The conception of substitution of the equals sign plays a unique role in students' algebra performance

Students’ conceptions of the equals sign are related to algebraic success. Research has identified two common conceptions held by children: operational and relational. The latter has been widely operationalised in terms of the sameness of the values on each side of the equals sign, but it has been recently argued that the substitution component of relational equivalence should also be operationalised (Jones, Inglis, Gilmore, & Dowens, 2012, https://doi.org/10.1016/j.jecp.2012.05.003). In this study, we investigated whether students’ endorsement of the substitution definition of the equals sign is a unique predictor of their algebra performance independent of the other two definitions (operational and sameness). Secondary school students were asked to rate the ‘cleverness’ of operational, sameness, and substitution definitions of the equals sign and completed an algebra test. Our findings demonstrate that endorsement of substitution plays a unique role in explaining secondary school students’ algebra performance above and beyond school year and the other definitions. These findings contribute new insights into how students’ algebra learning relates to their conceptions of the equals sign. peerReviewed publishedVersion

学生对等号的认知与代数学习成效息息相关。过往研究已识别出儿童所持有的两种典型认知类型：运算性认知（operational conception）与关系性认知（relational conception）。后者常被基于等号两侧数值的等价性（sameness）进行操作化定义，但近期有研究指出，关系性等价性中的替换成分也应当被纳入操作化范畴（Jones, Inglis, Gilmore, & Dowens, 2012, https://doi.org/10.1016/j.jecp.2012.05.003）。本研究旨在探讨：相较于另外两种认知定义（运算性与数值等价性），学生对等号替换式定义（substitution definition）的认同程度，是否能独立预测其代数学习表现。研究招募中学生作为被试，要求他们对等号的运算性、数值等价性以及替换式三种定义的“巧妙程度”进行评分，并完成代数测试。本研究结果显示，相较于学年因素与另外两种定义，学生对替换式定义的认同程度，在解释中学生代数学习表现上具有独特的贡献价值。本研究为探究学生代数学习与对等号的认知之间的关联提供了全新视角。经同行评审的正式发表版本