Estudo de uma estratégia didática pró-argumentativa desenvolvida para estudantes de Licenciatura em Matemática

Abstract

This study investigates teaching with a focus on argumentation in Mathematics Education in Higher Education, more specifically in a Mathematics Teaching degree program. Our interest was attracted by practical situations we experienced with students in this educational context, mainly because of the difficulties they face when building justifications for mathematical arguments. Moreover, we understand that there is a need, which was emphasized by the literature, for conducting more research to assess the potential for teaching focused on argumentation in order to foster argumentation skills. Thus, we established four specific research goals: (I) Analyzing the literature encompassing empirical studies on the uses of argumentation in Mathematics Education in Higher Education through a systematic review; (II) Devising a theoretical argumentative model by linking Toulmin’s model to Perelman’s theoretical perspective so that it could be used as a teaching approach in the didactic strategy and as a tool to analyze students’ arguments; (III) Analyzing the quality of the arguments built by students in a Linear Algebra course; and (IV) investigating how the didactic strategy fosters the development of argumentation in students in a Mathematics Teaching degree program through Toulmin-Perelman Argumentation Model (TPAM). Each goal has been detailed in a chapter (article) of this thesis according to an organization based on the multipaper format, which was chosen for the research report. In order to reach the first goal, we performed a systematic review of the literature, for which we used the Educational Research Information Center (ERIC) database, through journals from the field of Mathematics Education published between 2012 and 2021. Through the review, we were able to identify ways of using argumentation and their characteristics, which were used to propose a teaching model with an argumentative approach. For goal II, we devised a theoretical argumentative model based on Toulmin’s and Perelman’s concepts, which we called TPAM (Toulmin-Perelman Argumentation Model), aiming to guide both the teaching approach and the analysis of students’ argumentation. We worked towards goals III and IV through an empirical qualitative study. Thus, we employed a didactic intervention and investigated argumentation quality in students from a Mathematics Teaching degree program at a federal university in the state of Bahia, Brazil, as well as the contributions provided by the intervention to the development of argumentation skills in the students. The analysis was performed through individual and group activities during Linear Algebra I classes. We combined observation, questionnaires, a semistructured interview, documents and the arguments produced in writing to build the database for the empirical studies, while we used comments, reflective notes, audio and video recordings to record the aforementioned data. To guide our didactic strategy, we employed TPAM. The results of the data analysis showed that most students had difficulty in developing strong arguments. There were gaps between premises and conclusions, as well as in the presentation of sound justifications. In addition, the use of rhetorical resources to support the persuasion in the discussed themes was limited. In spite of the aforementioned difficulties, the intervention was considered successful for the future development of students’ argumentation skills, mainly because many of them might pursue a career in Education after getting a degree in teaching. The didactic strategy provided students with opportunities to address questions and justify Linear Algebra themes, while both the students and the professor became familiar with the terms and the language used in argumentation theories. This approach allowed the participants to be involved in a type of teaching focused on pro-argumentative actions.