Granularity analysis for tutoring mathematical proofs:
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
[Amsterdam]
IOS Press
2011
Heidelberg AKA |
| Series: | Dissertationen zur künstlichen Intelligenz
334 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XX, 247 S. Ill., graph. Darst. 21 cm |
| ISBN: | 9783898383349 9781607507192 |
Staff View
MARC
| LEADER | 00000nam a2200000 cb4500 | ||
|---|---|---|---|
| 001 | BV037334626 | ||
| 003 | DE-604 | ||
| 005 | 20160829 | ||
| 007 | t | ||
| 008 | 110412s2011 ad|| m||| 00||| eng d | ||
| 016 | 7 | |a 1010474375 |2 DE-101 | |
| 020 | |a 9783898383349 |c (AKA) kart. : EUR 50.00 |9 978-3-89838-334-9 | ||
| 020 | |a 9781607507192 |c (IOS Press) kart. : EUR 50.00 |9 978-1-60750-719-2 | ||
| 035 | |a (OCoLC)712445708 | ||
| 035 | |a (DE-599)DNB1010474375 | ||
| 040 | |a DE-604 |b ger |e rakddb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-91G |a DE-355 | ||
| 082 | 0 | |a 511.360711 |2 22/ger | |
| 082 | 0 | |a 511.36028563 |2 22/ger | |
| 084 | |a ST 304 |0 (DE-625)143653: |2 rvk | ||
| 084 | |a DAT 706d |2 stub | ||
| 084 | |a MAT 036d |2 stub | ||
| 100 | 1 | |a Schiller, Marvin |e Verfasser |0 (DE-588)138518769 |4 aut | |
| 245 | 1 | 0 | |a Granularity analysis for tutoring mathematical proofs |c Marvin R. G. Schiller |
| 264 | 1 | |a [Amsterdam] |b IOS Press |c 2011 | |
| 264 | 1 | |a Heidelberg |b AKA | |
| 300 | |a XX, 247 S. |b Ill., graph. Darst. |c 21 cm | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Dissertationen zur künstlichen Intelligenz |v 334 | |
| 502 | |a Zugl.: Saarbrücken, Univ., Diss., 2010 | ||
| 650 | 0 | 7 | |a Mathematikstudium |0 (DE-588)4037947-4 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Automatisches Beweisverfahren |0 (DE-588)4069034-9 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Beweis |0 (DE-588)4132532-1 |2 gnd |9 rswk-swf |
| 655 | 7 | |0 (DE-588)4113937-9 |a Hochschulschrift |2 gnd-content | |
| 689 | 0 | 0 | |a Beweis |0 (DE-588)4132532-1 |D s |
| 689 | 0 | 1 | |a Mathematikstudium |0 (DE-588)4037947-4 |D s |
| 689 | 0 | 2 | |a Automatisches Beweisverfahren |0 (DE-588)4069034-9 |D s |
| 689 | 0 | |5 DE-604 | |
| 830 | 0 | |a Dissertationen zur künstlichen Intelligenz |v 334 |w (DE-604)BV005345280 |9 334 | |
| 856 | 4 | 2 | |m DNB Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022488463&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-022488463 | ||
Record in the Search Index
| _version_ | 1804145618553143296 |
|---|---|
| adam_text | IMAGE 1
CONTENTS
CONTENTS
ZUSAMMENFASSUNG XVII
EXTENDED ABSTRACT XIX
1 INTRODUCTION 1
1.1 TEACHING MATHEMATICAL PROOF - DIDACTIC CHALLENGES AND IMPLICA- TIONS
FOR AUTOMATED SYSTEMS 3
1.2 INTELLIGENT TUTORING SYSTEMS AND COMPUTER ASSISTED INSTRUCTION . . 7
1.3 COMPUTER-ASSISTED INTELLIGENT TEACHING OF MATHEMATICAL PROOFS . . 8
1.4 STATE-OF-THE-ART TUTORING AND E-ASSESSMENT SYSTEMS FOR MATHE-
MATICAL PROOFS 9
1.4.1 ADVANCED GEOMETRY TUTOR 9
1.4.2 ANGLE 10
1.4.3 THE EPGY THEOREM PROVING ENVIRONMENT 11
1.4.4 A P R OS AND THE CARNEGIE PROOF LAB 12
1.4.5 ETPS 14
1.4.6 PROOFWEB 14
