%0 Journal Article
%T Hands-On Equations Balance Model Enhances Algebraic Equation Solving in Upper Elementary and Middle School Students
%A Henry Borenson
%J Creative Education
%P 1600-1620
%@ 2151-4771
%D 2023
%I Scientific Research Publishing
%R 10.4236/ce.2023.148104
%X The struggle of students to solve algebraic equations
has been identified as a major challenge in mathematics education. This study
investigated the effectiveness of <a name=\"_Hlk135682365\"></a>the Hands-On Equations<span><sup><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"><span style=\"font-size:12.0pt;font-family:ËÎÌå;color:black;\">?</span></span></sup><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"> early algebra balance model in improv<span>ing
the equation-solving skills of upper elementary and middle school stu</span>dents</span></span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">. Fourth</span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">-grade (<i>n</i> = 123) and
eighth-grade (<i>n</i> = 105) students from
the <a name=\"_Hlk135682423\"></a>United States participated in this study. </span><span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">A </span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">pretest-to-posttest</span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"> design was used <span>to evaluate the
performance of </span></span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">the students </span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">on six algebraic equations, in</span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">cluding three equations with the unknown on both
sides of the equal sign.</span></span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"> The results showed that </span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">eighth</span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"> graders outperformed fourth graders on the <span>benchmark pretest. However, after seven lessons using this balance model,</span> the fourth <span>graders showed a statistically
significant gain of three standard deviations</span>, <span>outperforming the </span></span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">eighth</span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">-grade pretest scores. The model helped the
younger</span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"> stu<span>dents to make sense of formal
algebraic notation, the relational meaning of</span> the equal sign, and the
subtraction property of equality, which are <span>essential
concepts for future algebraic studies. The study also found a</span> statisti<span>cally significant gain in the </span></span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\">eighth</span><span style=\"font-size:10.0pt;font-family:;\" \"=\"\"> graders¡¯ performance with a
%K Balance Model
%K Teaching Linear Equations
%K Early Algebra
%K Isomorphism
%K Math Manipulatives
%K Hands-On Equations
%U http://www.scirp.org/journal/PaperInformation.aspx?PaperID=127269