Is a Substitute the Same? Learning from Lessons Centering Different Relational Conceptions of the Equal Sign

Autor/inn/en	Donovan, Andrea Marquardt; Stephens, Ana; Alapala, Burcu; Monday, Allison; Szkudlarek, Emily; Alibali, Martha W.; Matthews, Percival G.
Titel	Is a Substitute the Same? Learning from Lessons Centering Different Relational Conceptions of the Equal Sign
Quelle	In: ZDM: Mathematics Education, 54 (2022) 6, S.1199-1213 (15 Seiten)Infoseite zur Zeitschrift PDF als Volltext Verfügbarkeit
Zusatzinformation	ORCID (Stephens, Ana)
Sprache	englisch
Dokumenttyp	gedruckt; online; Zeitschriftenaufsatz
ISSN	1863-9690
DOI	10.1007/s11858-022-01405-y
Schlagwörter	Algebra; Elementary School Mathematics; Symbols (Mathematics); Mathematical Concepts; Problem Solving; Grade 4; Grade 5; Definitions + Suchen Sie Ihr Suchwort? Elementare Mathematik; Schulmathematik; Problemlösen; School year 04; 4. Schuljahr; Schuljahr 04; School year 05; 5. Schuljahr; Schuljahr 05; Begriffsbestimmung
Abstract	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. (As Provided).
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Erfasst von	ERIC (Education Resources Information Center), Washington, DC
Update	2024/1/01