1.4.7 THE P-LOGIC TUTOR 15
1.4.8 EASY 16
1.4.9 TUTCH 16
1.4.10 BAGHERA ASSESSMENT PROJECT 17
1.4.11 RISC PROOF NAVIGATOR 18
1.4.12 DISCUSSION 18
1.5 TUTORIAL DIALOG FOR MATHEMATICAL PROOFS - THE DIALOG PROJECT .. 20
1.5.1 SIMULATION EXPERIMENTS 21
1.5.2 ARCHITECTURE AND COMPONENTS OF THE DIALOG PROTOTYPE SYS- TEM 25
1.5.3 MATHEMATICAL DOMAIN REASONING IN DIALOG 26
1.6 THE MATHEMATICAL ASSISTANT SYSTEM QMEGA 26
1.6.1 PROOF REPRESENTATION IN QMEGA 27
1.6.2 ASSERTION LEVEL REASONING 29
1.6.3 STRATEGY FRAMEWORK 33
1.6.4 PROOF RECONSTRUCTION AND FTMEGA-TUTOR 35
BIBLIOGRAFISCHE INFORMATIONEN HTTP://D-NB.INFO/1010474375
DIGITALISIERT DURCH
IMAGE 2
CONTENTS
1.6.5 LEARNING OF PROOF PLANNING METHODS IN FTMEGA 38 1.6.6 DISCUSSION
39
1.7 ACTIVEMATH 41
1.7.1 USER MODELING IN ACTIVEMATH 42
1.7.2 PREDICTING STUDENT PERFORMANCE WITH ACTIVEMATH 44 1.7.3 DISCUSSION
AND RELATED WORK 45
1.8 SUMMARY AND DISCUSSION 46
MOTIVATION: GRANULARITY AND RELEVANCE 49
2.1 FRAMEWORKS AND THEORIES OF GRANULARITY 51
2.1.1 GENERAL THEORIES ON GRANULARITY 52
2.1.2 GRANULARITY IN PROOF ASSISTANTS 55
2.1.3 PREVIOUS WORK ON MODELING PROOF GRANULARITY 57
2.1.4 POSITIONING OF OUR APPROACH 58
2.2 GRANULARITY, RELEVANCE AND EXPLICITNESS 60
2.2.1 RELEVANCE 60
2.2.2 EXPLICITNESS 64
2.3 SUMMARY AND DISCUSSION 66
A LEARNING APPROACH TO GRANULARITY 69
3.1 METHODOLOGY 69
3.1.1 GRANULARITY CRITERIA 70
3.1.2 ARCHITECTURE 76
3.1.3 MACHINE LEARNING AND CLASSIFICATION 79
3.2 THE GRANULARITY JUDGMENT MODULE 83
3.2.1 EXAMPLE 84
3.2.2 ATTRIBUTES EMPLOYED FOR GRANULARITY EVALUATION 86 3.2.3
IMPLEMENTATION 89
3.3 STUDENT MODEL 90
3.3.1 DOMAIN MODEL &C KNOWLEDGE REPRESENTATION 91
3.3.2 STUDENT MODELS - STATE OF THE ART 92
3.3.3 OUR STUDENT MODEL 93
3.4 GRANULARITY-ADAPTED PROOF PRESENTATIONS 95
3.4.1 AUTOMATED PROOF PRESENTATION - STATE OF THE ART AND CHAL- LENGES
95
3.4.2 A GRANULARITY-ADAPTED PRESENTATION ALGORITHM 102 3.4.3 CASE STUDY
109
3.4.4 FURTHER CASE STUDIES 112
3.4.5 DISCUSSION 113
3.5 AN ENVIRONMENT FOR GRANULARITY CLASSIFIER LEARNING AND EMPIRICAL
EXPERIMENTS 115
3.5.1 MOTIVATION 115
3.5.2 THE APPROACH 117
IMAGE 3
CONTENTS
3.5.3 FUNCTIONS AND IMPLEMENTATION 120
3.6 DEPLOYMENT WITHIN A C T I V E M A TH 124
3.6.1 THE EXERCISE SYSTEM IN A C T I V E M A TH 126
3.6.2 STEP-WISE PROOF EXERCISES VIA A C T I V E M A TH 126
3.7 SUMMARY AND DISCUSSION 129
4 EMPIRICAL EXPERIMENTS AND EVALUATION 133
4.1 STUDY OBJECTIVES 134
4.2 SETUP 135
4.2.1 PROCEDURE 135
4.2.2 PARTICIPANTS 138
4.2.3 COLLECTED DATA 139
4.2.4 LEARNING OF MODELS FOR GRANULARITY 140
4.2.5 ANALYSIS AND EVALUATION TECHNIQUES 141
4.3 ANALYSIS 144
4.3.1 DISTRIBUTION OF RATINGS 144
4.3.2 AGREEMENT BETWEEN TUTORS 147
4.3.3 CLASSIFICATION ON A COMMON SAMPLE 148
4.3.4 INTER-SUBJECT COMPARISON 150
4.3.5 ANALYSIS FOR TUTOR 1 152
4.3.6 ANALYSIS FOR TUTOR 2 155
4.3.7 ANALYSIS FOR TUTOR 3 157
4.3.8 ANALYSIS FOR TUTOR 4 159
4.3.9 EVALUATION OF THE PRE-EXPERIMENTS 163
4.3.10 GENERATED PROOFS VS. STUDENT-AUTHORED PROOFS 164
4.4 DISCUSSION 165
4.4.1 DISCUSSION OF EXPERIMENTAL RESULTS 165
4.4.2 RECOMMENDATIONS FOR FURTHER STUDIES 167
4.4.3 SUMMARY 169
