https://mathed.net/w/index.php?action=history&feed=atom&title=Carraher_%26_Schliemann_%282007%29 2026-09-19T17:22:41Z Revision history for this page on the wiki MediaWiki 1.43.8 https://mathed.net/w/index.php?title=Carraher_%26_Schliemann_(2007)&diff=1673&oldid=prev 2015-05-27T21:43:08Z

<p>Created page with &quot;{{Title|Early Algebra and Algebraic Reasoning}} * Authors: <a href="/wiki/David_Carraher" title="David Carraher">David W. Carraher</a> and <a href="/wiki/Anal%C3%BAcia_Schliemann" title="Analúcia Schliemann">Analúcia D. Schliemann</a> * Book: Second Handbook...&quot;</p> <p><b>New page</b></p><div>{{Title|Early Algebra and Algebraic Reasoning}}<br /> <br /> * Authors: [[David Carraher|David W. Carraher]] and [[Analúcia Schliemann|Analúcia D. Schliemann]]<br /> * Book: [[Second Handbook of Research on Mathematics Teaching and Learning]]<br /> * Year: 2007<br /> * Source: http://www.infoagepub.com/products/Second-Handbook-Research-Mathematics-Teaching-Learning<br /> <br /> ==Outline of Headings==<br /> * Why Algebraic Reasoning?<br /> * Rationale and Structure of Chapter<br /> ** The Recent Focus on Algebraic Reasoning in the Early Grades<br /> ** A Decisive Moment<br /> *** Event 1: NCTM&#039;s Endorsement<br /> *** Event 2: The RAND Mathematics Study Panel Report<br /> ** Five Key Issues<br /> *** Issue 1: The Relations Between Arithmetic and Algebra<br /> *** Issue 2: Process versus Object<br /> *** Issue 3: The Referential Role of Algebra<br /> *** Issue 4: Symbolic Representation (narrowly defined)<br /> *** Issue 5: Symbolic Representation (broadly defined)<br /> * A Traveler&#039;s Guide to Early Algebra<br /> ** School Algebra and EA<br /> ** EA Versus Pre-Algebra<br /> *** Pre-Algebra Approaches<br /> *** EA Approaches<br /> *** On the Possibilities of EA<br /> *** Parsing (Early) Algebra<br /> ** Algebra Is Latent in the Existing Early Mathematics Curriculum<br /> * Arithmetic and Numerical Reasoning as an Entry Point Into EA<br /> ** The Field Axioms and Other Properties of Numbers<br /> ** Studies That Introduce Algebra Through Generalizations About Numbers<br /> ** Quasi-Variables<br /> ** Summary: Numerical Reasoning and EA<br /> * Arithmetic and Quantitative Reasoning as an Entry Point Into EA<br /> ** Quantities, Measures, and Magnitudes<br /> ** Quantitative Thinking and Number Lines<br /> ** Can Students Apply Other Properties of Arithmetic to Magnitudes?<br /> ** Referent-Transforming Properties<br /> ** EA Studies that Focus on Magnitudes and Measures<br /> ** Why Quantitative Thinking Is Unavoidable in EA<br /> ** The Davydov Approach to EA<br /> ** The Measure Up Project<br /> ** Summary: Quantitative Reasoning and EA<br /> * Arithmetic and Functions as an Entry Point Into EA<br /> ** Can Young Students Reason with Functions?<br /> ** Functions As Rules for Generating Collections of Figures<br /> ** Functions Expressed Through Multiple Representations: The Early Algebra, Early Arithmetic Project<br /> ** Summary: What Can Young Student Learn About Functions?<br /> * Concluding Thoughts<br /> ** What Kinds of Representations Express Algebraic Ideas?<br /> ** Patterns and Functions<br /> *** Issues Common to Patterns and Tables<br /> ** Is a Scalar Approach Valid?<br /> ** What Goals Are Achievable in the Short Term, Mid Term, and Long Term (for Students and Teachers)?<br /> <br /> ==Corrolary==<br /> ;APA<br /> : Carraher, D. W., &amp; Schliemann, A. D. (2007). Early algebra and algebraic reasoning. In F. K. Lester (Ed.), &#039;&#039;Second handbook of research on mathematics teaching and learning&#039;&#039; (pp. 669–705). Charlotte, NC: Information Age.<br /> ;BibTeX<br /> &lt;pre&gt;<br /> @incollection{Carraher2007,<br /> address = {Charlotte, NC},<br /> author = {Carraher, David W. and Schliemann, Anal\&#039;{u}cia D.},<br /> booktitle = {Second handbook of research on mathematics teaching and learning},<br /> chapter = {15},<br /> editor = {Lester, Frank K.},<br /> pages = {669--705},<br /> publisher = {Information Age},<br /> title = {{Early algebra and algebraic reasoning}},<br /> year = {2007}<br /> }<br /> &lt;/pre&gt;<br /> <br /> [[Category:Book Chapters]]<br /> [[Category:2007]]<br /> [[Category:Early Algebra]]<br /> [[Category:Algebraic Reasoning]]</div>

imported>Raymond Johnson