Estroboscopia digital: aplicações de interpolação e ajuste de curvas na educação básica

Abstract

This dissertation develops and validates an original educational product: a video-based kinematic analysis web app for inquiry-based teaching of Physics and Mathematics in Basic Education. It addresses the disconnect between the abstraction of school content and the concrete phenomena experienced by students through an interface that trans- forms audiovisual records of real motions into quantitative data, tables, graphs, and mathematical models. The study brings together Mathematics Education, mathemati- cal modeling, metacognition, digital technologies, and Design-Based Research, starting from the hypothesis that interaction with the software promotes investigation, hypothe- sis validation, and an integrated reading of multiple representation registers. From a mathematical standpoint, the system is grounded in the NyquistShannon Sampling Theorem, the Mean Value Theorem, polynomial interpolation, cubic splines, and the SavitzkyGolay filter, which underpin temporal discretization, trajectory reconstruction, and data smoothing. The product was developed and refined in iterative cycles and compared with the Tracker software in projectile motion experiments with different frame rates. The results show that the digital environment provides accuracy compara- ble to well-established tools, enhancing pedagogical accessibility, the transparency of mathematical procedures, and its potential for use in schools. It is concluded that the web app is a relevant contribution to inquiry-based teaching by integrating concrete ex- perience, mathematical modeling, and technological mediation, aligning with students scientific and mathematical education.