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Direct and Inverse Functions in Pre-school: A Case Study with a 4 Year-Old.

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Title: Direct and Inverse Functions in Pre-school: A Case Study with a 4 Year-Old.
Authors: Fuentes, Sandra1 (AUTHOR) sandrafuentesm@gmail.com, Cañadas, María C.1 (AUTHOR) mconsu@ugr.es
Source: Early Childhood Education Journal. Jan2026, Vol. 54 Issue 1, p357-369. 13p.
Subject Terms: *Visual aids, *Early childhood education, *Cognitive ability, Inverse functions, Mathematical functions, Scientific observation
Abstract: This paper is part of a broader research initiative examining algebraic thinking. It presents a case study involving a 4 year-old female student, examining her functional perspective through individual work. Our interest lies in early childhood functional thinking. Specifically, our research objective is to describe how the child completed two tasks involving linear functions and their respective inverse functions. We posed questions related to specific near numbers, specific far numbers, and the generalizations themselves. We gathered data from her individual written work on the two tasks and from an individual interview. We analyzed the strategies she employed to generalize, the representations and generalizations she made, and how she established relationships between variables. We observed that she used pictorial and verbal representations to complete the proposed tasks and successfully achieved generalization. As a strategy, she counted drawings; however, when verbalizing her approach, she created groups of similar elements and innately distributed them into equal groups when working with the inverse function. [ABSTRACT FROM AUTHOR]
Copyright of Early Childhood Education Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract. (Copyright applies to all Abstracts.)
Database: Education Research Complete
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  Data: <searchLink fieldCode="JN" term="%22Early+Childhood+Education+Journal%22">Early Childhood Education Journal</searchLink>. Jan2026, Vol. 54 Issue 1, p357-369. 13p.
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  Data: *<searchLink fieldCode="DE" term="%22Visual+aids%22">Visual aids</searchLink><br />*<searchLink fieldCode="DE" term="%22Early+childhood+education%22">Early childhood education</searchLink><br />*<searchLink fieldCode="DE" term="%22Cognitive+ability%22">Cognitive ability</searchLink><br /><searchLink fieldCode="DE" term="%22Inverse+functions%22">Inverse functions</searchLink><br /><searchLink fieldCode="DE" term="%22Mathematical+functions%22">Mathematical functions</searchLink><br /><searchLink fieldCode="DE" term="%22Scientific+observation%22">Scientific observation</searchLink>
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  Data: This paper is part of a broader research initiative examining algebraic thinking. It presents a case study involving a 4 year-old female student, examining her functional perspective through individual work. Our interest lies in early childhood functional thinking. Specifically, our research objective is to describe how the child completed two tasks involving linear functions and their respective inverse functions. We posed questions related to specific near numbers, specific far numbers, and the generalizations themselves. We gathered data from her individual written work on the two tasks and from an individual interview. We analyzed the strategies she employed to generalize, the representations and generalizations she made, and how she established relationships between variables. We observed that she used pictorial and verbal representations to complete the proposed tasks and successfully achieved generalization. As a strategy, she counted drawings; however, when verbalizing her approach, she created groups of similar elements and innately distributed them into equal groups when working with the inverse function. [ABSTRACT FROM AUTHOR]
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  Data: <i>Copyright of Early Childhood Education Journal is the property of Springer Nature and its content may not be copied or emailed to multiple sites without the copyright holder's express written permission. Additionally, content may not be used with any artificial intelligence tools or machine learning technologies. However, users may print, download, or email articles for individual use. This abstract may be abridged. No warranty is given about the accuracy of the copy. Users should refer to the original published version of the material for the full abstract.</i> (Copyright applies to all Abstracts.)
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              Text: Jan2026
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