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Article

Are Physical Experiences with the Balance Model Beneficial for Students’ Algebraic Reasoning? An Evaluation of two Learning Environments for Linear Equations

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Freudenthal Group, Faculty of Social and Behavioural Sciences, Utrecht University, Heidelberglaan 1, 3584 CS Utrecht, The Netherlands
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Faculty of Education and Arts, Nord University, 8026 Bodø, Norway
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iPabo University of Applied Sciences, 1061 AD Amsterdam, The Netherlands
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Department of Developmental Psychology, Utrecht University, Heidelberglaan 1, 3584 CS Utrecht, The Netherlands
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IPN—Leibniz Institute for Science and Mathematics Education, Olshausenstraße 62, D-24118 Kiel, Germany
*
Author to whom correspondence should be addressed.
Educ. Sci. 2020, 10(6), 163; https://doi.org/10.3390/educsci10060163
Received: 30 May 2020 / Revised: 8 June 2020 / Accepted: 15 June 2020 / Published: 17 June 2020
(This article belongs to the Special Issue Learning Environments)
The balance model is often used for teaching linear equation solving. Little research has investigated the influence of various representations of this model on students’ learning outcomes. In this quasi-experimental study, we examined the effects of two learning environments with balance models on primary school students’ reasoning related to solving linear equations. The sample comprised 212 fifth-graders. Students’ algebraic reasoning was measured four times over the school year; students received lessons in between two of these measurements. Students in Intervention Condition 1 were taught linear equation solving in a learning environment with only pictorial representations of the balance model, while students in Intervention Condition 2 were taught in a learning environment with both physical and pictorial representations of the balance model, which allowed students to manipulate the model. Multi-group latent variable growth curve modelling revealed a significant improvement in algebraic reasoning after students’ participation in either of the two intervention conditions, but no significant differences were found between intervention conditions. The findings suggest that the representation of the balance model did not differentially affect students’ reasoning. However, analyzing students’ reasoning qualitatively revealed that students who worked with the physical balance model more often used representations of the model or advanced algebraic strategies, suggesting that different representations of the balance model might play a different role in individual learning processes. View Full-Text
Keywords: early algebra; linear equation solving; balance model; representations; physical experiences early algebra; linear equation solving; balance model; representations; physical experiences
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MDPI and ACS Style

Otten, M.; van den Heuvel-Panhuizen, M.; Veldhuis, M.; Boom, J.; Heinze, A. Are Physical Experiences with the Balance Model Beneficial for Students’ Algebraic Reasoning? An Evaluation of two Learning Environments for Linear Equations. Educ. Sci. 2020, 10, 163. https://doi.org/10.3390/educsci10060163

AMA Style

Otten M, van den Heuvel-Panhuizen M, Veldhuis M, Boom J, Heinze A. Are Physical Experiences with the Balance Model Beneficial for Students’ Algebraic Reasoning? An Evaluation of two Learning Environments for Linear Equations. Education Sciences. 2020; 10(6):163. https://doi.org/10.3390/educsci10060163

Chicago/Turabian Style

Otten, Mara, Marja van den Heuvel-Panhuizen, Michiel Veldhuis, Jan Boom, and Aiso Heinze. 2020. "Are Physical Experiences with the Balance Model Beneficial for Students’ Algebraic Reasoning? An Evaluation of two Learning Environments for Linear Equations" Education Sciences 10, no. 6: 163. https://doi.org/10.3390/educsci10060163

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