Procedimentos utilizados por estudantes do nível médio técnico em problemas de semelhança de triângulos contextualizados e não contextualizados

Abstract

This study seeks to analyze the procedures used in Solving Mathematical Problems with similar triangles, with and without a realistic context, by sixteen students attending the technical/vocational high school level program at Instituto Federal de Pernambuco in the city of Caruaru. After attending classes and doing problem-solving activities with and without realistic context on Thales’ Theorem and Similarity of Triangles, the participants in this research did an assessment activity with four questions without realistic context, two on the Theorem of Tales and two on the Similarity of Triangles, and a second activity with four questions with realistic context, grouped by topics just like in the first activity. These activities have been prepared in such a way that for each question with context, another question without context was created, containing concise statements, using the same images and similar numerical data, and we called them equivalent questions. For this study, we chose Question 3 from the first activity and Question 1 from the second activity, considered equivalent, both on Similarity of Triangles. This study’s analysis took into account: geometric knowledge; the use of two models of mathematical problems, one with context and the other without context; the use of didactic instruments and the books adopted by the educational institution; problem solving; and error analysis. Thus, we decided to write about the teaching of Geometry in Brazil, the mathematical assessments in Brazil, and the mathematical modeling used in such assessments; about textbooks adopted, and Mathematics Education concepts involved in problem solving, highlighting important studies for the teaching of mathematics; and about ideas and concepts of error and error analysis. Problem-solving techniques used in this research are based on Polya’s ideas (1995) rather than in ideas developed after his time. Error analysis of assessment instruments was based on categories of errors proposed by Makhubele (2014), and also involved cognitive psychology benchmarks on the role of error in learning, repair theory by Makhubele (2014), and Cury’s definition of Error (2010). In the end we have observed that: for the majority of the students, the understanding of the mathematics of similarity were well-grounded in; for this sampling, the lag in a previous geometric concept about the shortest distance from a point to a line, and not the two models, with and without context, was responsible for errors or accurate responses; and that having a week between the two assessment activities to answer students’ questions, played an important role on their positive performance on the second activity.