As características e o nível do desenvolvimento do pensamento algébrico em tarefas introdutórias envolvendo funções exponenciais

Abstract

This research arose when we sought to understand what level of development of Algebraic Thinking (AT) that students in the 10th – grade, High School, who opted for a training itinerary in which mathematics is not present have when they begin studying Exponential Functions. To do this, we chose to use the model proposed by Almeida (2016), which describes the five characteristics of AT and how, based on them, we can determine the level of development of AT. As a way of complementing the analysis of activities, we used the theory of Semiotic Representation Records proposed by Duval (2009). To situate our research, we carried out a search for research present in the Brazilian Digital Library of Theses and Dissertations (BDTD) and in the Capes Catalog of Theses and Dissertations (BTD-CAPES), which addressed Algebraic Thinking and Records of Semiotic Representation, Algebraic Thinking and exponential functions, Semiotic Representation Register and exponential functions, and finally presenting the three themes. The objectives of this work are to identify characteristics and the level of development of Algebraic Thinking present in tasks of 10th – grade, High School students, when starting studies related to the Exponential Function. Our research is qualitative in nature, therefore, we seek to describe the group participating in the research and how the activities were applied with the aim of answering the question “What are the levels of development and characteristics of Algebraic Thinking present in solving tasks involving exponential function for 10th – grade high school students?” To answer the research question, we chose to use a Didactic Sequence based on Didactic Engineering as a research methodology, thus carrying out analysis, experimentation and validation of the results. As a result of our research, we observed that the AT characteristics “Establishing relationships” and “Modeling” were more frequent during the application of the two activity sequence proposals and that the majority of students were at level 1 of development of algebraic thinking when starting studies related to the Exponential Function, in addition to observing how the mobilization of various representation records contributes to better development of the AT.