Proportional Division: an investigation of the strategies used by High School graduates

Authors

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.

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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

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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.

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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.

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Published

2022-03-09

How to Cite

MARTINS, H. do C. B.; SILVA, A. da F. G. Proportional Division: an investigation of the strategies used by High School graduates. REMAT: Revista Eletrônica da Matemática, Bento Gonçalves, RS, v. 8, n. 1, p. e2004, 2022. DOI: 10.35819/remat2022v8i1id5154. Disponível em: https://periodicos.ifrs.edu.br/index.php/REMAT/article/view/5154. Acesso em: 3 jul. 2024.

Issue

Vol. 8 No. 1 (2022)

Section

Mathematics Education

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