Geometria e as ilusões: uma proposta interdisciplinar nas aulas de matemática.

Abstract

In the school context, in order to foster students’ interest in mathematical knowledge, many teachers revisit pedagogical planning and teaching practices, diversify instructional methodologies, and propose interdisciplinary didactic sequences. The objective of this study, therefore, is to present a didactic sequence on geometric transformations through experimentation and the construction of illusion models with a group of first-year high school students from the State Public School System. This is a qualitative research study based on the theoretical principles of didactic sequences as proposed by Antoni Zabala (1998). The structured activities are divided into three independent modules, each based on a proposed visual illusion—namely, the Ames Room, Moiré Patterns, and Cylindrical Anamorphosis—addressing, respectively, the concepts of homothety, translation, and rotation of geometric figures. Methodological aspects include the development of a lesson plan and the administration of a post-lesson questionnaire. The Content Analysis technique is used to identify students’ interests or resistance regarding the proposed methodologies, such as experimentation, use of concrete materials, digital technologies, and interdisciplinarity. As results, illusion models were constructed using GeoGebra and Anamorph Me! software, as well as recyclable materials. The didactic sequence is validated based on theoretical foundations, implementation in practice, records of student activities, and student assessments.