Conceptual distinctions and preferential alignment across rational number representations

• Autores: Kailun Qiu, Yunqi Wang
• Localización: European journal of psychology of education, ISSN-e 1878-5174, ISSN 0256-2928, Vol. 36, Nº 3, 2021, págs. 865-881
• Idioma: inglés
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• Resumen

  • Rational numbers can be represented in multiple formats (e.g., fractions, decimals, and percentages), and a rational number notation can be used to express different concepts in different contexts. The present study investigated the distribution of the multiple concepts expressed by these different rational number notations in real-world contexts as well as the semantic alignment between entity type (discrete vs. continuous) and rational number format (decimal vs. fraction) in the Chinese context. Textbook analysis and two paper-and-pencil experiments yielded the following four major findings: (1) Decimals were more likely used to represent numerical magnitudes, while fractions were more likely used to represent relations between two numerical magnitudes. (2) Decimals were more often used to represent continuous entities while fractions were preferred to represent discrete entities. (3) The strength of the association between different formats of rational numbers and their preferred conceptual meanings seemed more pronounced than the semantic alignment between number type and entity type. (4) Percentages were used in a way more similar to fractions than decimals in terms of the concepts they express. These findings indicate that different formats of rational numbers differ dramatically in their use in real-world contexts both in terms of the conceptual meanings they express and the entities they model. Educational implications of this study are discussed.