Opportunities to learn mathematical proofs in geometry: comparative analyses of textbooks from Germany and Taiwan
Gespeichert in:
| 1. Verfasser: | |
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
| Veröffentlicht: |
2013
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| Schlagworte: | |
| Online-Zugang: | Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130720-1144037-0-1 Inhaltsverzeichnis |
| Beschreibung: | XII, 209 S. graph. Darst. |
Internformat
MARC
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| 245 | 1 | 0 | |a Opportunities to learn mathematical proofs in geometry |b comparative analyses of textbooks from Germany and Taiwan |c Yu-Ping Chang |
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| 300 | |a XII, 209 S. |b graph. Darst. | ||
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Datensatz im Suchindex
| _version_ | 1804150627302899712 |
|---|---|
| adam_text | IMAGE 1
TABLE OF CONTENTS
LIST OF FIGURES VII
LIST OF TABLES IX
LIST OF APPENDICES XI
CHAPTER 1. INTRODUCTION 1
CHAPTER 2. PRACTICAL BACKGROUND 5
2.1 SCHOOL SYSTEMS 5
2.2 NATIONAL MATHEMATICS STANDARDS 6
2.2.1 NATIONAL STANDARDS IN GERMANY 7
2.2.2 NATIONAL STANDARDS IN TAIWAN 10
2.2.3 COMPARISON 12
2.3 MATHEMATICS TEXTBOOKS 13
2.3.1 MATHEMATICS CURRICULUM AND TEXTBOOKS 14
2.3.2 ROLE OF TEXTBOOKS IN GERMAN AND TAIWANESE SCHOOLS 15
CHAPTER 3. THEORETICAL BACKGROUND 19
3.1 MATHEMATICAL KNOWLEDGE 19
3.1.1 MATHEMATICAL KNOWLEDGE IN LEARNING MATHEMATICS 19
3.1.2 THE PROCESS OF ACQUIRING MATHEMATICAL KNOWLEDGE 20
3.1.3 EPISTEMOLOGICAL BELIEFS 22
3.1.4 PRAGMATIC ISSUES 23
3.1.4.1 RELATIONSHIP BETWEEN MATHEMATICAL REASONING AND PROBLEM SOLVING
23
3.1.4.2 THE MECHANISM OF MATHEMATICAL KNOWLEDGE, STRATEGIES, AND PROBLEM
SOLVING 24
3.2 MATHEMATICAL PROOFS 26
3.2.1 THE FUNCTIONS OF MATHEMATICAL PROOFS 27
I
HTTP://D-NB.INFO/1042483302
IMAGE 2
3.2.2 THE TYPES OF MATHEMATICAL PROOFS 29
3.2.3 TEACHING AND LEARNING MATHEMATICAL PROOFS 31
3.2.4 MATHEMATICAL PROOFS IN SCHOOL CURRICULUM 35
3.3 GEOMETRY 37
3.3.1 GEOMETRIC CURRICULUM 38
3.3.2 TEACHING AND LEARNING GEOMETRY 39
3.3.2.1 FIGURAL COMPREHENSION 39
3.3.2.2 GEOMETRIC CALCULATION 40
3.3.3 GEOMETRY PROOF 41
3.4 MATHEMATICS TEXTBOOKS 43
3.4.1 ROLES OF MATHEMATICS TEXTBOOKS 43
3.4.1.1 TEXTBOOKS AS MATERIALS TO TRANSMIT MATHEMATICAL KNOWLEDGE 44
3.4.1.2 TEXTBOOKS AS MATERIALS TO FACILITATE TEACHING AND LEARNING 44
3.4.1.3 THE QUALITY OF MATHEMATICS TEXTBOOKS 45
3.4.2 DESIGN OF MATHEMATICS TEXTBOOKS 46
3.4.2.1 PURPOSES OF TEXTS 46
3.4.2.2 TYPES OF TEXTS 47
3.4.3 MODELS OF TEXTBOOK ANALYSES 48
3.4.3.1 MODEL FOR ANALYZING REASONING-AND-PROVING 48
3.4.3.2 MODEL FOR ALL (DEALING WITH A GENERAL ISSUE) 49
3.4.3.3 MODEL FOR ANALYZING PROOF-RELATED REASONING 50
3.4.3.4 MODEL FOR ANALYZING THE NATURE OF PROOF 51
