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
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