Teaching and Learning Proof Across the Grades (eBook, ePUB)
A K-16 Perspective
Redaktion: Stylianou, Despina A.; Knuth, Eric J.; Blanton, Maria L.
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Teaching and Learning Proof Across the Grades (eBook, ePUB)
A K-16 Perspective
Redaktion: Stylianou, Despina A.; Knuth, Eric J.; Blanton, Maria L.
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This new collection provides a much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. This book both highlights the ideas that have recently emerged on proof research and defines an agenda for future study.
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This new collection provides a much-needed forum for mathematics educators to articulate a connected K-16 "story" of proof. This book both highlights the ideas that have recently emerged on proof research and defines an agenda for future study.
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Produktdetails
- Produktdetails
- Verlag: Taylor & Francis
- Seitenzahl: 408
- Erscheinungstermin: 23. September 2010
- Englisch
- ISBN-13: 9781135856748
- Artikelnr.: 38249499
- Verlag: Taylor & Francis
- Seitenzahl: 408
- Erscheinungstermin: 23. September 2010
- Englisch
- ISBN-13: 9781135856748
- Artikelnr.: 38249499
Despina A. Stylianou is an Associate Professor of Mathematics Education at the City College of the City University of New York. Maria L. Blanton is a Senior Executive Research Associate at the James J. Kaput Center for Research and Innovation in Mathematics Education and an Associate Professor of Mathematics Education at the University of Massachusetts, Dartmouth. Eric J. Knuth is an Associate Professor of Mathematics Education at the University of Wisconsin-Madison.
Series Editor's Foreword: The Soul of Mathematics, Alan H. Schoenfeld
Preface
List of Contributors
Introduction
Section I: Theoretical Considerations on the Teaching and Learning of Proof
1. What I Would Like My Students to Already Know About Proof, Reuben Hersh
2. Exploring Relationships Between Disciplinary Knowledge and School
Mathematics: Implications For Understanding the Place of Reasoning And
Proof in School Mathematics, Daniel Chazan and H. Michael Lueke
3. Proving and Knowing In Public: The Nature of Proof in A Classroom,
Patricio Herbst and Nicolas Balacheff
Section II: Teaching and Learning of Proof in the Elementary Grades
4. Representation-based Proof in the Elementary Grades, Deborah Schifter
5. Representations that Enable Children To Engage in Deductive Argument,
Anne K. Morris
6. Young Mathematicians At Work: The Role of Contexts And Models in the
Emergence of Proof, Catherine Twomey Fosnot and Bill Jacob
7. Children's Reasoning: Discovering the Idea of Mathematical Proof,
Carolyn A. Maher
8. Aspects of Teaching Proving In Upper Elementary School, David A. Reid
and Vicki Zack
Section III: Teaching and Learning of Proof in Middle Grades and High
School
9. Middle School Students' Production of Mathematical Justifications, Eric
J. Knuth, Jeffrey M. Choppin and Kristen N. Bieda
10. From Empirical to Structural Reasoning in Mathematics: Tracking Changes
Over Time, Dietmar Küchemann and Celia Hoyles
11. Developing Argumentation and Proof Competencies in the Mathematics
Classroom, Aiso Heinze and Kristina Reiss
12. Formal Proof in High School Geometry: Student Perceptions of Structure,
Validity And Purpose, Sharon M. Soucy McCrone and Tami S. Martin
13. When is an Argument Just An Argument? The Refinement of Mathematical
Argumentation, Kay McClain
14. Reasoning-and-Proving in School Mathematics: The Case of Pattern
Identification, Gabriel J. Stylianides and Edward A. Silver
15. "Doing Proofs" in Geometry Classrooms, Patricio Herbst, Chialing Chen,
Michael Weiss, and Gloriana González, with Talli Nachlieli, Maria Hamlin
and Catherine Brach
Section IV: Teaching and Learning of Proof in College
16. College Instructors' Views of Students Vis-á-Vis Proof, Guershon Harel
and Larry Sowder
17. Understanding Instructional Scaffolding in Classroom Discourse on
Proof, Maria L. Blanton, Despina A. Stylianou and M. Manuela David
18. Building a Community of Inquiry in a Problem-Based Undergraduate Number
Theory Course: The Role of the Instructor, Jennifer Christian Smith,
Stephanie Ryan Nichols, Sera Yoo and Kurt Oehler
19. Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning
in the Representation System of Proof, Keith Weber and Lara Alcock
