Profiles in understanding the density of rational numbers among primary and secondary school students

Artigo2022

Juan Manuel González Forte; Ceneida Fernández; Jo Van Hoof; Wim Van Dooren

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Resumo

The present cross-sectional study investigated 953 fifth to tenth grade students’ understanding of the dense structure of rational numbers. After an inductive analysis, coding the answers based on three types of items on density, a TwoStep Cluster Analysis revealed different intermediate profiles in the understanding of density along grades. The analysis highlighted qualitatively different ways of thinking: i) the idea of consecutiveness, ii) the idea of a finite number of numbers, and iii) the idea that between fractions, there are only fractions, and between decimals, there are only decimals. Furthermore, our profiles showed differences regarding rational number representation since students first recognised the dense nature of decimal numbers and then of fractions. Learners, however, were still found to have a natural number-based idea of the rational number structure by the end of secondary school, especially when they had to write a number between two pseudo-consecutive rational numbers.

Dados da obra

Tipo: Artigo
Periódico: Avances de Investigación en Educación Matemática, n. 22
Editora: Sociedad Española de Investigación en Educación Matemática
Ano: 2022
Idioma: en
Palavras-chave: Rational numbers; Density; Discreteness; Learner profiles; Fractions
DOI: 10.35763/aiem22.4034
ISSN: 2254-4313
Acesso: Acesso aberto
Fontes: DOAJ — Directory of Open Access Journals
Na Biblioteca desde: 01/10/2026 · verificada em 03/10/2026

Como citar

ABNT
FORTE, Juan Manuel González et al.. Profiles in understanding the density of rational numbers among primary and secondary school students. Avances de Investigación en Educación Matemática, n. 22, 2022. DOI: https://doi.org/10.35763/aiem22.4034.

APA

Forte, J. M. G., Fernández, C., Hoof, J. V., & Dooren, W. V. (2022). Profiles in understanding the density of rational numbers among primary and secondary school students. Avances de Investigación en Educación Matemática. https://doi.org/10.35763/aiem22.4034

BibTeX

@article{forte2022,
  author = {Forte, Juan Manuel González and Fernández, Ceneida and Hoof, Jo Van and Dooren, Wim Van},
  title = {Profiles in understanding the density of rational numbers among primary and secondary school students},
  year = {2022},
  journal = {Avances de Investigación en Educación Matemática},
  number = {22},
  publisher = {Sociedad Española de Investigación en Educación Matemática},
  doi = {10.35763/aiem22.4034},
  language = {en}
}

RIS

TY  - JOUR
AU  - Forte, Juan Manuel González
AU  - Fernández, Ceneida
AU  - Hoof, Jo Van
AU  - Dooren, Wim Van
TI  - Profiles in understanding the density of rational numbers among primary and secondary school students
PY  - 2022
JO  - Avances de Investigación en Educación Matemática
IS  - 22
DO  - 10.35763/aiem22.4034
LA  - en
ER  -

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