TEACHING GEOMETRY MEDIATED BY MATHEMATICAL MODELING: A PROPOSAL TO ADDRESS THE SUM OF INTERIOR ANGLES
DOI:
https://doi.org/10.61164/m44pnn54Keywords:
Geometry teaching, Mathematical modeling., Sum of interior angles. , Geometric visualization., Active learning.Abstract
Geometry is a relevant component of school mathematics education; however, part of the student population presents difficulties related to visualization, spatial understanding, and the interpretation of geometric properties. In this context, pedagogical practices that foster experimentation and the active construction of mathematical knowledge become pertinent. This article analyzes the use of mathematical modeling and figure construction as instructional strategies for teaching the sum of the interior angles of triangles and quadrilaterals. The study was carried out with 8th-grade middle school students from a private school in the municipality of Floriano, Piauí, Brazil, through hands-on activities involving cutting, coloring, and folding polygons. These activities enabled empirical observation that the sum of the interior angles of a triangle equals 180 degrees and that of a quadrilateral equals 360 degrees. Based on these experiences, students were guided to formulate conjectures, validate hypotheses, and understand the relationship between the number of sides of a polygon and its decomposition into triangles, supporting the construction of the general rule for the sum of the interior angles of polygons. The results indicate progress in student participation and conceptual understanding of the contents addressed, suggesting contributions of the adopted strategies to inquiry-based learning processes. The practices analyzed dialog with Mathematics Education frameworks related to visualization and active learning and are aligned with the guidelines of the Brazilian National Common Curricular Base.
Downloads
References
BIEMBENGUT, Maria Salett; HEIN, Nelson. Modelagem Matemática no Ensino. 3. ed. São Paulo: Contexto, 2013.
BRASIL. Ministério da Educação. Base Nacional Comum Curricular. Brasília, DF: MEC, 2018.
BURAK, Dionísio. Modelagem Matemática: aplicações e implicações para o ensino. Bolema, v. 23, n. 37, p. 19–42, 2010.
COSTA NETO, A. Do medo ao encanto: a formação do professor de matemática como ferramenta de transformação da cultura do fracasso escolar. In: Diálogos acadêmicos na perspectiva norte-sul: um apanhado sobre pesquisas em educação. Porto Alegre: Editora Cirkula, 2025. p. 109–120.
GIL, Antônio Carlos. Como elaborar projetos de pesquisa. 4. ed. São Paulo: Atlas, 2008.
GRANDO, Neiva Irene. Jogos e Resolução de Problemas: uma perspectiva para o ensino de Matemática. 2. ed. Campinas: Papirus, 2010.
GRAVINA, Maria Alice. Ambientes de geometria dinâmica e aprendizagem. Bolema, v. 28, n. 50, p. 1–22, 2014.
LIMA, M. B. R.; MENDES, C. O.; OLIVEIRA, L. C. B. I exposição de matemática da unidade escolar Monsenhor José Almeida. Cointer, 2025. DOI: 10.31692/2358-9728.
LORENZATO, Sérgio. Laboratório de Ensino de Matemática: da teoria à prática. Campinas: Autores Associados, 2006.
NASSER, Lilian. Geometria Dinâmica e os Processos Cognitivos no Aprendizado da Matemática. São Paulo: Livraria da Física, 2018.
NARCISO, R.; SANTANA, A. C. de A.; FERNANDES, A. B. Explorando as metodologias científicas: tipos de pesquisa, abordagens e aplicações práticas. Caderno Pedagógico, v. 22, n. 1, p. e13333, 2025. DOI: 10.54033/cadpedv22n1-130.
PAVANELLO, Regina Maria. O ensino da Geometria no Brasil: uma perspectiva histórica. 1993. Tese (Doutorado em Educação) — Universidade Estadual de Campinas, Campinas, 1993.
PIAGET, Jean. A formação do símbolo na criança. Rio de Janeiro: Zahar, 1975.
(A obra citada no texto refere-se ao pensamento construtivista; esta é a edição brasileira mais utilizada.)
SANTANA, A. C. de A.; NARCISO, R.; FERNANDES, A. B. Explorando as metodologias científicas: tipos de pesquisa, abordagens e aplicações práticas. Caderno Pedagógico, v. 22, n. 1, p. e13333, 2025. DOI: https://doi.org/10.54033/cadpedv22n1-130
SILVA, Jonas Santana da; MADRUGA, Zulma Elizabete de Freitas. Teias de aranha e Modelagem Matemática: a construção de modelo como possibilidade para o ensino de Matemática. Revista Profissão Docente, v. 25, n. 50, p. 1–26, 2025. DOI: 10.31496/rpd.v25i50.1673. DOI: https://doi.org/10.31496/rpd.v25i50.1673
Downloads
Published
Issue
Section
License
Copyright (c) 2025 Lays Santana Lima, Valdemir Silva Oliveira Junior, Joselyto Barros de Aguiar, Ronaldo Campelo da Costa, Roberto Arruda Lima Soares
This work is licensed under a Creative Commons Attribution 4.0 International License.
Authors who publish in this journal agree to the following terms:
Authors retain copyright and grant the journal the right of first publication, with the work simultaneously licensed under the Creative Commons Attribution License, which permits the sharing of the work with proper acknowledgment of authorship and initial publication in this journal;
Authors are authorized to enter into separate, additional agreements for the non-exclusive distribution of the version of the work published in this journal (e.g., posting in an institutional repository or publishing it as a book chapter), provided that authorship and initial publication in this journal are properly acknowledged, and that the work is adapted to the template of the respective repository;
Authors are permitted and encouraged to post and distribute their work online (e.g., in institutional repositories or on their personal websites) at any point before or during the editorial process, as this may lead to productive exchanges and increase the impact and citation of the published work (see The Effect of Open Access);
Authors are responsible for correctly providing their personal information, including name, keywords, abstracts, and other relevant data, thereby defining how they wish to be cited. The journal’s editorial board is not responsible for any errors or inconsistencies in these records.
PRIVACY POLICY
The names and email addresses provided to this journal will be used exclusively for the purposes of this publication and will not be made available for any other purpose or to third parties.
Note: All content of the work is the sole responsibility of the author and the advisor.
