The balance model for teaching linear equations: a systematic literature review

Abstract

This paper reports a systematic literature review of the balance model, an often-used aid to teach linear equations. The purpose of the review was to report why such a model is used, what types of models are used, and when they are used. In total, 34 peer-reviewed journal articles were analyzed, resulting in a comprehensive overview of described rationales for using the balance model, its appearances, situations in which it was used, and the gained learning outcomes. Some trends appeared about how rationales, appearances, situations, and learning outcomes are related. However, a clear pattern could not be identified. Our study shows that this seemingly simple model actually is a rather complex didactic tool of which in-depth knowledge is lacking. Further systematic research is needed for making informed instructional decisions on when and how balance models can be used effectively for teaching linear equation solving.

Assessing the Effect of an Ethnomathematics Teaching Material on Students’ Understanding of Mathematics

“…Question 1 requires simpler and straightforward calculation, while question 2 requires more complex manipulations of variables such as elimination and substitution strategies. In their review, Otten et al (2019) summarize that the basic knowledge needed to solve a linear equation problem is the concept of balance or equality. Through the activity of solving a linear equation, a student must keep in mind that the mathematical expressions on the right and left sides of the equal sign have the same value, and then the student should be able to carry out necessary calculation to solve a linear equation problem whether it is with one or two variables.…”

The Potentials of Tangible Technologies for Learning Linear Equations

“…Mastering equation solving is often challenging for students, e.g., [2,[21][22][23]. To learn how to solve equations, students need to understand several concepts.…”

“…Promote understanding of equation solving: A manipulative should assist students in learning equation solving by concretising the concepts of mathematical equivalence [21], different terms in an equation [22], and equation solving [23]. DP 2.…”

“…This algebraic strategy was chosen because of its emphasis on the equivalence principle (DP 1). The balance model is used as a didactic model to assist students' understanding of linear equation solving [23]. Either side of the scale represents either side of the equation, while the movement of the scale (tilting or balance) represents the equality of the mathematical expressions on either side of the equation.…”

Research and trends in STEM education: a systematic analysis of publicly funded projects

“…The rapid development of science, technology, engineering, and mathematics (STEM) education and research since the beginning of this century has benefited from strong, ongoing support from many different entities, including government agencies, professional organizations, industries, and education institutions (Li, 2014). Typically, studies that summarized the status of research in STEM education have used publications as the unit of their analyses (e.g., Li et al, 2020;Margot & Kettler, 2019;Minichiello et al, 2018;Otten, Van den Heuvel-Panhuizen, & Veldhuis, 2019;Schreffler et al, 2019). Another approach, which has been used less frequently, is to study research funding.…”