Pre-algebraic aspects in arithmetic strategies – The generalization and conceptual understanding of the ‘Auxiliary Task’

Taha Ertuğrul Kuzu

doi:10.29333/ejmste/12656

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Taha Ertuğrul Kuzu ¹ ^*

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¹ University of Münster, Münster, GERMANY^* Corresponding Author

Abstract

In the last decades, a broad international reform approach was visible in support of mental calculation strategies: Instead of being solely ‘transition strategies’ for learning the standard algorithms, the understanding of numerical relations is essential for mental calculation strategies, making them highly important for a viable understanding of arithmetics. Yet, mental calculation strategies are not only important for understanding arithmetics, but highly relational strategies such as the ‘Auxiliary Task’ might have an important role in the emergence of a pre-algebraic understanding of numerical relations. In this qualitative study from Germany, 4^th and 5^th grade learners’ (n=18) processes of interpreting the ‘Auxiliary Task’ are examined by conducting linguistic and epistemological analyzes of their conceptual understanding of the ‘Auxiliary Task’ utilizing a design-based research framework. Insights are given into specific, language-related forms of pre-algebraic generalizations of the ‘Auxiliary Task’ as well as into developmental processes within the designed learning-environment.

Keywords

Auxiliary Task
cognitive gap
design-based research
pre-algebraic thinking

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This is an open access article distributed under the Creative Commons Attribution License which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.

Article Type: Research Article

EURASIA J Math Sci Tech Ed, Volume 18, Issue 12, December 2022, Article No: em2192

https://doi.org/10.29333/ejmste/12656

Publication date: 20 Nov 2022

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Article Downloads: 1110

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How to cite this article

APA

Kuzu, T. E. (2022). Pre-algebraic aspects in arithmetic strategies – The generalization and conceptual understanding of the ‘Auxiliary Task’. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2192. https://doi.org/10.29333/ejmste/12656

Vancouver

Kuzu TE. Pre-algebraic aspects in arithmetic strategies – The generalization and conceptual understanding of the ‘Auxiliary Task’. EURASIA J Math Sci Tech Ed. 2022;18(12):em2192. https://doi.org/10.29333/ejmste/12656

AMA

Kuzu TE. Pre-algebraic aspects in arithmetic strategies – The generalization and conceptual understanding of the ‘Auxiliary Task’. EURASIA J Math Sci Tech Ed. 2022;18(12), em2192. https://doi.org/10.29333/ejmste/12656

Chicago

Kuzu, Taha Ertuğrul. "Pre-algebraic aspects in arithmetic strategies – The generalization and conceptual understanding of the ‘Auxiliary Task’". Eurasia Journal of Mathematics, Science and Technology Education 2022 18 no. 12 (2022): em2192. https://doi.org/10.29333/ejmste/12656

Harvard

Kuzu, T. E. (2022). Pre-algebraic aspects in arithmetic strategies – The generalization and conceptual understanding of the ‘Auxiliary Task’. Eurasia Journal of Mathematics, Science and Technology Education, 18(12), em2192. https://doi.org/10.29333/ejmste/12656

MLA

Kuzu, Taha Ertuğrul "Pre-algebraic aspects in arithmetic strategies – The generalization and conceptual understanding of the ‘Auxiliary Task’". Eurasia Journal of Mathematics, Science and Technology Education, vol. 18, no. 12, 2022, em2192. https://doi.org/10.29333/ejmste/12656