Does Understanding the Equal Sign Matter? Evidence from Solving Equations

By Eric J. Knuth, Ana C. Stephens, Nicole M. McNeil, Martha W. Alibali. 2006

452 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/3f19ee19f7ea4b7745977c665994e0ab56aa2a8d

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Citations in the corpus

How to develop mathematics-for-teaching and for understanding: the case of meanings of the equal sign (2010, background): “Many researchers have emphasized the important distinction between two meanings for equality, namely, the operational and the relational meaning (Kieran 1981; Winter 1982; Wolters 1991; Filloy et al. 2003; Theis 2005; Knuth et al. 2006):”
Measure for Measure: what Combining Diverse Measures Reveals About Children's Understanding of the Equal Sign as an Indicator of Mathematical Equality (2012, methodology): “…Ambrose, 2006; Rittle-Johnson & Alibali, 1999; Seo & Ginsburg, 2003); and (c) equal-sign-definition items, such as asking children to provide an explicit verbal definition of what the equal sign means (Behr et al., 1980; Ginsburg, 1977; Knuth et al., 2006; McNeil et al. 2006; Seo & Ginsburg, 2003).”
Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable (2007, background): “A relational view of the equal sign is important when working with algebraic equations and is necessary for understanding that the transformations performed in solving an equation preserve the equivalence relation (Alibali et al., this issue; Kieran, 1992; Knuth et al., 2005; Knuth et al., 2006).”
Mother and Child Emotions during Mathematics Homework (2008, background): “Previous findings indicate that children have difficulty with such tasks, in part because they lack a conceptual understanding of the equal sign as an operation of equivalence ( Baroody & Ginsburg, 1983 ; Carpenter et al, 2003 ; Knuth, Stephens, McNeil, & Alibali, 2006 ; McNeil & Alibali, 2005 ).”
Students’ Reasoning With Reversible Multiplicative Relationships (2010, background): “Undoubtedly this nature of reasoning with reciprocal relationships is one reason that operating arithmetically on unknowns to solve equations is considered more solidly algebraic than undoing arithmetical operations to solve equations ( Bednarz & Janvier, 1996 ; Filloy & Rojano, 1989 ; Herscovics ”
Design-Based Research Within the Constraints of Practice: AlgebraByExample (2015, background): “…Stephens, McNeil, & Alibali, 2006); that negative signs represent only the subtraction operation and do not modify terms (Vlassis, 2004); that subtraction is commutative (Warren, 2003); and that variables cannot take on multiple values (L. R. Booth, 1984; Knuth et al., 2006; K€uchemann, 1978).”
Sources of Differences in Children's Understandings of Mathematical Equality: Comparative Analysis of Teacher Guides and Student Texts in China and the United States (2008, background): “& Nichols 1980; National Council of Teachers of Mathematics [NCTM], 2000; Sáenz-Ludlow & Walgamuth, 1998; Thompson & Babcock, 1978). Falkner, Levi, and Carpenter (1999) reported from their investigation in a single school of the problem “8 + 4 = a + 5”, all 145 sixth-graders filled the box with 12 o”