Developing Conceptions of Algebraic Reasoning in the Primary Grades. Research Report.

By T. P. Carpenter, L. Levi. 2000

98 citations recorded by the source corpus.

View Paper: https://www.semanticscholar.org/paper/e0c6564ebd917bc4482702a602428d62aa0eb6f4

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Citations in the corpus

Arithmetic and Algebra in Early Mathematics Education (2006, background): “Asothers have shown (Carpenter & Franke, 2001; Carpenter & Levi, 2000; Schifter, 1999), there are many opportunities for introducing algebraic oncepts into the curriculum during the early years of mathematics education.”
Professional development focused on children's algebraic reasoning in elementary school (2007, background): “…and researchers have provided evidence that even elementary school children are capable of making generalizations (Bastable & Schifter, in press; Blanton & Kaput, 2005; Carpenter & Levi, 2000; Carraher, Schliemann, Brizuela, & Earnest, 2006; Davis, 1964; Schifter, 1999; Tierney & Monk, in press).”
Middle School Mathematics Teachers' Knowledge of Students' Understanding of Core Algebraic Concepts: Equal Sign and Variable (2007, background): “The integration of algebra in the elementary grades implies recognition of algebraic reasoning as more than mastery of equation manipulation (Carpenter & Levi, 2000; Schifter, 1999) and involves viewing algebra as including new forms of reasoning accessible to students across the grades.”
Connections Between Generalizing and Justifying: Students' Reasoning with Linear Relationships (2007, background): “…which has led to a wealth of studies focused on the promotion of generalizing activities (Blanton & Kaput, 2000, 2002; Carpenter & Franke, 2001; Carpenter & Levi, 2000; Schliemann, Carraher, & Brizuela, 2001) and to the publication of curricula geared toward promoting generalizing activities…”
Content Knowledge for Teaching (2008, unknown): “Likewise, in the Cognitively Guided Instruction project, researchers found that students overgeneralize from experiences with problems in which the equals sign acts as a signal to compute (as it does in many programming languages) (Carpenter, Franke, & Levi, 2003; Carpenter & Levi, 2000).”
Knowledge Change as a Function of Mathematics Experience: All Contexts are Not Created Equal (2005, result): “In contrast, work by Carpenter and colleagues (Carpenter, Franke, & Levi, 2003; Carpenter & Levi, 2000) suggests that even first- and second-grade students have the potential to learn the relational interpretation of the equal sign in arithmetic contexts.”
Reasoning-and-proving opportunities in elementary mathematics textbooks (2014, background): “The absence of such problems in the written curriculum may indicate a key missed opportunity in curriculum development; Carpenter and Levi (2000) suggest that students may be able to recognize weaknesses in justifications at the elementary grades, while they are less likely to be able to produce…”