Modelagem matemática e pensamento algébrico no 6º ano do ensino fundamental

Abstract

This dissertation aimed to investigate how Mathematical Modelling activities, from the perspective of Model-Eliciting Activities (MEAs), can contribute to the development of algebraic thinking in the 6th year of Elementary School and is based on the practice of Mathematical Modelling for the elicitation of models, that is, to cause the externalization of students' thoughts and conclusions in relation to the problem situation through mathematical models. It is, therefore, a possibility that offers support for observing evidence of algebraic thinking. Six Mathematical Modelling activities were developed in this perspective in a 6th grade class, with students from 11 to 14 years old, from a State College located in the North of Paraná. For data collection, a camcorder, three audio recorders and a cell phone were used, with the objective of recording students' speeches and gestures, as well as notes in a field diary and collection of written records produced by them. The analysis of the activities was guided by a qualitative approach, with selection of episodes that presented evidence of the five forms of algebraic thinking indicated by Kaput (1999), namely, (i) algebra as generalization and formalization of patterns and constraints; (ii) algebra as syntactically guided manipulation of (opaque) formalisms; (iii) algebra as the study of structures abstracted based from computations and relations; (iv) algebra as the study of functions, relations and joint variation; and (v) algebra as a cluster of modelling and phenomena-controlling languages. The results indicate the potential of the activities of Mathematical Modelling, from the perspective of MEAs, to develop algebraic thinking in the classroom, particularly with regard to the production of mathematical models. The students showed to be able to solve problems, using knowledge consistent with their age and school grade, which justifies the observation of some of the five forms of algebraic thinking more often than others, as these five forms are configured as an interrelated structure which can be developed over the school years, enabling the establishment of structures capable of providing a basis for higher levels of abstraction and formalization. The results also suggest the students' engagement in solving problems, autonomous decision-making, thinking and evaluating the projects carried out, reflections on mathematical discussions and, mainly, the arguments and justifications for the choices made.