Arithmetic and Algebra in Early Mathematics Education

By David W. Carraher, A. Schliemann, B. Brizuela, D. Earnest. 2006

342 citations recorded by the source corpus.

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Citations in the corpus

Teaching Conceptual Model—Based Word Problem Story Grammar to Enhance Mathematics Problem Solving (2008, unknown): “As suggested by Booth (1988), “students’ difficulties with algebra may result from the limited ways that they are taught about arithmetic and elementary mathematics” (Carraher et al., 2006, p. 92).”
A Longitudinal Examination of Middle School Students' Understanding of the Equal Sign and Equivalent Equations (2007, background): “For example, Falkner et al. (1999) found that a substantial number of first- through sixth-grade students’ solutions to the equation 8 + 4 = + 5 included 12, 17, or 12 and 17—solutions that are consistent with a view of the equal sign as announcing the result of an arithmetic operation. Although the”
Relationships between Students' Fractional Knowledge and Equation Writing. (2015, background): “Much of the research on early algebra focuses on how students may transform their whole-number knowledge to develop algebraic ideas (e.g., Bastable & Schifter, 2008; Carpenter, Franke, & Levi, 2003; Carraher et al., 2006).”
A Is for Apple: Mnemonic Symbols Hinder the Interpretation of Algebraic Expressions (2010, background): “Thus, materials based on this approach seem to help children develop a conceptual understanding of variables (Blanton & Kaput, 2005; Brizuela & Schliemann, 2004; Carraher et al., 2006; Kaput, 2000).”
A Comparison of Two Mathematics Problem-Solving Strategies: Facilitate Algebra-Readiness (2011, background): “The good news is that elementary students, those with learning disabilities or problems (LP) in particular, are able to benefit from experiences that prepare them for algebra readiness in their elementary mathematics learning (Carraher, Schliemann, Brizuela, & Earnest, 2006 ; Xin, 2008 ; Xin, Wile”
A Learning Trajectory in 6-Year-Olds' Thinking about Generalizing Functional Relationships. (2015, background): “Age Difference: If Janice is 2 years younger than Keisha, the relationship between Keisha’s age and Janice’s age (Carraher et al., 2006).”
Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable (2007, background): “The impact of this reconceptualization has been most apparent in elementary school, where mathematics educators have recently made concerted efforts to integrate algebraic ideas (e.g., Carpenter, Franke, & Levi, 2003; Carraher, Schliemann, Brizuela, & Earnest, 2006; Kaput, Carraher, & Blanton, 200”
Assessing the Development of Preschoolers' Mathematical Patterning (2011, background): “However, there remain many unanswered questions about how and when early algebraic thinking develops in the years prior to formal schooling (Carraher et al., 2006; Sarama & Clements, 2009).”
Towards understanding the origins of children's difficulties in mathematics learning (2011, background): “Pre-algebraic thinking also develops through a structural awareness of patterns (Carraher et al., 2006).”