The use of dynamic geometry and mathematical investigation in the validation of geometric properties
DOI:
https://doi.org/10.5902/2179460X33752Keywords:
Geometry, Mathematical investigation, Dynamic ggeometryAbstract
This paper presents an activity on Geometry of position using GeoGebra software, based on Mathematical Investigation. The Dynamic Geometry, through software, becomes a tool for the formation of a mental image of abstract objects and motivation to introduce the idea of justifying its properties through arguments external to software. Allied to Dynamic Geometry, Mathematical Investigation guides the possible ways to construct conjectures and justifications and emphasizes that conjecture and looking for properties are as important as demonstrating them, since it shows the Mathematics as a knowledge in construction and favors the cognitive evolution of the relation between perception and abstraction. The activity was applied and it was observed that, from it, the student can formulate conjectures and develop logical and formal argumentation skills that are essential to construct geometric objects from their properties.
Downloads
References
do Amaral Rodriguez, B. D., Meneghetti, C. M. S., Poffal, C. A. (2015). Estudo do perfil dos alunos do curso de matemática aplicada – bacharelado: entendendo aow razões para o baixo rendimento dos acadêmicos. Ciência e Natura, 37, 151–162, URL https://periodicos.ufsm.br/cienciaenatura/article/viewFile/14785/pdf.
Arzarello, F., Olivero, F., Domingo, P., Robutti, O. (2002). A cognitive analysis of dragging practises in cabri environments. ZDM, 34, URL http://www.matematica.it/paola/ArticoloZDM.pdf.
Balacheff, N. (1987). Processus de preuve et situations de validation. Educational Studies in Mathematics, 18(2), 147, URL http://dx.doi.org/10.1007/BF00314724.
BRASIL (2000). Parâmetros Curriculares Nacionais Ensino Médio - Parte III. Secretaria da Educação Média e Tecnológica, Brasília, URL http://portal.mec.gov.br/seb/arquivos/pdf/ciencian.pdf.
Brasil (2004). PCNEM+:Orientações Educacionais Complementares aos Parâmetros Curriculares Nacionais; Ciências da Natureza, Matemática e suas Tecnologias. Ministério da Educação, URL http://portal.mec.gov.br/seb/arquivos/ pdf/CienciasNatureza.pdf.
Brasil (2006). Orientações Curriculares para o Ensino Médio ; volume 2. Ministério da Educação.
Carvalho, P. C. P. (2005). Introdução à Geometria Espacial, 4o edn. SBM, Rio de Janeiro.
Fiorentini, D., Lorenzato, S. (2006). Investigação em educação matemática percursos teóricos e metodológicos. Autores Associados.
Fischbein, E. (1993). The theory of figural concepts. Educational studies in mathematics, 24(2), 139–162, URL http://web. math.unifi.it/users/dolcetti/Fischbein.pdf.
Giraldo, V., Caetano, P., Mattos, F. (2013). Recursos Computacionais no Ensino de Matemática, 1o edn. SBM, Rio de Janeiro.
Gravina, M. A. (1996). Geometria dinâmica: uma nova abordagem para o aprendizado da geometria. Em: Anais do VII Simpósio Brasileiro de Informática na Educação, pp. 1–13, URL http://www.educadores.diaadia.pr.gov.br/ arquivos/File/2010/artigos_teses/EDUCACAO_E_TECNOLOGIA/GEODINAMICA.PDF.
Harel, G., Sowder, L. (1998). Students’ proof schemes: Results from exploratory studies. Research in collegiate mathematics education III, pp. 234–283.
Iezzi, G., Dolce, O., Degenszajn, D., Périgo, R., de Almeida, N. (2013). Matemática: ciência e aplicações, vol 1. Saraiva.
Ordem, J. (2015). Prova e demonstração em geometria plana: concepções de estudantes da licenciatura em ensino de matemática em moçambique. Tese de Doutorado, Pontifícia Unversidade Católica de São Paulo, URL https://tede2.pucsp.br/ handle/handle/11035.
da Ponte, J. P., Brocado, J., de Oliveira, H. (2005). Investigações
Matemáticas na sala de aula. Autêntica, Belo Horizonte.
Ribeiro, R. S. (2013). Geometrias não-euclidianas na escola: uma proposta de ensino através da geometria dinâmica. Dissertação de Mestrado, Universidade Federal do Rio Grande do Sul, URL http://hdl.handle.net/10183/79482.
dos Santos, C. A., Nacarato, A. M. (2014). Aprendizagem em Geometria na educação básica: A fotografia e a escrita na sala de aula, 1o edn. Tendências em educação matemática, Autêntica.
Downloads
Published
How to Cite
Issue
Section
License
To access the DECLARATION AND TRANSFER OF COPYRIGHT AUTHOR’S DECLARATION AND COPYRIGHT LICENSE click here.
Ethical Guidelines for Journal Publication
The Ciência e Natura journal is committed to ensuring ethics in publication and quality of articles.
Conformance to standards of ethical behavior is therefore expected of all parties involved: Authors, Editors, Reviewers, and the Publisher.
In particular,
Authors: Authors should present an objective discussion of the significance of research work as well as sufficient detail and references to permit others to replicate the experiments. Fraudulent or knowingly inaccurate statements constitute unethical behavior and are unacceptable. Review Articles should also be objective, comprehensive, and accurate accounts of the state of the art. The Authors should ensure that their work is entirely original works, and if the work and/or words of others have been used, this has been appropriately acknowledged. Plagiarism in all its forms constitutes unethical publishing behavior and is unacceptable. Submitting the same manuscript to more than one journal concurrently constitutes unethical publishing behavior and is unacceptable. Authors should not submit articles describing essentially the same research to more than one journal. The corresponding Author should ensure that there is a full consensus of all Co-authors in approving the final version of the paper and its submission for publication.
Editors: Editors should evaluate manuscripts exclusively on the basis of their academic merit. An Editor must not use unpublished information in the editor's own research without the express written consent of the Author. Editors should take reasonable responsive measures when ethical complaints have been presented concerning a submitted manuscript or published paper.
Reviewers: Any manuscripts received for review must be treated as confidential documents. Privileged information or ideas obtained through peer review must be kept confidential and not used for personal advantage. Reviewers should be conducted objectively, and observations should be formulated clearly with supporting arguments, so that Authors can use them for improving the paper. Any selected Reviewer who feels unqualified to review the research reported in a manuscript or knows that its prompt review will be impossible should notify the Editor and excuse himself from the review process. Reviewers should not consider manuscripts in which they have conflicts of interest resulting from competitive, collaborative, or other relationships or connections with any of the authors, companies, or institutions connected to the papers.
