Os três mundos da Matemática: fundamentos teóricos por meio de uma trajetória hipotética de aprendizagem

Abstract

This master's research has as a theoretical framework the Theoretical Framework of the Three Worlds of Mathematics by David Orme Tall, which studies how people learn to think mathematically, how they elaborate/refine their mathematical knowledge based on perception, action and reflection, and thus, identify through those already-found, when transiting through the Worlds: Embodied, Symbolic and Formal. Learning is individual, each individual has their own pace, so it is important that teachers use different methodologies in their practice. In line with this perspective, the Hypothetical Learning Path (THA) by Martin Simon is presented, a methodological strategy that is based on the teaching experience, with well-defined learning objectives, planning of learning activities and the prediction of possible doubts that students may have. can have on the content easily. Based on these references, this research aims to present the characteristics of the Three Worlds of Mathematics in the learning of Quadratic Functions through a Hypothetical Learning Path. The developed research is investigated as an applied qualitative approach. The proposed task involves a problematic situation with a quadratic function mediated by a THA, implemented with students from a 1st year high school class at a state school in the city of Ponta Grossa in the state of Paraná. The research data were collected through two instruments: the resolution developed by the students and the audio of the implementation classes. Data analysis was performed using Tall's Theoretical Framework of the Three Worlds of Mathematics. Some difficulties are evident in relation to the subject of quadratic functions on the part of the students, appearing some already-found difficulties related to the representation of the variables, and graphical construction.