Students' language in computer-assisted tutoring of mathematical proofs:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Saarbrücken
universaar
[2015]
|
| Series: | Saarbrücken dissertations in language science and technology
Volume 40 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | 297 Seiten Diagramme |
| ISBN: | 9783862231119 |
Staff View
MARC
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Record in the Search Index
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| adam_text |
CONTENTS
INTRODUCTION 29
1 BACKGROUND AND RELATED WORK 33
1.1 TARGET SCENARIOS 33
1.2 HIGH-LEVEL SYSTEM ARCHITECTURE 35
1.3 RELATED WORK 44
1.3.1 NATURAL LANGUAGE PROOF TUTORING WITH EXCHECK . 44
1.3.2 FORMAL ANALYSIS OF MATHEMATICAL LANGUAGE 47
1.3.3 PROCESSING NATURAL LANGUAGE PROOFS 47
1.3.4 CONTROLLED (NATURAL) LANGUAGES FOR PROOFS 52
1.3.5 PROOF ANNOTATION LANGUAGES 52
1.4 DISCUSSION 56
2 CORPUS ACQUISITION 59
2.1 MOTIVATION 59
2.2 METHODOLOGICAL CONSIDERATIONS 62
2.3 EXPERIMENTAL SETUP 67
2.4 OVERVIEW OF THE EXPERIMENTS 71
2.4.1 COMMON ASPECTS 71
2.4.2 THE FIRST EXPERIMENT 72
2.4.3 THE SECOND EXPERIMENT 74
2.5 OVERVIEW OF THE CORPORA 79
2.6 SUMMARY AND CONCLUSIONS 80
3 LANGUAGE PHENOMENA IN MATHEMATICAL PROOFS 85
3.1 INTRODUCTION 86
3.1.1 MATHEMATICAL LANGUAGE AS A SPECIAL LANGUAGE 86
3.1.2 LEARNING MATHEMATICS AND MATHEMATICAL LANGUAGE . . 88
3.2 THE LANGUAGE OF MATHEMATICAL PROOFS 91
3.2.1 THE SYMBOLIC LANGUAGE 93
HTTP://D-NB.INFO/1077378041
3.2.1.1 LEXICON 94
3.2.1.2 SYNTAX 95
3.2.1.3 SEMANTICS 102
3.2.1.4 CONVENTIONS AND CONTEXT 104
3.2.1.5 ERRORS IN THE SYMBOLIC LANGUAGE 106
3.2.2 THE INFORMAL LANGUAGE 112
3.2.2.1 MULTI-MODALITY 112
3.2.2.2 LEXICON 115
3.2.2.3 SYNTACTIC PHENOMENA 119
3.2.2.4 SEMANTIC PHENOMENA 124
3.2.2.5 DISCOURSE PHENOMENA 132
3.3 PRAGMATIC ASPECTS OF MATHEMATICAL DISCOURSE 142
3.4 CONCLUSIONS 145
4 QUANTITATIVE ANALYSIS OF THE STUDENTS' LANGUAGE 149
4.1 UTTERANCE TYPOLOGY 151
4.2 PREPROCESSING 155
4.2.1 TURN AND UTTERANCE PREPROCESSING 155
4.2.2 PREPROCESSING MATHEMATICAL EXPRESSIONS 156
4.2.3 TEXTUAL NORMALISATIONS 157
4.3 DIVERSITY OF VERBALISATION PATTERNS 159
4.3.1 MATHEMATICAL SYMBOLS VS. NATURAL LANGUAGE 160
4.3.2 THE EFFECT OF THE STUDY MATERIAL PRESENTATION 161
4.3.3 DISTRIBUTION OF UTTERANCE TYPES 164
4.3.4 PROOF CONTRIBUTIONS 167
4.3.5 GROWTH OF THE DIVERSITY OF FORMS 170
4.4 CONCLUSIONS 171
5 PROCESSING INFORMAL MATHEMATICAL DISCOURSE 175
5.1 RATIONALE OF THE APPROACH 175
5.2 LANGUAGE PROCESSING ARCHITECTURE 180
5.2.1 PARAMETERS 181
5.2.2 PREPROCESSING 182
5.2.2.1 SENTENCE AND WORD TOKENISATION 183
5.2.2.2 DOMAIN TERM IDENTIFICATION 184
5.2.2.3 PROCESSING MATHEMATICAL EXPRESSIONS . 185
5.2.3 CORE INTERPRETATION STRATEGY FOR PROOF DISCOURSE . 188
5.2.3.1 PARSING 189
5.2.3.2 DOMAIN INTERPRETATION 197
5.3 A WALK-THROUGH EXAMPLE 200
5.4 SUMMARY 201
6 MODELLING SELECTED LANGUAGE PHENOMENA IN PROOFS 205
6.1 SYNTACTIC PHENOMENA 206
6.1.1 BASIC GERMAN WORD ORDER IN COMBINATORY CATEGORIAL
GRAMMAR 206
6.1.2 MATHEMATICAL EXPRESSIONS IN THE CONTEXT OF
SCOPE-BEARING WORDS 213
6.1.3 MATHEMATICAL EXPRESSION FRAGMENTS 214
6.1.4 IRREGULAR SYNTAX 215
6.2 SEMANTIC PHENOMENA 216
6.2.1 IMPRECISION AND AMBIGUITY 216
6.2.2 "THE OTHER WAY ROUND" SEMANTICS 223
6.3 REFERENCE PHENOMENA 234
6.3.1 FORMS OF REFERRING AND THE SCOPE OF REFERENCE 236
6.3.2 MODELLING CONCEPTS RELEVANT IN REFERENCE RESOLUTION . . 241
6.4 COOPERATIVE CORRECTION OF MATHEMATICAL EXPRESSIONS 244
6.5 SUMMARY 250
7 PROSPECTS FOR AUTOMATED PROOF TUTORING 253
7.1 METHODOLOGY AND THE SCOPE OF EVALUATION 253
7.2 DESIGN 256
7.3 DATA 258
7.3.1 PREPROCESSING 258
7.3.2 EVALUATED GRAMMARS 259
7.3.2.1 SHARED LEXICON 259
7.3.2.2 DIALOGUE-SPECIFIC LEXICA 260
7.3.2.3 BASELINE 261
7.3.2.4 PERFORMANCE OPTIMISATION 261