CHAPTER 4. AIMS AND RESEARCH QUESTIONS 53
4.1 AIMS 53
4.2 RESEARCH QUESTIONS 53
II
IMAGE 3
CHAPTER 5. ANALYTIC FRAMEWORK AND PRINCIPLES 55
5.1 ANALYTIC FRAMEWORK 55
5.1.1 UNIT OF ANALYSIS: TYPES OF TEXT 57
5.1.1.1 OPERATIONAL DEFINITIONS 58
5.1.1.2 DECISION ON UNITS 59
5.1.1.3 UNIT OF EXPLANATORY TEXT 61
5.1.1.4 UNIT OF WORKED EXAMPLE 65
5.1.1.5 UNIT OF EXPLORATION 66
5.1.1.6 UNIT OF IMMEDIATE PRACTICE 67
5.1.2 CONTENT OF UNIT: FEATURES OF TEXT 70
5.1.2.1 SUB-CATEGORY: FIGURE 70
5.1.2.2 SUB-CATEGORY: KNOWLEDGE 71
5.1.2.3 SUB-CATEGORY: ACTION 71
5.1.2.3.1 DENOTATION 71
5.1.2.3.2 CALCULATION 72
5.1.2.3.3 PHYSICAL OPERATION 72
5.1.2.3.4 FIGURAL CONSTRUCTION 73
5.1.2.3.5 FIGURAL DECOMPOSITION 73
5.1.2.3.6 FIGURAL TRANSFORMATION 73
5.1.2.4 SUB-CATEGORY: SITUATION 74
5.1.2.4.1 CONTENT LINKAGE 74
5.1.2.4.2 CONTEXT LINKAGE 74
5.1.3 CONTENT OF UNIT: FUNCTION OF TEXT 75
5.1.4 CONTENT OF UNIT: SUPPORT TO CLAIMS 75
5.2 THREE PRINCIPLES FOR SPECIFIC COMPARISON 81
III
IMAGE 4
5.2.1 PRINCIPLE ONE: CONTINUITY 82
5.2.2 PRINCIPLE TWO: ACCESSIBILITY 83
5.2.3 PRINCIPLE THREE: CONTEXTUALIZATION 84
5.3 APPLICATION 85
CHAPTER 6. METHOD 87
6.1 RESEARCH DESIGN 87
6.2 INTERVIEWS WITH TEXTBOOK AUTHORS 88
6.3 RESEARCH MATERIALS 90
6.3.1 SELECTION OF TEXTBOOKS 90
6.3.2 DISTRIBUTION AND SEQUENCE OF GEOMETRY CONTENT IN STRUCTURE 91
6.3.3 ANALYZED PAGES TO THE GEOMETRY CONTENT 94
6.3.4 TEXTUAL PATTERN WITHIN CHAPTER AND ITS SECTIONS 95
6.4 CODING AND DATA ANALYSIS 98
6.4.1 CODING PROCESS 98
6.4.2 INTER-RATER RELIABILITY 99
CHAPTER 7. RESULTS 101
7.1 DISTRIBUTIONS AND SEQUENCES GEOMETRY CONTENT 101
7.1.1 DIFFERENT DISTRIBUTIONS OF GEOMETRY CONTENT 101
7.1.2 DIFFERENT ROUTES OF SEQUENCE OF GEOMETRY CONTENT 103
7.2 THE FINDINGS OF THE TEXTUAL FEATURES 105
7.2.1 TYPES OF TEXT 105
7.2.2 PRESENTATIONS OF FIGURES IN GEOMETRY 110
7.2.3 THE CONNECTION WITH MATHEMATICAL IDEAS 112
7.2.4 COMPARISON OF SELECTED ACTIONS USED IN GEOMETRY 114
7.2.4.1 CALCULATION 114
IV
IMAGE 5
7.2.4.2 PHYSICAL OPERATION 116
7.2.4.3 FIGURAL CONSTRUCTION 116
7.2.4.4 THE DECOMPOSITION OF FIGURE 118
7.2.5 THE CONTENTS AND THE CONTEXTS OF UNITS 120
7.2.6 THE PRACTICAL FUNCTIONS IN GENERAL 122
7.2.7 THE SUPPORTS TO CLAIM IN GENERAL 123
7.3 THREE EXAMPLES OF GEOMETRY DESIGNS 124
7.3.1 THE SUM OF INTERIOR ANGLES OF A TRIANGLE 125
7.3.1.1 INTRODUCTION AND PROOFS IN THE GERMAN TEXTBOOKS 125
7.3.1.2 INTRODUCTION AND PROOFS IN THE TAIWANESE TEXTBOOKS 127
7.3.1.3 COMPARISON OF APPROACHES USED IN GERMAN AND TAIWANESE TEXTBOOKS
128
7.3.2 THE THALES THEOREM 131
7.3.2.1 INTRODUCTION AND PROOFS IN THE GERMAN TEXTBOOKS 131
7.3.2.2 INTRODUCTION AND PROOFS IN THE TAIWANESE TEXTBOOKS 133
7.3.2.3 COMPARISON OF APPROACHES USED IN GERMAN AND TAIWANESE TEXTBOOKS
137
7.3.3 THE PYTHAGOREAN THEOREM 139
