to take advantage of learning opportunities when solving similarity tasks._x000D_ A theoretical framework is suggested in which the concept of mathematical learning opportunity is introduced and situated within the context of a classroom discussion. We then present considerations on the student’s prior knowledge based on the similarity contents that appear in the secondary school mathematics curriculum. Likewise, we also discuss considerations on the teacher’s knowledge bearing in mind both mathematical and pedagogical factors._x000D_ A methodology was chosen that is included in the qualitative paradigm of research in mathematics education. An instructional sequence of three similarity tasks was chosen, and it was implemented in two secondary schools with students aged 14 and 15. Three secondary mathematics teachers were involved in the experiment, which was conducted in two phases. To obtain the research data, we recorded the classroom discussions with three video cameras and later transcribed the scripts for the analysis. We also collected the written protocols of the tasks solved by the students. The first phase of the experiment in which two teachers participated was used as a pilot study. In the second phase we got data from a secondary school teacher when she implemented the sequence of three similarity tasks in her classroom._x000D_ In the analysis, we study the data obtained in both phases of experimentation. In the first phase we only analyse the in-class implementation of the first task in the instructional sequence. We introduce the analysis of the preparation of the classroom discussion and the analysis of episodes and actions, and we determine mathematical learning opportunities. In the second phase, we analyse the preparation of the classroom discussions of the three similarity tasks, and for each task we analyse the ways of teacher action and interaction, exemplify mathematical learning opportunities and examine to what extent the students took advantage of these opportunities._x000D_ In the results of the first phase of experimentation, we find two ways of teacher action, namely magisterial and participative, when managing a classroom discussion. What is more, we establish a direct relationship between each way of action and the creation of given learning opportunities. In the second phase of experimentation, we obtain results that determine a methodical preparation of classroom discussions in the sequence of three similarity tasks. We also obtain a way of teacher action with instrumental balance and discursive completeness and a predominant way of participative, bilateral interaction. We group together the learning opportunities obtained in the analysis according to their conceptual, procedural and argumentative nature. We further present three degrees to which the students took advantage of these mathematical learning opportunities._x000D_ In the conclusions we determine that the teacher’s management of classroom discussions in which both the teacher and students participate actively fosters the creation of a larger number of mathematical learning opportunities, which are taken advantage of by the majority of students in the class. Nonetheless, not all students are capable of getting actively involved in the discussions, nor do all manage to take advantage of the learning opportunities available to them.

Date of Award	29 Jan 2016
Original language	Undefined/Unknown
Supervisor	Lluís Bibiloni Matos (Director)