Thinking Mathematically : Integrating Arithmetic and Algebra in Elementary School

By T. P. Carpenter, M. Franke, L. Levi. 2003

642 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/5d9d070e29e16c24c90d567b61ae72d2adb16d49

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Citations in the corpus

Teacher Questioning to Elicit Students’ Mathematical Thinking in Elementary School Classrooms (2009, background): “We also paid attention to the types of explanations that students gave in relation to our algebraic reasoning work (specifically, computational and relational thinking explanations; see Carpenter et al., 2003).”
A Is for Apple: Mnemonic Symbols Hinder the Interpretation of Algebraic Expressions (2010, background): “Within this approach, even very young students are frequently taught to use literal symbols as tools for expressing intuitive ideas about varying quantities in real-world problem situations (Carraher et al., 2006; Schoenfeld & Arcavi, 1988; Stephens, 2005). Third-grade students in Carraher et al.’s ”
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).”
Algebra in elementary school: Developing relational thinking (2005, background): “Essentially what algorithms do is to use basic properties of number operations to reduce complex calculations to simpler calculations that can be carried out using well-known procedures or knowledge of number facts (Carpenter et al. 2003).”
A Comparative Analysis of the Distributive Property in U.S. and Chinese Elementary Mathematics Textbooks (2010, background): “Our findings suggest that the Chinese text approach to the DP may play an important role in this and demonstrate how an understanding of the DP could pay a big dividend in the upper elementary grades (Carpenter et al., 2003).”
Does Understanding the Equal Sign Matter? Evidence from Solving Equations (2006, methodology): “Carpenter et al. (2003) questioned the meaning such students might make of the procedures one might use to solve equations such as 5x + 32 = 97 (starting with subtracting 32 from each side resulting in 5x + 32 - 32 = 97 - 32): "What kind of meaning can students who exhibit ... misconceptions of the…”
Early algebra and mathematical generalization (2008, background): “Carpenter, Franke, and Levi (2003), Carpenter and Franke (2001) and Carpenter and Levi (2000) show fairly young children talking meaningfully about the truth or falsity of issues such as ‘‘Is it true that a + b - b = a, for any numbers a and b?’’ and producing generalizations about arithmetical…”
Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable (2007, background): “…algebraic reasoning throughout the K–8 curriculum, however, researchers have begun to move toward teachers’ knowledge of student thinking in the domain of early algebra in elementary school mathematics (e.g., Blanton & Kaput, 2003; Carpenter et al., 2003; Kaput et al., 2007; Stephens, 2006).”
Obstacles and Affordances for Integer Reasoning: An Analysis of Children's Thinking and the History of Mathematics (2014, background): “Initially, the content focus of CGI was on whole number operations (addition, subtraction, multiplication, and division), but it has been expanded to include base-ten concepts, algebraic reasoning (Carpenter et al., 2003), and fractions and decimals (Empson, 1999, 2001; Empson & Levi, 2011).”