7.3.2.5 GRAMMAR DEVELOPMENT SETS 263
7.3.3 TEST SETS 263
7.4 RESULTS 265
7.4.1 COVERAGE ON SEEN DATA 265
7.4.2 COVERAGE ON UNSEEN DATA 269
7.4.3 PARSE AMBIGUITY 270
7.4.4 OVERALL PERFORMANCE OF THE DEEP PARSER 270
7.5 CONCLUSIONS 275
SUMMARY AND OUTLOOK 277 |
| any_adam_object | 1 |
| author | Wolska, Magdalena 1972- |
| author_GND | (DE-588)1077173407 |
| author_facet | Wolska, Magdalena 1972- |
| author_role | aut |
| author_sort | Wolska, Magdalena 1972- |
| author_variant | m w mw |
| building | Verbundindex |
| bvnumber | BV043877475 |
| ctrlnum | (OCoLC)966300303 (DE-599)DNB1077378041 |
| dewey-full | 510.711 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.711 |
| dewey-search | 510.711 |
| dewey-sort | 3510.711 |
| dewey-tens | 510 - Mathematics |
| discipline | Sprachwissenschaft Mathematik |
| format | Thesis Book |
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| series2 | Saarbrücken dissertations in language science and technology |
| spelling | Wolska, Magdalena 1972- (DE-588)1077173407 aut Students' language in computer-assisted tutoring of mathematical proofs Magdalena A. Wolska Saarbrücken universaar [2015] 297 Seiten Diagramme txt rdacontent n rdamedia nc rdacarrier Saarbrücken dissertations in language science and technology Volume 40 Dissertation Universität des Saarlandes 2013 Intelligentes Tutorsystem (DE-588)4201713-0 gnd rswk-swf Fachsprache (DE-588)4016216-3 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf Sprachverarbeitung (DE-588)4116579-2 gnd rswk-swf Computerlinguistik (DE-588)4035843-4 gnd rswk-swf Korpus Linguistik (DE-588)4165338-5 gnd rswk-swf Mathematikstudent (DE-588)4660110-7 gnd rswk-swf Sprache Mathematik Beweis (DE-588)4113937-9 Hochschulschrift gnd-content Mathematikstudent (DE-588)4660110-7 s Beweis (DE-588)4132532-1 s Intelligentes Tutorsystem (DE-588)4201713-0 s Fachsprache (DE-588)4016216-3 s Korpus Linguistik (DE-588)4165338-5 s Computerlinguistik (DE-588)4035843-4 s Sprachverarbeitung (DE-588)4116579-2 s DE-604 Universität des Saarlandes universaar - Universitätsverlag des Saarlandes (DE-588)1068101644 pbl Erscheint auch als Online-Ausgabe 978-3-86223-112-6 B:DE-101 application/pdf http://d-nb.info/1077378041/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029287158&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| title | Students' language in computer-assisted tutoring of mathematical proofs |
| title_auth | Students' language in computer-assisted tutoring of mathematical proofs |
| title_exact_search | Students' language in computer-assisted tutoring of mathematical proofs |
| title_full | Students' language in computer-assisted tutoring of mathematical proofs Magdalena A. Wolska |
| title_fullStr | Students' language in computer-assisted tutoring of mathematical proofs Magdalena A. Wolska |
| title_full_unstemmed | Students' language in computer-assisted tutoring of mathematical proofs Magdalena A. Wolska |
| title_short | Students' language in computer-assisted tutoring of mathematical proofs |
| title_sort | students language in computer assisted tutoring of mathematical proofs |
| topic | Intelligentes Tutorsystem (DE-588)4201713-0 gnd Fachsprache (DE-588)4016216-3 gnd Beweis (DE-588)4132532-1 gnd Sprachverarbeitung (DE-588)4116579-2 gnd Computerlinguistik (DE-588)4035843-4 gnd Korpus Linguistik (DE-588)4165338-5 gnd Mathematikstudent (DE-588)4660110-7 gnd |
| topic_facet | Intelligentes Tutorsystem Fachsprache Beweis Sprachverarbeitung Computerlinguistik Korpus Linguistik Mathematikstudent Hochschulschrift |
| url | http://d-nb.info/1077378041/04 http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=029287158&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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