A produção de significados matemáticos em um contexto de aulas exploratório-investigativas

Abstract

This thesis offers an answer to the following question: in a semiotic-cultural perspective, how is the process of producing meanings (learning) by the students, when involved in exploratory-investigative activities in the classroom? This investigation focuses on the process of teaching and learning experienced by a group of students of the 7th grade of a basic public school of Belo Horizonte (MG) while performing exploratory-investigative activities implemented in mathematics classes. The research, of primarily qualitative nature, had as objectives: 1) identify the constitutive aspects of the production of mathematical meanings in the context of exploratory-investigative classes; 2) Evaluate the didactic suitability of the process experienced. From a semiotic-cultural perspective to the production of meanings (RADFORD, 2006, 2006a, DA ROCHA FALCÃO, 2009), and based on the social interactionist view of learning of Vygotsky, were seized, in this research, the acts and processes of meaning explicit in the alluded educational experience in terms of the language in its verbal, gestural, graphic and graphic -symbolic dimensions. The data were produced from the transcription of audio and video recordings of the process experienced, written records generated by the students during the activities and field diary. For data analysis, five levels of analysis proposed by the Onto-semiotic Approach of Mathematical Knowledge (OSA) were used, theoretical-methodological model devised by Godino and co-workers (GODINO, BATANERO e FONT, 2007, 2008; FONT, PLANAS e GODINO, 2010). Regarding the first objective of the research, the results indicate that the exploratory-investigative activities in the classroom are strongly conditioned by the following aspects: affectivity (standards and meta-standards, attitudes, emotions, motivation, etc.); materiality (time availability, means, etc.); forms of interaction; proposed task (mathematical representation, possible emergence of ZPDs, adapting the curriculum, society, etc.), familiarity of the students (and the teacher) with this type activity, etc. The analysis and interpretation of the data showed that, in the context of the proposed study (students approximately 12 years old who had not had contact with investigative activities), the students need great support from the teacher. This fact leads us to the complexity of the work of this professional, since it is not enough for it to offer rich situations or create a space where students have to argue and express what they think, nor it is enough to evaluate t heir ideas as right or wrong. It is necessary for the teacher to question and problematize the student's ideas, to make them overcome the difficulties and make progress. As pedagogical implication, I highlight the potentiality of the exploratory-investigative activities as a scenario for the production of mathematical meanings, since, in this study, the overall level of didactic suitability achieved by the practice analyzed (from medium to high) the second objective of the research suggests that working with this type of activity can provide a context highly adequate for the production of meanings. This context, however, is obviously dependent on the aspects which constitute it (ASSIS, GODINO and FRADE, submitted 2).