Solving algebraic equations by using the bar model: Theoretical and empirical considerations

Anna-Katharina Roos; Leander Kempen

doi:10.29333/ejmste/15147

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Anna-Katharina Roos ¹ , Leander Kempen ² ^*

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¹ Institute for Development and Research in Mathematics Education, TU Dortmund University, Dortmund, GERMANY² Institute of Mathematics and Computer Science, University of Greifswald, Greifswald, GERMANY^* Corresponding Author

Abstract

Solving equations is known to bear several challenges for learners. We discuss an approach based on conceptual understanding regarding the transformation of equations with the help of the so-called bar model in combination with the transposing strategy. First, we sketch shortly the main ideas that guided the development of the learning environment. Second, we discuss insights from the first design experiments with six students working with equation transformation in their regular school curriculum. These design experiments are embedded in a design research approach. In particular, we zoom into the semiotic processes of how learners connect several representations and emphasize a varying difficulty regarding single concept elements necessary to understand the concept of equivalent equations as a whole. Based on that, obstacles that come along with using the bar model are highlighted. Finally, we point to theoretical insights and implications for enhancing our learning environment.

Keywords

algebra
bar model
solving equations
multiple representations
conceptual understanding

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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 20, Issue 9, September 2024, Article No: em2505

https://doi.org/10.29333/ejmste/15147

Publication date: 10 Sep 2024

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Article Downloads: 96

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How to cite this article

APA

Roos, A.-K., & Kempen, L. (2024). Solving algebraic equations by using the bar model: Theoretical and empirical considerations. Eurasia Journal of Mathematics, Science and Technology Education, 20(9), em2505. https://doi.org/10.29333/ejmste/15147

Vancouver

Roos AK, Kempen L. Solving algebraic equations by using the bar model: Theoretical and empirical considerations. EURASIA J Math Sci Tech Ed. 2024;20(9):em2505. https://doi.org/10.29333/ejmste/15147

AMA

Roos AK, Kempen L. Solving algebraic equations by using the bar model: Theoretical and empirical considerations. EURASIA J Math Sci Tech Ed. 2024;20(9), em2505. https://doi.org/10.29333/ejmste/15147

Chicago

Roos, Anna-Katharina, and Leander Kempen. "Solving algebraic equations by using the bar model: Theoretical and empirical considerations". Eurasia Journal of Mathematics, Science and Technology Education 2024 20 no. 9 (2024): em2505. https://doi.org/10.29333/ejmste/15147

Harvard

Roos, A.-K., and Kempen, L. (2024). Solving algebraic equations by using the bar model: Theoretical and empirical considerations. Eurasia Journal of Mathematics, Science and Technology Education, 20(9), em2505. https://doi.org/10.29333/ejmste/15147

MLA

Roos, Anna-Katharina et al. "Solving algebraic equations by using the bar model: Theoretical and empirical considerations". Eurasia Journal of Mathematics, Science and Technology Education, vol. 20, no. 9, 2024, em2505. https://doi.org/10.29333/ejmste/15147