20. Teaching Proving by Coordinating Aspects of Proofs with Students'
Abilities, John Selden and Annie Selden
21. Current Contributions toward Comprehensive Perspectives on the Learning
and Teaching of Proof, Guershon Harel & Evan Fuller
References
Index
Preface
List of Contributors
Introduction
Section I: Theoretical Considerations on the Teaching and Learning of Proof
1. What I Would Like My Students to Already Know About Proof, Reuben Hersh
2. Exploring Relationships Between Disciplinary Knowledge and School
Mathematics: Implications For Understanding the Place of Reasoning And
Proof in School Mathematics, Daniel Chazan and H. Michael Lueke
3. Proving and Knowing In Public: The Nature of Proof in A Classroom,
Patricio Herbst and Nicolas Balacheff
Section II: Teaching and Learning of Proof in the Elementary Grades
4. Representation-based Proof in the Elementary Grades, Deborah Schifter
5. Representations that Enable Children To Engage in Deductive Argument,
Anne K. Morris
6. Young Mathematicians At Work: The Role of Contexts And Models in the
Emergence of Proof, Catherine Twomey Fosnot and Bill Jacob
7. Children's Reasoning: Discovering the Idea of Mathematical Proof,
Carolyn A. Maher
8. Aspects of Teaching Proving In Upper Elementary School, David A. Reid
and Vicki Zack
Section III: Teaching and Learning of Proof in Middle Grades and High
School
9. Middle School Students' Production of Mathematical Justifications, Eric
J. Knuth, Jeffrey M. Choppin and Kristen N. Bieda
10. From Empirical to Structural Reasoning in Mathematics: Tracking Changes
Over Time, Dietmar Küchemann and Celia Hoyles
11. Developing Argumentation and Proof Competencies in the Mathematics
Classroom, Aiso Heinze and Kristina Reiss
12. Formal Proof in High School Geometry: Student Perceptions of Structure,
Validity And Purpose, Sharon M. Soucy McCrone and Tami S. Martin
13. When is an Argument Just An Argument? The Refinement of Mathematical
Argumentation, Kay McClain
14. Reasoning-and-Proving in School Mathematics: The Case of Pattern
Identification, Gabriel J. Stylianides and Edward A. Silver
15. "Doing Proofs" in Geometry Classrooms, Patricio Herbst, Chialing Chen,
Michael Weiss, and Gloriana González, with Talli Nachlieli, Maria Hamlin
and Catherine Brach
Section IV: Teaching and Learning of Proof in College
16. College Instructors' Views of Students Vis-á-Vis Proof, Guershon Harel
and Larry Sowder
17. Understanding Instructional Scaffolding in Classroom Discourse on
Proof, Maria L. Blanton, Despina A. Stylianou and M. Manuela David
18. Building a Community of Inquiry in a Problem-Based Undergraduate Number
Theory Course: The Role of the Instructor, Jennifer Christian Smith,
Stephanie Ryan Nichols, Sera Yoo and Kurt Oehler
19. Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning
in the Representation System of Proof, Keith Weber and Lara Alcock
20. Teaching Proving by Coordinating Aspects of Proofs with Students'
Abilities, John Selden and Annie Selden
21. Current Contributions toward Comprehensive Perspectives on the Learning
and Teaching of Proof, Guershon Harel & Evan Fuller
References
Index
Series Editor's Foreword: The Soul of Mathematics, Alan H. Schoenfeld
Preface
List of Contributors
Introduction
Section I: Theoretical Considerations on the Teaching and Learning of Proof
1. What I Would Like My Students to Already Know About Proof, Reuben Hersh
2. Exploring Relationships Between Disciplinary Knowledge and School
Mathematics: Implications For Understanding the Place of Reasoning And
Proof in School Mathematics, Daniel Chazan and H. Michael Lueke
3. Proving and Knowing In Public: The Nature of Proof in A Classroom,
Patricio Herbst and Nicolas Balacheff
Section II: Teaching and Learning of Proof in the Elementary Grades
4. Representation-based Proof in the Elementary Grades, Deborah Schifter
5. Representations that Enable Children To Engage in Deductive Argument,
Anne K. Morris
6. Young Mathematicians At Work: The Role of Contexts And Models in the
Emergence of Proof, Catherine Twomey Fosnot and Bill Jacob
7. Children's Reasoning: Discovering the Idea of Mathematical Proof,
Carolyn A. Maher
8. Aspects of Teaching Proving In Upper Elementary School, David A. Reid
and Vicki Zack
Section III: Teaching and Learning of Proof in Middle Grades and High
School
9. Middle School Students' Production of Mathematical Justifications, Eric
J. Knuth, Jeffrey M. Choppin and Kristen N. Bieda
10. From Empirical to Structural Reasoning in Mathematics: Tracking Changes
