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Araya, R., Calfucura, P., Jiménez, A., Aguirre, C., Palavicino, M. A., Lacourly, N., Soto-Andrade, J., & Dartnell, P. (2010). The Effect of Analogies on Learning to Solve Algebraic Equations. Pedagogies: An International Journal, 5, 216-232.
https://doi.org/10.1080/1554480X.2010.486160

has been cited by the following article:

• TITLE: Hands-On Equations Balance Model Enhances Algebraic Equation Solving in Upper Elementary and Middle School Students

  AUTHORS: Henry Borenson

  KEYWORDS: Balance Model, Teaching Linear Equations, Early Algebra, Isomorphism, Math Manipulatives, Hands-On Equations

  JOURNAL NAME: Creative Education, Vol.14 No.8, August 28, 2023

  ABSTRACT: The struggle of students to solve algebraic equations has been identified as a major challenge in mathematics education. This study investigated the effectiveness of the Hands-On Equations? early algebra balance model in improving the equation-solving skills of upper elementary and middle school students. Fourth-grade (n = 123) and eighth-grade (n = 105) students from the United States participated in this study. A pretest-to-posttest design was used to evaluate the performance of the students on six algebraic equations, including three equations with the unknown on both sides of the equal sign. The results showed that eighth graders outperformed fourth graders on the benchmark pretest. However, after seven lessons using this balance model, the fourth graders showed a statistically significant gain of three standard deviations, outperforming the eighth-grade pretest scores. The model helped the younger students to make sense of formal algebraic notation, the relational meaning of the equal sign, and the subtraction property of equality, which are essential concepts for future algebraic studies. The study also found a statistically significant gain in the eighth graders’ performance with a moderate effect size. Therefore, upper elementary and middle school students should use this algebra balance model to enhance their equation-solving ability.