Divisão Proporcional: uma investigação sobre as estratégias utilizadas por alunos concluintes do Ensino Médio

Helena do Carmo Borba Martins; Angélica da Fontoura Garcia Silva

doi:10.35819/remat2022v8i1id5154

Authors

Helena do Carmo Borba Martins Colégio Adventista da Liberdade (CAL), São Paulo, SP, Brasil https://orcid.org/0000-0001-9894-3020
Angélica da Fontoura Garcia Silva Universidade Anhanguera de São Paulo (UNIAN-SP), São Paulo, SP, Brasil https://orcid.org/0000-0002-2435-9240

DOI:

https://doi.org/10.35819/remat2022v8i1id5154

Keywords:

Mathematics Education, Proportional Reasoning, Studant Strategies, High School

Abstract

This article aims to analyze the strategies used by 3rd-grade high school students to solve a situation involving the idea of proportional division in the ratio of 3 to 1. It is a qualitative research, carried out in a private school in the metropolitan area of São Paulo, SP, Brazil, with 43 students from two groups finishing basic education. Data collection was carried out through the presentation of problem situations in a questionnaire ? of a diagnostic nature ?, which were solved and sent digitally by e-mail to the coauthor of the article, who is their mathematics teacher. Students were requested to solve resolutions in different ways, if possible. As for the solution, the analysis revealed that most of the students used algebra (equation modelling and equation systems), while the others used arithmetic (notions of division, fraction, triple, and partition). The need for a broader focus on the didactic approach of this type of reasoning in high school was identified.

Downloads

Download data is not yet available.

Author Biographies

Helena do Carmo Borba Martins, Colégio Adventista da Liberdade (CAL), São Paulo, SP, Brasil

http://lattes.cnpq.br/9591739484369425
Angélica da Fontoura Garcia Silva, Universidade Anhanguera de São Paulo (UNIAN-SP), São Paulo, SP, Brasil

http://lattes.cnpq.br/5279665144777466

References

BEHR, M.; HAREL, G.; POST, T.; LESH, R. Rational number, ratio and proportion. In: GROUWS, D. A. (Ed.). Handbook of Research on Mathematics Teaching and Learning. New York: MacMillan,1992. p. 296-333.

BOGDAN, R. C.; BIKLEN, S. K. Investigação qualitativa em educação. Tradução de Maria João Alvarez, Sara Bahia dos Santos e Telmo Mourinho Baptista. Porto: Porto Editora, 1994.

BRASIL. Ministério da Educação. Secretaria da Educação Fundamental. Parâmetros Curriculares Nacionais: Matemática. v. 3. Brasília: MEC/SEF, 1997. Disponível em: http://portal.mec.gov.br/seb/arquivos/pdf/livro03.pdf. Acesso: 3 mar. 2022.

BRASIL. Base Nacional Comum Curricular. Brasília: MEC, 2018. Disponível em: http://basenacionalcomum.mec.gov.br/images/BNCC_EI_EF_110518_versaofinal_site.pdf. Acesso em: 6 set. 2020.

FARIA, R. W. S. C.; MALTEMPI, M. V. Raciocínio proporcional na matemática escolar. Revista Educação em Questão, Natal, v. 58, n. 57, p. 1-18, 3 set. 2020. DOI: https://doi.org/10.21680/1981-1802.2020v58n57ID20024.

LAMON, S. J. Teaching Fractions and Ratios for Understanding: Essential Content Knowledge and Instrutional Strategies for Teachers. 2. ed. Mahwa: Lawrence Erlbaum Associates Publishers, 2006.

LESH, R.; POST, T.; BEHR, M. Proportional reasoning. In: BEHR, M.; HIELBERT, J. (Ed.). Number concepts and operations for the middle grades. Hillsdale: Lawrence Erlbaum, 1988. p. 93-118.

NCTM. National Council of Teachers of Mathematics. Curriculum Evaluation: Standards for School Mathematics. Washington: NCTM, 1989.

PONTE, J. P. da; BRANCO, N.; MATOS, A. Álgebra no Ensino Básico. Lisboa: Ministério da Educação, 2009. Disponível em: https://repositorio.ul.pt/bitstream/10451/7105/1/Ponte-Branco-Matos%20(Brochura_Algebra)%20Set%202009.pdf. Acesso em: 13 out. 2020.

SPINILLO, A. G. A importância do referencial de “metade” e o desenvolvimento do conceito de proporção. Psicologia: Teoria e Pesquisa, Brasília, v. 8, n. 3, p. 305- 317, 1992. Disponível em: https://www.gestaoesaude.unb.br/index.php/revistaptp/article/view/17142. Acesso em: 2 mar. 2022.

VERGNAUD, G. A criança, a matemática e a realidade. Curitiba: Editora UFPR, 2009.