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Plenty of literature has highlighted elementary students’ misinterpretation and difficulty in dealing with an equal sign at different grade levels (e.g., Jones, Inglis, Gilmore & Evans, 2013; Sherman & Bisanz, 2009; Stephens et al., 2013). Studies have suggested various tools to develop a relational understanding of equality (e.g., Ellis & Yeh, 2008; Jones & Pratt, 2006). Leavy, Hourigan, and McMahon (2013) reported evidence of a relational understanding of the equal sign, rather than an operational understanding, in elementary students’ work when using a physical balance. In this study, we investigate how often elementary students use their relational understanding of equality using a balance to write a balanced equation of the given situation.
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Is a substitute the same? Learning from lessons centering different relational conceptions of the equal sign
Understanding of the equal sign is associated with early algebraic competence in the elementary grades and equation solving success in middle school. Thus, it is important to find ways to build foundational understanding of the equal sign as a relational symbol. Past work promoted a conception of the equal sign as meaning “the same as”. However, recent work highlights another dimension of relational understanding—a substitutive conception, which emphasizes the idea that an expression can be substituted for another equivalent one. This work suggests a substitutive conception may support algebra performance above and beyond a sameness conception alone. In this paper, we share a subset of results from an online intervention designed to foster a relational understanding of the equal sign among fourth and fifth graders (n = 146). We compare lessons focused on a sameness conception alone and a dual sameness and substitutive conception to each other, and we compare both to a control condition. The lessons influenced students’ likelihood of producing and endorsing sameness and substitutive definitions of the equal sign. However, the impact of the lessons on students’ approaches to missing value equations was less clear. We discuss possible interpretations, and we argue that further research is needed to explore the roles of sameness and substitutive views of the equal sign in supporting structural approaches to algebraic equation solving.
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- Award ID(s):
- 1824182
- PAR ID:
- 10357260
- Date Published:
- Journal Name:
- ZDM – Mathematics Education
- ISSN:
- 1863-9690
- Format(s):
- Medium: X
- Sponsoring Org:
- National Science Foundation
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- Free Publicly Accessible Full Text
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Accepted Manuscript1.0
- Journal Article:
- https://doi.org/10.1007/s11858-022-01405-y