7.3.3.1 INTRODUCTION AND PROOFS IN THE GERMAN TEXTBOOKS 140
7.3.3.2 INTRODUCTION AND PROOFS IN THE TAIWANESE TEXTBOOKS 143
7.3.3.3 COMPARISON OF APPROACHES USED IN GERMAN AND TAIWANESE TEXTBOOKS
145
7.4 TEXTBOOKS DEVELOPMENT IN GERMANY AND TAIWAN 148
CHAPTER 8. DISCUSSION 151
8.1 THE MAJOR FINDINGS 151
8.1.1 PRESENTATIONS OF THE TEXTBOOKS 152
8.1.2 ACTIONS USED IN THE GEOMETRY DESIGN 154
8.1.3 PURPOSES OF MATHEMATICAL PROOFS IN GEOMETRY CONTENT 155
V
IMAGE 6
8.1.4 TYPICAL APPROACHES TO MATHEMATICAL PROOFS IN THE TWO COUNTRIES 156
8.1.5 DISCUSSION ON THE ANALYTIC FRAMEWORK AND PRINCIPLES 157
8.2 LIMITATIONS OF THE STUDY 158
8.3 DIRECTIONS FOR FUTURE RESEARCH AND CURRICULUM DEVELOPMENT 160
REFERENCES 163
APPENDICES 175
VI
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| spelling | Chang, Yu-Ping Verfasser aut Opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from Germany and Taiwan Yu-Ping Chang 2013 XII, 209 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier München, Techn. Univ., Diss., 2013 (DE-588)4113937-9 Hochschulschrift gnd-content Erscheint auch als Online-Ausgabe urn:nbn:de:bvb:91-diss-20130720-1144037-0-1 http://mediatum.ub.tum.de/node?id=1144037 Verlag kostenfrei Volltext https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130720-1144037-0-1 Resolving-System DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026175806&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Chang, Yu-Ping Opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from Germany and Taiwan |
| subject_GND | (DE-588)4113937-9 |
| title | Opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from Germany and Taiwan |
| title_auth | Opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from Germany and Taiwan |
| title_exact_search | Opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from Germany and Taiwan |
| title_full | Opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from Germany and Taiwan Yu-Ping Chang |
| title_fullStr | Opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from Germany and Taiwan Yu-Ping Chang |
| title_full_unstemmed | Opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from Germany and Taiwan Yu-Ping Chang |
| title_short | Opportunities to learn mathematical proofs in geometry |
| title_sort | opportunities to learn mathematical proofs in geometry comparative analyses of textbooks from germany and taiwan |
| title_sub | comparative analyses of textbooks from Germany and Taiwan |
| topic_facet | Hochschulschrift |
| url | http://mediatum.ub.tum.de/node?id=1144037 https://nbn-resolving.org/urn:nbn:de:bvb:91-diss-20130720-1144037-0-1 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=026175806&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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