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

• Autores: Juan Manuel González Forte, Ceneida Fernández Verdú , Jo Van Hoof, Wim Van Dooren
• Localización: Avances de investigación en educación matemática, ISSN-e 2254-4313, Nº. 22, 2022, págs. 48-70
• Idioma: inglés
• Títulos paralelos:
  • Perfiles en la comprensión de la densidad de los números racionales en estudiantes de educación primaria y secundaria
• Enlaces
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• Resumen
  • español

    En este estudio transversal sobre la densidad de los números racionales participaron 953 es-tudiantes desde 5º curso de educación primaria hasta 4º curso de educación secundaria. Tras un análisis inductivo, codificando las respuestas a tres tipos de ítems, se llevó a cabo un análisis clúster, que reveló diferentes perfiles intermedios en la comprensión de la densidad. Se identificaron formas de pensar dife-rentes: i) la idea de consecutivo, ii) la idea de número finito de números, y iii) la idea de que entre fracciones solo hay fracciones y entre decimales solo hay decimales. Además, se obtuvieron diferenciascon respecto a la representación de los números racionales: los estudiantes primero reconocieron la densidad en núme-ros decimales y posteriormente, en fracciones. Se destaca que los estudiantes al final de la educación se-cundaria todavía tenían una idea basada en el conocimiento del número natural, especialmente cuando tenían que escribir un número entre dos números racionales pseudo-consecutivos.

  • English

    The present cross-sectional study investigated 953 fifth to tenth grade students’ understand-ing 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 Analysisrevealed 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 pro-files 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 nat-ural 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.

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