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Prospective teachers’ understanding of the multiplicative part-whole relationship of fraction

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Abstract

The part-whole multiplicative relationship, as a topic that gives rise to the concept of fraction, is fundamental in education at the primary school level, and must therefore be included in training courses for prospective primary school teachers (PSTs). In this paper, we introduce a first study of a larger project, which aims to understand the usefulness of a semantic triangle in studying prospective teachers’ knowledge of various mathematical topics. In particular, we present the results of a study focused in the starting level of the fraction concept, based on the multiplicative part-whole relationship. We carried out this study with PSTs by means of a questionnaire. We analyzed the collected responses using a framework of three components that form a semantic triangle, in terms of their conceptual structure, system of representations, and contexts and modes of use of the part-whole relationship. The results show different typologies of meaning expressed by the participants in terms of the semantic triangle. Each typology emphasizes some aspects of the meaning of the part-whole relationship such as the equality of parts, the model of area as representation and the context of division.

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Acknowledgment

This study was supported from project “Procesos de aprendizaje del profesor de matemáticas en formación” EDU2012-33030 (MICINN) and by the Group FQM-193 of the 3rd Andalusian Research Plan (PAIDI).

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Authors and Affiliations

  1. Department Didactics of Mathematics, Facultad de Ciencias de la Educación, Granada University, Campus Cartuja s/n, 18011, Granada, Spain

    Elena Castro-Rodríguez & Luis Rico

  2. Department Education, Cyprus University, P.O. Box 20537, 1678, Nicosia, Cyprus

    Demetra Pitta-Pantazi

  3. CIFE, Universidad de los Andes, Carrera 1 N° 18A – 12, Bogotá, Colombia

    Pedro Gómez

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  1. Elena Castro-Rodríguez
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  2. Demetra Pitta-Pantazi
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  3. Luis Rico
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  4. Pedro Gómez
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Correspondence to Elena Castro-Rodríguez.

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Castro-Rodríguez, E., Pitta-Pantazi, D., Rico, L. et al. Prospective teachers’ understanding of the multiplicative part-whole relationship of fraction. Educ Stud Math 92, 129–146 (2016). https://doi.org/10.1007/s10649-015-9673-4

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