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From collective consciousness to individual consciousness: Dialectical analysis of a fifth-grade class performing a pattern generalization task.

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Title: From collective consciousness to individual consciousness: Dialectical analysis of a fifth-grade class performing a pattern generalization task.
Authors: Joya, Sindy1,2 (AUTHOR) sindy.joya@gmail.com, Vergel, Rodolfo1 (AUTHOR) rvergelc@udistrital.edu.co
Source: European Journal of Psychology of Education - EJPE (Springer Science & Business Media B.V.). Jun2026, Vol. 41 Issue 2, p1-22. 22p.
Abstract: This article is part of a broader investigation into algebraic thinking in primary education from the perspective of the theory of objectification. This study aims to characterize how collective consciousness is transformed into individual consciousness in a fifth-grade classroom as a pattern generalization task related to the function y = 2 x - 1 is addressed and developed. The emphasis is on the development of consciousness through joint activity, considering the layers of generality in algebraic thinking. The analysis identified five moments: (1) exploration of the first terms of the sequence, (2) transition toward non-perceptual forms of reasoning, (3) adoption of generalization schemes, (4) resolution of a distant case in which students make the generalization explicit, and (5) production of a message so that another person can calculate any given term. Each phase reveals how semiotic means of objectification —gestures, graphic representations, and language— mediate the construction of meanings and allow knowledge to be socialized and internalized. The results show that the class exhibited three characteristics of algebraic thinking: A sense of indeterminacy, analyticity, and symbolic designation, which developed and evolved as expressions of the emerging consciousness within the activity. Simultaneously, the appropriation of algebraic knowledge is a dialectical process in which collective interaction and the materialization of objects of knowledge lead to the development of individual consciousness and the consolidation of theoretical forms of mathematical thinking. [ABSTRACT FROM AUTHOR]
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Database: Education Research Complete
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Abstract:This article is part of a broader investigation into algebraic thinking in primary education from the perspective of the theory of objectification. This study aims to characterize how collective consciousness is transformed into individual consciousness in a fifth-grade classroom as a pattern generalization task related to the function y = 2 x - 1 is addressed and developed. The emphasis is on the development of consciousness through joint activity, considering the layers of generality in algebraic thinking. The analysis identified five moments: (1) exploration of the first terms of the sequence, (2) transition toward non-perceptual forms of reasoning, (3) adoption of generalization schemes, (4) resolution of a distant case in which students make the generalization explicit, and (5) production of a message so that another person can calculate any given term. Each phase reveals how semiotic means of objectification —gestures, graphic representations, and language— mediate the construction of meanings and allow knowledge to be socialized and internalized. The results show that the class exhibited three characteristics of algebraic thinking: A sense of indeterminacy, analyticity, and symbolic designation, which developed and evolved as expressions of the emerging consciousness within the activity. Simultaneously, the appropriation of algebraic knowledge is a dialectical process in which collective interaction and the materialization of objects of knowledge lead to the development of individual consciousness and the consolidation of theoretical forms of mathematical thinking. [ABSTRACT FROM AUTHOR]
ISSN:02562928
DOI:10.1007/s10212-026-01077-2