Teaching and learning proof across the grades: A K - 16 perspective
These essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. --from publisher description
Gespeichert in:
| Format: | Buch |
|---|---|
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Routledge
2009
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Zusammenfassung: | These essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. --from publisher description |
| Beschreibung: | XX, 388 S. |
| ISBN: | 9780514989848 |
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| 650 | 4 | |a Mathematical analysis |x Study and teaching | |
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Datensatz im Suchindex
| _version_ | 1804139197375709184 |
|---|---|
| adam_text | Titel: Teaching and learning proof across the grades
Autor: Stylianou, Despina A.
Jahr: 2009
Contents
Series Editor s Foreword: The Soul of Mathematics
ALAN H. SCHOENFELD xii
Preface xvii
List of Contributors xix
Introduction 1
SectionI
Theoretical Considerations on the Teaching and Learning of Proof 13
1 What I Would Like My Students to Already Know About Proof 17
REUBEN HERSH
2 Exploring Relationships Between Disciplinary Knowledge and School
Mathematics: Implications for Understanding the Place of Reasoning
and Proof in School Mathematics 21
DANIEL CHAZAN AND H. MICHAEL LUEKE
3 Proving and Knowing in Public: The Nature of Proof in a Classroom 40
PATRICIO HERBST AND NICOLAS BALACHEFF
Sectionll
Teaching and Learning of Proof in the Elementary Grades 65
4 Representation-based Proof in the Elementary Grades 71
DEBORAH SCHIFTER
5 Representations that Enable Children to Engage in
Deductive Argument 87
ANNE K. MORRIS
6 Young Mathematicians at Work: The RoIe of Contexts and Models
in the Emergence of Proof 102
CATHERINE TWOMEY FOSNOT AND BILL JACOB
7 Children s Reasoning: Discovering the Idea of Mathematical Proof 120
CAROLYN A. MÄHER
x Contents
8 AspectsofTeaching Proving in Upper Elementary School 133
DAVID A. REID AND VICKI ZACK
Section III
Teaching and Learning of Proof in Middle Grades and High School 147
9 Middle School Students Production of Mathematical Justifkations 153
ERIC J. KNUTH, JEFFREY M. CHOPPIN, AND KRISTEN N. BIEDA
10 From Empirical to Structural Reasoning in Mathematics: Tracking
Changes Over Time 171
DIETMAR KÜCHEMANN AND CELIA HOYLES
11 Developing Argumentation and Proof Competencies in the
Mathematics Classroom 191
AISO HEINZE AND KRISTINA REISS
12 Formal Proof in High School Geometry: Student Perceptions of
Structure, Validity, and Purpose 204
SHARON M. SOUCY MCCRONE AND TAMI S. MARTIN
13 When is an Argument Just an Argument? The Refinement of
Mathematical Argumentation 222
KAY MCCLAIN
14 Reasoning-and-Proving in School Mathematics: The Case of
Pattern Identification 235
GABRIEL J. STYLIANIDES AND EDWARD A. SILVER
15 Doing Proofs in Geometry Classrooms 250
PATRICIO HERBST, CHIALING CHEN, MICHAEL WEISS, AND
GLORIANA GONZALEZ, WITH TALLI NACHLIELI, MARIA HAMLIN, AND
CATHERINE BRACH
Section IV
Teaching and Learning of Proof in College 269
16 College Instructors Views of Students Vis-ä-Vis Proof 275
GUERSHON HAREL AND LARRY SOWDER
17 Understanding Instructional Scaffolding in Classroom Discourse
on Proof 290
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 RoIe of the Instructor 307
JENNIFER CHRISTIAN SMITH, STEPHANIE RYAN NICHOLS, SERA YOO,
AND KURT OEHLER
Contents xi
19 Proof in Advanced Mathematics Classes: Semantic and Syntactic
Reasoning in the Representation System of Proof 323
KEITH WEBER AND LARA ALCOCK
20 Teaching Proving by Coordinating Aspects of Proofs with Students
Abilities 339
JOHN SELDEN AND ANNIE SELDEN
21 Current Contributions Toward Comprehensive Perspectives on the
Learning and Teaching of Proof 355
GUERSHON HAREL AND EVAN FULLER
References 371
Index 386
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| spelling | Teaching and learning proof across the grades A K - 16 perspective ed. by Despina A. Stylianou ... New York [u.a.] Routledge 2009 XX, 388 S. txt rdacontent n rdamedia nc rdacarrier These essays inform educators and researchers at different grade levels about the teaching and learning of proof at each level and, thus, help advance the design of further empirical and theoretical work in this area. --from publisher description Logic, Symbolic and mathematical Study and teaching Mathematical analysis Study and teaching Problem solving Study and teaching Proof theory Study and teaching Stylianou, Despina A. Sonstige oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017607953&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Teaching and learning proof across the grades A K - 16 perspective Logic, Symbolic and mathematical Study and teaching Mathematical analysis Study and teaching Problem solving Study and teaching Proof theory Study and teaching |
| title | Teaching and learning proof across the grades A K - 16 perspective |
| title_auth | Teaching and learning proof across the grades A K - 16 perspective |
| title_exact_search | Teaching and learning proof across the grades A K - 16 perspective |
| title_full | Teaching and learning proof across the grades A K - 16 perspective ed. by Despina A. Stylianou ... |
| title_fullStr | Teaching and learning proof across the grades A K - 16 perspective ed. by Despina A. Stylianou ... |
| title_full_unstemmed | Teaching and learning proof across the grades A K - 16 perspective ed. by Despina A. Stylianou ... |
| title_short | Teaching and learning proof across the grades |
| title_sort | teaching and learning proof across the grades a k 16 perspective |
| title_sub | A K - 16 perspective |
| topic | Logic, Symbolic and mathematical Study and teaching Mathematical analysis Study and teaching Problem solving Study and teaching Proof theory Study and teaching |
| topic_facet | Logic, Symbolic and mathematical Study and teaching Mathematical analysis Study and teaching Problem solving Study and teaching Proof theory Study and teaching |
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