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<p>Created page with &quot;{{Title|Learning and Teaching Algebra at the Middle School Through College Levels: Building Meaning for Symbols and Their Manipulation}} * Author: <a href="/wiki/Carolyn_Kieran" title="Carolyn Kieran">Carolyn Kieran</a> * Book: ...&quot;</p> <p><b>New page</b></p><div>{{Title|Learning and Teaching Algebra at the Middle School Through College Levels: Building Meaning for Symbols and Their Manipulation}}<br /> <br /> * Author: [[Carolyn Kieran]]<br /> * Book: &#039;&#039;[[Second Handbook of Research on Mathematics Teaching and Learning]]&#039;&#039;<br /> * Year: 2007<br /> * Source: http://www.infoagepub.com/products/Second-Handbook-Research-Mathematics-Teaching-Learning<br /> <br /> == Outline of Headings ==<br /> <br /> * Part 1. School Algebra: Background Issues and Theoretical Considerations<br /> ** The Current Content of School Algebra: Competing Views<br /> ** Sources of Meaning<br /> *** Algebraic Meaning: Where Does It Come From?<br /> *** Meaning From the Algebraic Structure Itself, Involving the Letter-Symbolic Form<br /> *** Meaning From Other Mathematical Representations, Including Multiple Representations<br /> *** Meaning From the Problem Context<br /> *** Meaning Derived From That Which Is Exterior to the Mathematics/Problem Context<br /> ** Models for Conceptualizing Algebraic Activity<br /> * Part 2. School Algebra: Findings from Research Studies<br /> ** The Middle Grade and Lower Secondary Level Student<br /> *** Background: International Assessments<br /> *** Generational Activity: The Middle Grade and Lower Secondary Student<br /> **** Generational Activity with a Primary Focus on the Letter-Symbolic Form<br /> ***** Variables, Expressions, and Equations<br /> ***** The Minus Sign and Negative Numbers<br /> ***** Beginnings of Structure Sense<br /> **** Generational Activity with Multiple Representations<br /> ***** Tabular Representations and the Letter-Symbolic<br /> ***** Graphical Representations and the Letter-Symbolic<br /> ***** Connections Among Representations<br /> **** Generational Activity Within the Context of Word Problems<br /> ***** Generating Multiple Representations in the Solving of Word Problems<br /> ***** Generating Equations in the Solving of Word Problems<br /> *** Transformational Activity: The Middle Grade and Lower Secondary Level Student<br /> **** Theoretical Elements of Transformational Activity: Equivalence and Theoretical Control<br /> **** Technical Elements of Transformational Activity: Expressions, Equations, and Equation Solving<br /> **** The Use of Concrete Manipulatives in Transformational Activity<br /> *** Global/Meta-Level Activity: The Middle Grade and Lower Secondary Level Student<br /> **** Global/Meta-Level Activity Involving Generalizing<br /> **** Global/Meta-Level Activity Involving Proof and Proving<br /> **** Global/Meta-Level Activity Involving Modeling<br /> *** The Impact of Technology on Algebraic Activity With the Middle Grade and Lower Secondary Level Student<br /> *** Concluding Remarks on the Algebra Research Involving the Middle Grade and Lower Secondary Level Student<br /> ** The Upper Secondary and College Level Student<br /> *** Generational Activity: The Upper Secondary and College Level Student<br /> **** Generational Activity With a Primary Focus on the Letter-Symbolic Form<br /> ***** Form and structure<br /> ***** On parameters<br /> **** Generational Activity with Multiple Representations<br /> ***** Functions and Their Meaning<br /> ***** The Interplay Between Symbolic and Graphical Representations and the Role of Visualization<br /> *** Transformational Activity: The Upper Secondary and College Level Student<br /> **** Transformational Activity Related to Notions of Equivalence<br /> **** Transformational Activity Related to Expressions and Inequalities<br /> **** Transformational Activity Related to Factoring Expressions<br /> **** Transformational Activity Involving the Integration of Graphical and Symbolic Work<br /> *** Global/Meta-Level Activity: The Upper Secondary and College Level Student<br /> **** Global/Meta-Level Activity Involving Problem Solving<br /> **** Global/Meta-Level Activity Involving Modeling<br /> *** The Impact of Technology on Algebraic Activity With the Upper Secondary and College Level Student<br /> **** Large-Scale Studies on the Effects of Technology Use<br /> ***** Calculators<br /> ***** Graphing Calculators<br /> ***** Computer Algebra Systems (CAS)<br /> **** Technology and the Changing Roles of Students and Teachers<br /> *** Concluding Remarks on the Algebra Research Involving the Upper Secondary and College Level Student<br /> ** Algebra Teaching and the Algebra Teacher<br /> *** Research Involving the Practicing Algebra Teacher<br /> **** Algebra Teachers&#039; Knowledge and Beliefs<br /> **** The Practice of Algebra Teaching and Influences on That Practice<br /> *** Research Involving the Algebra Teacher Within a Context of Professional Development or Inservice Training<br /> **** Integrating New Curricula, Approaches, and Technological Environments Into the Algebra Classroom<br /> **** Algebra Content Knowledge and Beliefs<br /> *** Research Involving the Preservice Teacher of Algebra<br /> *** Concluding Remarks on the Research Focusing on Algebra Teaching and the Algebra Teacher<br /> * In Conclusion: What Does this Body of Research Tell Us?<br /> <br /> == Also ==<br /> <br /> ;APA<br /> : Kieran, C. (2007). Learning and teaching algebra at the middle school through college levels. In F. K. Lester (Ed.), &#039;&#039;Second handbook of research on mathematics teaching and learning&#039;&#039; (pp. 707–762). Charlotte, NC: Information Age.<br /> ;BibTeX<br /> &lt;pre&gt;<br /> @incollection{Kieran2007,<br /> address = {Charlotte, NC},<br /> author = {Kieran, Carolyn},<br /> booktitle = {Second handbook of research on mathematics teaching and learning},<br /> chapter = {16},<br /> editor = {Lester, Frank K.},<br /> pages = {707--762},<br /> publisher = {Information Age},<br /> title = {{Learning and teaching algebra at the middle school through college levels}},<br /> year = {2007}<br /> }<br /> &lt;/pre&gt;<br /> <br /> [[Category:Book Chapters]]<br /> [[Category:2007]]<br /> [[Category:Algebra]]</div>

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