Proof in mathematics education: research, learning and teaching
Gespeichert in:
| Hauptverfasser: | , |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Rotterdam [u.a.]
Sense Publ.
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | Literaturverz. S. 227 - 239 |
| Beschreibung: | XIV, 251 S. graph. Darst. |
| ISBN: | 9789460912443 9789460912450 |
Internformat
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Datensatz im Suchindex
| _version_ | 1804145571992174592 |
|---|---|
| adam_text | Titel: Proof in mathematics education
Autor: Reid, David A
Jahr: 2010
TABLE OF CONTENTS
Introduction...........................................................................................................xiii
Part I: What is Proof?
1. History of Proof...................................................................................................3
The Standard View............................................................................................3
Other Views of the History of Proof................................................................10
Summary.........................................................................................................24
2. Usages of Proof and Proving .....................................................................25
Everyday Usages.............................................................................................25
Scientific Usages.............................................................................................26
Mathematical Usages......................................................................................26
Usages in Mathematics Education Research...................................................27
Demonstration and Proof in Other Languages.........................................32
Summary.........................................................................................................33
3. Researcher Perspectives.....................................................................................35
Philosophies of Mathematics...........................................................................37
Research Based on an a Priorist Philosophy of Mathematics.........................39
Research Based on an Infallibilist Philosophy of Mathematics.......................40
Research Based on a Quasi-Empiricist Philosophy of Mathematics...............46
Research Based on a Social-Constructivist Philosophy of Mathematics.........48
Summary.........................................................................................................52
BalachefiFs Epistemologies of Proof...............................................................53
Diverse or Comprehensive Perspectives?........................................................54
Part 2: Important Research Foci, Past and Present
4. Empirical Results..............................................................................................59
Key Studies......................................................................................................59
Many Students Accept Examples as Verification............................................59
Many Students Do Not Accept Deductive Proofs as Verification...................62
Many Students Do Not Accept Counterexamples as Refutation.....................63
Students Accept Flawed Deductive Proofs as Verification..............................64
Students Criteria for the Acceptance of Arguments.......................................65
Students Offer Empirical Arguments to Verify................................................67
Most Students Cannot Write Correct Proofs....................................................68
Ideas for Research...........................................................................................70
5. The Role of Proof.............................................................................................73
The Roles of Proof in Mathematics.................................................................73
V
TABLE OF CONTENTS
What is Proving in School Mathematics?......................................................79
The Roles of Proof for Students.....................................................................80
Possible Roles of Proof in Teaching..............................................................81
Ideas for Research..........................................................................................82
6. Types of Reasoning.........................................................................................83
Deductive Reasoning.....................................................................................84
Inductive Reasoning......................................................................................88
Abductive Reasoning.....................................................................................99
Reasoning by Analogy..................................................................................110
Other Kinds of Reasoning...........................................................................123
Summary......................................................................................................126
Ideas for research.........................................................................................127
7. Classifying Proofs and Arguments................................................................129
Proofs and Arguments Described According to the Representations
Involved.......................................................................................................130
Other Classifications of Proofs and Arguments...........................................142
Ideas for Research........................................................................................151
8. Argumentation...............................................................................................153
Argumentation Versus Proof........................................................................155
Argumentation in Accord with Proof...........................................................158
Argumentation According to Krummheuer.................................................161
Summary......................................................................................................163
Argumentation in Japan...............................................................................164
Ideas for Research........................................................................................164
9. Teaching Experiments...................................................................................165
Fawcett................................................................................................;........165
The Debate Approach..................................................................................169
Expecting Explanations...............................................................................172
Italy..............................................................................................................173
Summary......................................................................................................175
Ideas for Research........................................................................................176
Part 3: Processes of Reasoning and Argumentation
10. Argumentation Structures..............................................................................179
Toulmin s Functional Model and Argumentation Structures.......................179
The Source-Structure...................................................................................180
The Reservoir-Structure...............................................................................185
The Spiral-Structure.....................................................................................187
The Gathering-Structure..............................................................................189
Ideas for Research.......................................................................................191
vi
TABLE OF CONTENTS
11. Patterns of Reasoning....................................................................................193
Deduce-Conjecture-Test cycle.....................................................................194
Proof Analysis..............................................................................................198
Scientific Verification..................................................................................201
Surrender......................................................................................................202
Exception and Monster Barring...................................................................204
Summary......................................................................................................207
Ideas for Research........................................................................................208
Part 4: Conclusions
12. Implications for Teaching...............................................................................211
What is Proof and what is it for?..................................................................211
Formality......................................................................................................212
Results from New Math and Two-Column Proof Teaching.........................215
Starting where Students and Teachers are....................................................217
Teaching Experiments..................................................................................218
Summary......................................................................................................219
13. Directions for Research.................................................................................221
Teaching Proof.............................................................................................221
Students Understandings of Proof...............................................................223
Conceptional Issues.....................................................................................224
Conclusion...................................................................................................225
References............................................................................................................227
Author Index........................................................................................................241
Subject Index........................................................................................................245
vii
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| id | DE-604.BV026932673 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:21:35Z |
| institution | BVB |
| isbn | 9789460912443 9789460912450 |
| language | English |
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| physical | XIV, 251 S. graph. Darst. |
| publishDate | 2010 |
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| publisher | Sense Publ. |
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| spelling | Reid, David A. Verfasser aut Proof in mathematics education research, learning and teaching David A. Reid ; Christine Knipping Rotterdam [u.a.] Sense Publ. 2010 XIV, 251 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Literaturverz. S. 227 - 239 Mathematik (DE-588)4037944-9 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Mathematik (DE-588)4037944-9 s Beweis (DE-588)4132532-1 s DE-604 Knipping, Christine Verfasser aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022454775&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Reid, David A. Knipping, Christine Proof in mathematics education research, learning and teaching Mathematik (DE-588)4037944-9 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4037944-9 (DE-588)4132532-1 |
| title | Proof in mathematics education research, learning and teaching |
| title_auth | Proof in mathematics education research, learning and teaching |
| title_exact_search | Proof in mathematics education research, learning and teaching |
| title_full | Proof in mathematics education research, learning and teaching David A. Reid ; Christine Knipping |
| title_fullStr | Proof in mathematics education research, learning and teaching David A. Reid ; Christine Knipping |
| title_full_unstemmed | Proof in mathematics education research, learning and teaching David A. Reid ; Christine Knipping |
| title_short | Proof in mathematics education |
| title_sort | proof in mathematics education research learning and teaching |
| title_sub | research, learning and teaching |
| topic | Mathematik (DE-588)4037944-9 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Mathematik Beweis |
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