A TRAJETÓRIA HIPOTÉTICA DA APRENDIZAGEM E A MODELAGEM MATEMÁTICA: possibilidades e desafios.

Abstract

The planning of a teacher's classes is one of tuhe main factors for him to do a cohesive. Such planning can be considered as a hypothetical trajectory, where the teacher traces a path so that his students learn the contents. To make learning happen, the teacher establishes teaching strategies and, in general, when these strategies are differentiated, there is the possibility for the professional to reflect on their practice, even before it happens, this reflection will start from their hypothetical trajectory. In this research, we used Mathematical Modeling as a teaching strategy that allows the teacher's reflection when contextualizing content involving real situations, so that when makes your planning, they trace their Hypothetical Learning Trajectory, developing tasks that can be reformulated according to the development of the class. In this sense, the main objective of this research is to study the theory of the Learning Hypothetical Trajectory with the use of Mathematical Modeling to understand the changes and directions that may emerge in a planning, contributing for the teacher to reflect on their practice, allowing to search for an improvement in the learning process. In turn, the specific objectives are (1) To present real situations to develop activities in an Elementary Mathematics course; (2) Carry out an initial planning and reassess it during and at the end of the activities and, finally, (3) Assess how the reformulation and reflection of a planning can improve a class. In search of the objectives, we developed two plannings, aiming at teaching Basic Mathematics in a course remotely, with an emphasis on Mathematical Modeling, and then we analyzed the plannings and their respective changes during the course. We realized that providing the teacher with means of analyzing their practice while it happens, can make a difference in the referrals given, providing opportunities for them to adapt or create new actions when necessary and, consequently, impact on learning.