Mathematics as a constructive activity: learners generating examples
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Mahwah, N.J. [u.a.]
Erlbaum
2005
New York [u.a.] Routledge |
| Schriftenreihe: | Studies in mathematical thinking and learning
|
| Schlagworte: | |
| Online-Zugang: | Publisher description Table of contents Inhaltsverzeichnis |
| Beschreibung: | XIV, 228 S. |
| ISBN: | 0805843434 0805843442 |
Internformat
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Datensatz im Suchindex
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|---|---|
| adam_text | Titel: Mathematics as a constructive activity
Autor: Watson, Anne
Jahr: 2005
Contents
Preface ix
1 Introduction to Exemplification in Mathematics 1
What Is an Example? 3
On Whose Shoulders Are We Standing? 6
Summary 9
2 Learner-Generated Examples in Classrooms 10
Teacher-Initiated, Learner-Generated Examples 12
Learners Using Examples, Counterexamples,
and Extreme Examples 25
Initial Theorizing: Shifting Responsibility 30
Summary 32
3 From Examples to Example Spaces 33
A Difference of 2 34
Inter-Rootal Distances 39
How Do These Themes Relate to Our Work
With Other Groups? 51
Summary 57
4 The Development of Learners Example Spaces 59
Reminder: What Is an Example Space? 59
Metaphors 60
Central Examples 62
vii
Nonexamples and Counterexamples 65
Promoting Development 70
Summary 90
5 Pedagogical Tools for Developing Example Spaces 92
Kinds of Examples 92
Encountering Important Examples 103
Constructing New Objects for Oneself 220
Being Asked to Give Examples: The Larder Metaphor 230
Summary 232
6 Strategies for Prompting and Using Learner-Generated
Examples 133
Case Studies 133
Summary of Strategies 250
Focus on Action 257
Practice and Fluency 158
Summary 253
7 Mathematics as a Constructive Activity 160
Constructive Constraints 262
Building Confidence 168
Learning as Construction 276
Gathering Threads 283
Constructed Outcomes 292
Epilogue: Constructing Tasks 295
Appendix A: Some Historical Remarks
on Teaching by Examples 197
Early Practices and Implicit Theories 298
Explicit Theories and Implicit Practices 200
The Inductive Method 204
Toward the More Active Learner 206
Summary 208
Appendix B: Suggestions About Some of the Tasks 210
References 213
Author Index 223
Subject Index 227
|
| adam_txt |
Titel: Mathematics as a constructive activity
Autor: Watson, Anne
Jahr: 2005
Contents
Preface ix
1 Introduction to Exemplification in Mathematics 1
What Is an Example? 3
On Whose Shoulders Are We Standing? 6
Summary 9
2 Learner-Generated Examples in Classrooms 10
Teacher-Initiated, Learner-Generated Examples 12
Learners Using Examples, Counterexamples,
and Extreme Examples 25
Initial Theorizing: Shifting Responsibility 30
Summary 32
3 From Examples to Example Spaces 33
A Difference of 2 34
Inter-Rootal Distances 39
How Do These Themes Relate to Our Work
With Other Groups? 51
Summary 57
4 The Development of Learners'Example Spaces 59
Reminder: What Is an Example Space? 59
Metaphors 60
Central Examples 62
vii
Nonexamples and Counterexamples 65
Promoting Development 70
Summary 90
5 Pedagogical Tools for Developing Example Spaces 92
Kinds of Examples 92
Encountering Important Examples 103
Constructing New Objects for Oneself 220
Being Asked to Give Examples: The Larder Metaphor 230
Summary 232
6 Strategies for Prompting and Using Learner-Generated
Examples 133
Case Studies 133
Summary of Strategies 250
Focus on Action 257
Practice and Fluency 158
Summary 253
7 Mathematics as a Constructive Activity 160
Constructive Constraints 262
Building Confidence 168
Learning as Construction 276
Gathering Threads 283
Constructed Outcomes 292
Epilogue: Constructing Tasks 295
Appendix A: Some Historical Remarks
on Teaching by Examples 197
Early Practices and Implicit Theories 298
Explicit Theories and Implicit Practices 200
The Inductive Method 204
Toward the More Active Learner 206
Summary 208
Appendix B: Suggestions About Some of the Tasks 210
References 213
Author Index 223
Subject Index 227 |
