imported>Raymond Johnson |
imported>Raymond Johnson |
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| {{Title|Early Algebra and Algebraic Reasoning}}
| | ==Publications== |
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| * Authors: [[David Carraher|David W. Carraher]] and [[Analúcia Schliemann|Analúcia D. Schliemann]]
| | [[Edward Silver|Silver, E. A.]], & [[Patricio Herbst|Herbst, P. G.]] (2007). [[Silver & Herbst (2007)|Theory in mathematics education scholarship]]. In [[Frank Lester|F. K. Lester]] (Ed.), ''[[Second handbook of research on mathematics teaching and learning]]'' (pp. 39–67). Charlotte, NC: Information Age. |
| * Book: [[Second Handbook of Research on Mathematics Teaching and Learning]]
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| * Year: 2007
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| * Source: http://www.infoagepub.com/products/Second-Handbook-Research-Mathematics-Teaching-Learning
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| ==Outline of Headings==
| | [[Category:People|Herbst, Patricio]] |
| * Why Algebraic Reasoning?
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| * Rationale and Structure of Chapter
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| ** The Recent Focus on Algebraic Reasoning in the Early Grades
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| ** A Decisive Moment
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| *** Event 1: NCTM's Endorsement
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| *** Event 2: The RAND Mathematics Study Panel Report
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| ** Five Key Issues
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| *** Issue 1: The Relations Between Arithmetic and Algebra
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| *** Issue 2: Process versus Object
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| *** Issue 3: The Referential Role of Algebra
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| *** Issue 4: Symbolic Representation (narrowly defined)
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| *** Issue 5: Symbolic Representation (broadly defined)
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| * A Traveler's Guide to Early Algebra
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| ** School Algebra and EA
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| ** EA Versus Pre-Algebra
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| *** Pre-Algebra Approaches
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| *** EA Approaches
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| *** On the Possibilities of EA
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| *** Parsing (Early) Algebra
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| ** Algebra Is Latent in the Existing Early Mathematics Curriculum
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| * Arithmetic and Numerical Reasoning as an Entry Point Into EA
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| ** The Field Axioms and Other Properties of Numbers
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| ** Studies That Introduce Algebra Through Generalizations About Numbers
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| ** Quasi-Variables
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| ** Summary: Numerical Reasoning and EA
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| * Arithmetic and Quantitative Reasoning as an Entry Point Into EA
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| ** Quantities, Measures, and Magnitudes
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| ** Quantitative Thinking and Number Lines
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| ** Can Students Apply Other Properties of Arithmetic to Magnitudes?
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| ** Referent-Transforming Properties
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| ** EA Studies that Focus on Magnitudes and Measures
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| ** Why Quantitative Thinking Is Unavoidable in EA
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| ** The Davydov Approach to EA
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| ** The Measure Up Project
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| ** Summary: Quantitative Reasoning and EA
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| * Arithmetic and Functions as an Entry Point Into EA
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| ** Can Young Students Reason with Functions?
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| ** Functions As Rules for Generating Collections of Figures
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| ** Functions Expressed Through Multiple Representations: The Early Algebra, Early Arithmetic Project
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| ** Summary: What Can Young Student Learn About Functions?
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| * Concluding Thoughts
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| ** What Kinds of Representations Express Algebraic Ideas?
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| ** Patterns and Functions
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| *** Issues Common to Patterns and Tables
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| ** Is a Scalar Approach Valid?
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| ** What Goals Are Achievable in the Short Term, Mid Term, and Long Term (for Students and Teachers)?
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| ==Corrolary==
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| ;APA
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| : Carraher, D. W., & Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), ''Second handbook of research on mathematics teaching and learning'' (pp. 669–705). Charlotte, NC: Information Age.
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| ;BibTeX
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| <pre>
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| @incollection{Carraher2007,
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| address = {Charlotte, NC},
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| author = {Carraher, David W. and Schliemann, Anal\'{u}cia D.},
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| booktitle = {Second handbook of research on mathematics teaching and learning},
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| chapter = {15},
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| editor = {Lester, Frank K.},
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| pages = {669--705},
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| publisher = {Information Age},
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| title = {{Early algebra and algebraic reasoning}},
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| year = {2007}
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| }
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| </pre>
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| [[Category:Book Chapters]] | |
| [[Category:2007]]
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| [[Category:Early Algebra]]
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| [[Category:Algebraic Reasoning]]
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