Over Time, Dietmar Küchemann and Celia Hoyles
11. Developing Argumentation and Proof Competencies in the Mathematics
Classroom, Aiso Heinze and Kristina Reiss
12. Formal Proof in High School Geometry: Student Perceptions of Structure,
Validity And Purpose, Sharon M. Soucy McCrone and Tami S. Martin
13. When is an Argument Just An Argument? The Refinement of Mathematical
Argumentation, Kay McClain
14. Reasoning-and-Proving in School Mathematics: The Case of Pattern
Identification, Gabriel J. Stylianides and Edward A. Silver
15. "Doing Proofs" in Geometry Classrooms, Patricio Herbst, Chialing Chen,
Michael Weiss, and Gloriana González, with Talli Nachlieli, Maria Hamlin
and Catherine Brach
Section IV: Teaching and Learning of Proof in College
16. College Instructors' Views of Students Vis-á-Vis Proof, Guershon Harel
and Larry Sowder
17. Understanding Instructional Scaffolding in Classroom Discourse on
Proof, Maria L. Blanton, Despina A. Stylianou and M. Manuela David
18. Building a Community of Inquiry in a Problem-Based Undergraduate Number
Theory Course: The Role of the Instructor, Jennifer Christian Smith,
Stephanie Ryan Nichols, Sera Yoo and Kurt Oehler
19. Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning
in the Representation System of Proof, Keith Weber and Lara Alcock
20. Teaching Proving by Coordinating Aspects of Proofs with Students'
Abilities, John Selden and Annie Selden
21. Current Contributions toward Comprehensive Perspectives on the Learning
and Teaching of Proof, Guershon Harel & Evan Fuller
References
Index
Preface
List of Contributors
Introduction
Section I: Theoretical Considerations on the Teaching and Learning of Proof
1. What I Would Like My Students to Already Know About Proof, Reuben Hersh
2. Exploring Relationships Between Disciplinary Knowledge and School
Mathematics: Implications For Understanding the Place of Reasoning And
Proof in School Mathematics, Daniel Chazan and H. Michael Lueke
3. Proving and Knowing In Public: The Nature of Proof in A Classroom,
Patricio Herbst and Nicolas Balacheff
Section II: Teaching and Learning of Proof in the Elementary Grades
4. Representation-based Proof in the Elementary Grades, Deborah Schifter
5. Representations that Enable Children To Engage in Deductive Argument,
Anne K. Morris
6. Young Mathematicians At Work: The Role of Contexts And Models in the
Emergence of Proof, Catherine Twomey Fosnot and Bill Jacob
7. Children's Reasoning: Discovering the Idea of Mathematical Proof,
Carolyn A. Maher
8. Aspects of Teaching Proving In Upper Elementary School, David A. Reid
and Vicki Zack
Section III: Teaching and Learning of Proof in Middle Grades and High
School
9. Middle School Students' Production of Mathematical Justifications, Eric
J. Knuth, Jeffrey M. Choppin and Kristen N. Bieda
10. From Empirical to Structural Reasoning in Mathematics: Tracking Changes
Over Time, Dietmar Küchemann and Celia Hoyles
11. Developing Argumentation and Proof Competencies in the Mathematics
Classroom, Aiso Heinze and Kristina Reiss
12. Formal Proof in High School Geometry: Student Perceptions of Structure,
Validity And Purpose, Sharon M. Soucy McCrone and Tami S. Martin
13. When is an Argument Just An Argument? The Refinement of Mathematical
Argumentation, Kay McClain
14. Reasoning-and-Proving in School Mathematics: The Case of Pattern
Identification, Gabriel J. Stylianides and Edward A. Silver
15. "Doing Proofs" in Geometry Classrooms, Patricio Herbst, Chialing Chen,
Michael Weiss, and Gloriana González, with Talli Nachlieli, Maria Hamlin
and Catherine Brach
Section IV: Teaching and Learning of Proof in College
16. College Instructors' Views of Students Vis-á-Vis Proof, Guershon Harel
and Larry Sowder
17. Understanding Instructional Scaffolding in Classroom Discourse on
Proof, Maria L. Blanton, Despina A. Stylianou and M. Manuela David
18. Building a Community of Inquiry in a Problem-Based Undergraduate Number
Theory Course: The Role of the Instructor, Jennifer Christian Smith,
Stephanie Ryan Nichols, Sera Yoo and Kurt Oehler
19. Proof in Advanced Mathematics Classes: Semantic and Syntactic Reasoning
in the Representation System of Proof, Keith Weber and Lara Alcock
20. Teaching Proving by Coordinating Aspects of Proofs with Students'
Abilities, John Selden and Annie Selden
21. Current Contributions toward Comprehensive Perspectives on the Learning
and Teaching of Proof, Guershon Harel & Evan Fuller
References
Index