Banca de DEFESA: JAILSON CAVALCANTE DE ARAÚJO

Uma banca de DEFESA de DOUTORADO foi cadastrada pelo programa.
STUDENT : JAILSON CAVALCANTE DE ARAÚJO
DATE: 25/08/2023
TIME: 09:00
LOCAL: Centro de Educação - UFPE
TITLE:

IMBRICATIONS BETWEEN THE CONCEPTUAL FIELDS OF GEOMETRY AND QUANTITIES AND MEASURES IN THE TEACHING AND LEARNING OF THE AREA OF PARALLELOGRAMS

KEY WORDS:

Conceptual Fields Theory. Didactic Engineering. Quantities and Measures. Geometry. Area of parallelograms.

PAGES: 469
BIG AREA: Outra
AREA: Multidisciplinar
SUMMARY:

This research aimed to understand the implications of the design and experimentation of a didactic sequence supported in the sets of situations that give meaning to the concept of area and the concept of remarkable quadrilateral, prioritizing the imbrications between the fields of Geometry and Magnitudes and Measures, in deepening the understanding and reducing persistent conceptual difficulties of learning
related to the area of parallelograms by students of the 9th grade of elementary school. The theoretical framework is composed by the Conceptual Fields Theory by Gérard Vergnaud and his collaborators, and by the model of area as an autonomous quantity proposed by Régine Douady and Marie-Jeanne Perrin-Glorian. Didactic engineering, from the perspective of Guy Brousseau, Michelle Artigue and others, is the methodology adopted in the research. Initially, the previous analysis was performed, which allowed us to observe the main difficulties of students and the recurrent errors when dealing with situations about the area of parallelograms, how area and parallelograms are addressed in national, state and municipal curriculum guidance documents, in the teachers' plans and activity handouts, as well as in the collection of textbooks adopted in the field school.
It was possible to observe difficulties in the use of these materials. From them, it was possible to observe students' difficulties in situations involving the area and parallelograms, especially when it came to non-square rhombuses and parallelograms not rectangles and not rhombuses. There was also a predominance of measurement situations, prototypical drawings, and emphasis on the figures of the square and the non-square rectangle, reinforcing the need for research that contemplates all parallelograms. These and
other findings served as support for the construction and a priori analysis of the situations that composed the didactic sequence about the area of parallelograms, including situations in the fields of Geometry and Magnitudes and Measures, which was tested with students of the 9th grade of elementary school in a municipal public school in the city of Ferreiros/PE. The results indicated that looking at the different steps of solving an activity as elementary tasks of the Geometry conceptual field, necessary for the full domain of a more complex situation of the Magnitudes field, favors the understanding of aspects related to the area of parallelograms. As for the contributions to the students' learning, we highlight: expansion in the diversity of quadrilaterals and mastery of properties related to definitions; dissociation between area, surface and number; use of geometric procedures such as decomposition and recomposition; improvement of the predicative form of knowledge and appropriation of logical mathematical thinking as a tool for debate and argumentation, among others. The students who presented a good general performance in the work done in the Geometry field, reflected it in the activities of the Quantities and Measures field, thus contributing to the reduction of conceptual learning difficulties related to the area of the region bounded by parallelograms. However, other aspects would require further study in a longer study, such as the meaning of the expressions of area and the invariance of the area in relation to the choice of the side taken as a basis in a parallelogram that is not rectangular and not rhombus.

COMMITTEE MEMBERS:
Presidente - 2345694 - PAULA MOREIRA BALTAR BELLEMAIN
Interna - ***.085.004-** - MARILENE ROSA DOS SANTOS - UPE
Interna - 2377374 - ROSINALDA AURORA DE MELO TELES
Externa à Instituição - MARILENA BITTAR - UFMS
Externo à Instituição - ANDRE PEREIRA DA COSTA