NUMERICAL METHODS IN HIGH SCHOOL: A DIDACTIC SEQUENCE FOR THE STUDY OF BISECTION AND FALSE POSITION WITH PYTHON

Abstract

This work investigates the numerical methods of Bisection and False Position for the approximate determination of real roots of continuous functions, articulating mathematical fundamentals, Python programming, and teaching practices aimed at high school students. The research arose from the need to employ iterative methods in situations where there are no simple analytical solutions for nonlinear equations, a recurring problem in areas such as Engineering, Physics, and Applied Mathematics. The study is characterized as quantitative and exploratory research, based on theoretical frameworks related to error theory, numerical representations, and the operational principles of the investigated methods. In addition to the mathematical and computational analysis, a didactic sequence composed of eleven lessons was developed and applied with first-year high school students from a public school. The proposal included the study of functions, graphical interpretation, the Intermediate Value Theorem, application of numerical methods, and implementation of algorithms in the Python language. During the activities, students used resources such as GeoGebra and a computer lab to explore mathematical and computational concepts in an integrated way. The results indicated that both methods were effective in approximating roots, although the False Position method demonstrated faster convergence in certain cases. In the educational field, progress was observed in the understanding of functions, algorithms, programming, and problem-solving. It is concluded that the proposal favors the integration between Mathematics and Computer Science, promoting meaningful learning and bringing students closer to practical applications of Mathematics in scientific and technological contexts.