TEACHING TRIGONOMETRIC FUNCTIONS USING COMPUTATIONAL TOOLS: DYNAMIC VISUALIZATION AND PROGRAMMING LOGIC IN GEOGEBRA AND MAXIMA

Abstract

Trigonometric functions are usually one of the hardest topics for Brazilian high school students, which is reflected in the low math scores seen in large-scale assessments. This paper is an experience report on using GeoGebra and Maxima to solve Question 180 of the 2015 ENEM exam, which models the seasonal price of an agricultural product through the function P(x) = 8 + 5cos((πx − π)/6). The same question was solved in four different ways: the traditional analytical method (pencil and paper), reading the graph in GeoGebra, a price list built and searched inside GeoGebra itself (using the commands Sequence, Min and IndexOf, plus a button-triggered script), and a small search algorithm written in Maxima. All four reach the same answer, the month of July (x = 7), but each one asks something different from the student: algebraic reasoning, visual reading, data organization, and programming logic. The paper also describes, in detail, a syntax error that came up while building the script in GeoGebra, and how it was fixed, arguing that this kind of stumble is part of learning and should not be hidden from students. The conclusion is that combining both tools with traditional calculation helps students understand the same content from different angles, in line with what the BNCC asks for.