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| spelling | Watson, Anne 1948- Verfasser (DE-588)136206999 aut Mathematics as a constructive activity learners generating examples Anne Watson, John Mason Mahwah, N.J. [u.a.] Erlbaum 2005 New York [u.a.] Routledge XIV, 228 S. txt rdacontent n rdamedia nc rdacarrier Studies in mathematical thinking and learning Activité - Apprentissage - Constructif - Construction - Développement - éducation - Enseignement - Exemple - Mathématique - Pédagogie Pédagogique Apprentissage de concepts Apprentissage des concepts ram Exemple Exemple ram Mathématiques - Étude et enseignement - Méthodologie Mathématiques - Étude et enseignement ram Mathematik Concept learning Example Mathematics Study and teaching Methodology Unterrichtsmethode (DE-588)4078637-7 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Konstruktive Didaktik (DE-588)4325193-6 gnd rswk-swf Lerntechnik (DE-588)4074168-0 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 s Konstruktive Didaktik (DE-588)4325193-6 s Lerntechnik (DE-588)4074168-0 s Unterrichtsmethode (DE-588)4078637-7 s DE-604 Mason, John Verfasser aut http://www.loc.gov/catdir/enhancements/fy0659/2004050657-d.html Publisher description http://www.loc.gov/catdir/toc/fy055/2004050657.html Table of contents HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=015859762&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Watson, Anne 1948- Mason, John Mathematics as a constructive activity learners generating examples Activité - Apprentissage - Constructif - Construction - Développement - éducation - Enseignement - Exemple - Mathématique - Pédagogie Pédagogique Apprentissage de concepts Apprentissage des concepts ram Exemple Exemple ram Mathématiques - Étude et enseignement - Méthodologie Mathématiques - Étude et enseignement ram Mathematik Concept learning Example Mathematics Study and teaching Methodology Unterrichtsmethode (DE-588)4078637-7 gnd Mathematikunterricht (DE-588)4037949-8 gnd Konstruktive Didaktik (DE-588)4325193-6 gnd Lerntechnik (DE-588)4074168-0 gnd |
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| title | Mathematics as a constructive activity learners generating examples |
| title_auth | Mathematics as a constructive activity learners generating examples |
| title_exact_search | Mathematics as a constructive activity learners generating examples |
| title_exact_search_txtP | Mathematics as a constructive activity learners generating examples |
| title_full | Mathematics as a constructive activity learners generating examples Anne Watson, John Mason |
| title_fullStr | Mathematics as a constructive activity learners generating examples Anne Watson, John Mason |
| title_full_unstemmed | Mathematics as a constructive activity learners generating examples Anne Watson, John Mason |
| title_short | Mathematics as a constructive activity |
| title_sort | mathematics as a constructive activity learners generating examples |
| title_sub | learners generating examples |
| topic | Activité - Apprentissage - Constructif - Construction - Développement - éducation - Enseignement - Exemple - Mathématique - Pédagogie Pédagogique Apprentissage de concepts Apprentissage des concepts ram Exemple Exemple ram Mathématiques - Étude et enseignement - Méthodologie Mathématiques - Étude et enseignement ram Mathematik Concept learning Example Mathematics Study and teaching Methodology Unterrichtsmethode (DE-588)4078637-7 gnd Mathematikunterricht (DE-588)4037949-8 gnd Konstruktive Didaktik (DE-588)4325193-6 gnd Lerntechnik (DE-588)4074168-0 gnd |
| topic_facet | Activité - Apprentissage - Constructif - Construction - Développement - éducation - Enseignement - Exemple - Mathématique - Pédagogie Pédagogique Apprentissage de concepts Apprentissage des concepts Exemple Mathématiques - Étude et enseignement - Méthodologie Mathématiques - Étude et enseignement Mathematik Concept learning Example Mathematics Study and teaching Methodology Unterrichtsmethode Mathematikunterricht Konstruktive Didaktik Lerntechnik |
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