The Progressive Development of Early Embodied Algebraic Thinking

Radford, Luis

doi:10.1007/s13394-013-0087-2

Cited by 120 publications

(147 citation statements)

References 21 publications

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“…This aspect of the study relates to Radford (2014) theorising on students' development of gestural and symbolic activity but focused on translating inner speech to written approaches (colouring and describing in writing) rather than to physical and verbal approaches (gestures and outer speech). The students' colouring also provided a useful way for collecting data from a large cohort that provided insight into their visualisation strategies.…”

Section: Implications and Conclusionmentioning

confidence: 99%

Developing students’ functional thinking in algebra through different visualisations of a growing pattern’s structure

Wilkie

Clarke

2015

Math Ed Res J

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Spatial visualisation of geometric patterns and their generalisation have become a recognised pathway to developing students' functional thinking and understanding of variables in algebra. This design-based research project investigated upper primary students' development of explicit generalisation of functional relationships and their representation descriptively, graphically and symbolically. Ten teachers and their classes were involved in a sequence of tasks involving growing patterns and geometric structures over 1 year. This article focuses on two aspects of the study: visualising the structure of a geometric pattern in different ways and using this to generalise the functional relationship between two quantifiable aspects (variables). It was found that in an initial assessment task (n =222), students' initial visualisations could be categorised according to different types and some of these were more likely to lead either to recursive or explicit generalisation. In a later task, a small number of students demonstrated the ability to find more than one way to visualise the same geometric structure and thus represent their explicit generalisations as different but equivalent symbolic equations (using pronumerals). Implications for the teaching of functional thinking in middle-school algebra are discussed.

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Section: Implications and Conclusionmentioning

confidence: 99%

Developing students’ functional thinking in algebra through different visualisations of a growing pattern’s structure

Wilkie

Clarke

2015

Math Ed Res J

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“…Elle a été développée en contexte réel avec 29 élèves (8-9 ans) de 3 e année de l'école primaire. Les données recueillies montrent que les interactions verbales élèves-enseignantes favorisent le développement de la pensée algébrique sans l'introduction du langage mathématique (Mason, 2007;Radford, 2013Radford, , 2014.…”

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“…Esta investigación fue realizada en el marco de un acuerdo entre profesores de primaria e investigadores asociados a una maestría; ella fue aplicada con 29 alumnos (de 8 a 9 años) de tercer año de primaria. Los datos recogidos muestran que las interacciones verbales "alumnos-profesores" favorecen el desarrollo del pensamiento algebraico sin la introducción del lenguaje matemático (Mason, 2007;Radford, 2013Radford, , 2014.…”

Section: El Rol De La Interacción Verbal En La Adquisición Del Pensamunclassified

Le rôle de l’interaction verbale pour l’acquisition de la pensée algébrique dans l’enseignement primaire

Nacarato

Anjos

Santos

et al. 2019

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L’objectif de ce travail a été d’analyser les interactions verbales élèves-enseignantes mettant en évidence le rôle du langage dans le développement de la pensée algébrique dans une perspective historico-culturelle. Les interactions ont eu lieu grâce à des tâches dont la construction se basait sur la perception des régularités dans des suites non numériques. Cette recherche a été réalisée dans le cadre d’un partenariat entre des enseignantes de l’école primaire et des chercheurs associés à un master académique. Elle a été développée en contexte réel avec 29 élèves (8-9 ans) de 3e année de l’école primaire. Les données recueillies montrent que les interactions verbales élèves-enseignantes favorisent le développement de la pensée algébrique sans l’introduction du langage mathématique (Mason, 2007; Radford, 2013, 2014).

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“…Thus, the development of algebraic thinking cannot be reduced to the development of its symbolic component (notation use, for instance). The development of algebraic thinking must be studied as a whole, by taking into account the interrelated dialectic development of its various components (Radford 2012). If in a previous section I talked about the 'domestication of the eye,' this domestication has to be related to the 'domestication of the hand' as well.…”

Section: Thinking and Its Developmentmentioning

confidence: 99%

Early Algebraic Thinking: Epistemological, Semiotic, and Developmental Issues

Radford

2015

The Proceedings of the 12th International Congress on Mathematical Education

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In this article I present some findings of an ongoing 5-year longitudinal research program with young students. The chief goal of the research program is a careful and systematic investigation of the genesis of embodied, non-symbolic algebraic thinking and its progressive transition to culturally evolved forms of symbolic thinking. The investigation draws on a cultural-historical theory of teaching and learning-the theory of objectification-that emphasizes the sensible, embodied, social, and material dimension of human thinking and that articulates a cultural view of development as an unfolding dialectic process between culturally and historically constituted forms of mathematical knowing and semiotically mediated classroom activity.

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The Progressive Development of Early Embodied Algebraic Thinking

Cited by 120 publications

References 21 publications

Developing students’ functional thinking in algebra through different visualisations of a growing pattern’s structure

Developing students’ functional thinking in algebra through different visualisations of a growing pattern’s structure

Le rôle de l’interaction verbale pour l’acquisition de la pensée algébrique dans l’enseignement primaire

Early Algebraic Thinking: Epistemological, Semiotic, and Developmental Issues

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