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RESEARCH PAPER
Solving algebraic equations by using the bar model: Theoretical and empirical considerations
1
Institute for Development and Research in Mathematics Education, TU Dortmund University, Dortmund, GERMANY
2
Institute of Mathematics and Computer Science, University of Greifswald, Greifswald, GERMANY
Publication date: 2024-09-10
EURASIA J. Math., Sci Tech. Ed 2024;20(9):em2505
KEYWORDS
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.
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