Determination of the area of a parabola and the initial position of a water jet: a demonstrative proposal for the teaching of mathematics in 3rd year of Baccalaureate

Abstract

The study addressed the difficulties third-year high school students face in understanding quadratic functions and calculating the area under the curve, topics that are often presented as complex in traditional teaching. Its main objective was to strengthen learning about quadratic functions and the area under the curve among third-year high school students through a teaching approach that integrated technology and practical applications. A mixed-method approach was adopted, combining quantitative analysis, based on data obtained from parabolas formed by water jets, and qualitative analysis, focusing on students' perceptions. The research design was non-experimental and cross-sectional, with a non-probability sample of fifteen students. Measurement tools and GeoGebra software were used in the analysis to graphically represent the parabolas and calculate the area under the curves. The results showed that the use of GeoGebra facilitated the visualization and understanding of the concepts. Furthermore, more than 70% of the students positively evaluated the clarity, relevance, and usefulness of the methodology. It was concluded that this approach promoted meaningful learning by connecting theory and practice, highlighting its adaptability to diverse educational settings and its interdisciplinary potential. It was recommended that the approach's long-term effectiveness and implementation in broader populations be explored.