5 DISCUSSION AND FUTURE WORK 171
5.1 CONTRIBUTIONS 171
5.2 DISCUSSION 173
5.3 FUTURE WORK 174
A INSTRUCTIONS FROM THE EXPERIMENTS 197
IMAGE 4
CONTENTS
B DATA FROM THE EXPERIMENTS 203
B.I PROOFS FOR THE EXERCISE ON SET OPERATIONS 204
B.2 PROOFS FOR THE 1ST EXERCISE ON BINARY RELATIONS 215
B.3 PROOFS FOR THE 2ND EXERCISE ON BINARY RELATIONS 227
B.4 PROOFS FOR THE 3RD EXERCISE ON BINARY RELATIONS 232
B.5 PROOFS FOR THE 1ST EXERCISE IN TOPOLOGY 237
B.6 PROOFS FOR THE 2ND EXERCISE IN TOPOLOGY 242
B.7 PROOFS FOR THE GEOMETRY EXERCISE 243
INDEX 244
|
| any_adam_object | 1 |
| author | Schiller, Marvin |
| author_GND | (DE-588)138518769 |
| author_facet | Schiller, Marvin |
| author_role | aut |
| author_sort | Schiller, Marvin |
| author_variant | m s ms |
| building | Verbundindex |
| bvnumber | BV037334626 |
| classification_rvk | ST 304 |
| classification_tum | DAT 706d MAT 036d |
| ctrlnum | (OCoLC)712445708 (DE-599)DNB1010474375 |
| dewey-full | 511.360711 511.36028563 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 511 - General principles of mathematics |
| dewey-raw | 511.360711 511.36028563 |
| dewey-search | 511.360711 511.36028563 |
| dewey-sort | 3511.360711 |
| dewey-tens | 510 - Mathematics |
| discipline | Informatik Mathematik |
| format | Thesis Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>02047nam a2200493 cb4500</leader><controlfield tag="001">BV037334626</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20160829 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">110412s2011 ad|| m||| 00||| eng d</controlfield><datafield tag="016" ind1="7" ind2=" "><subfield code="a">1010474375</subfield><subfield code="2">DE-101</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9783898383349</subfield><subfield code="c">(AKA) kart. : EUR 50.00</subfield><subfield code="9">978-3-89838-334-9</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781607507192</subfield><subfield code="c">(IOS Press) kart. : EUR 50.00</subfield><subfield code="9">978-1-60750-719-2</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)712445708</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)DNB1010474375</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakddb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-91G</subfield><subfield code="a">DE-355</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.360711</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">511.36028563</subfield><subfield code="2">22/ger</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">ST 304</subfield><subfield code="0">(DE-625)143653:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">DAT 706d</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 036d</subfield><subfield code="2">stub</subfield></datafield><datafield tag="100" ind1="1" ind2=" "><subfield code="a">Schiller, Marvin</subfield><subfield code="e">Verfasser</subfield><subfield code="0">(DE-588)138518769</subfield><subfield code="4">aut</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Granularity analysis for tutoring mathematical proofs</subfield><subfield code="c">Marvin R. G. Schiller</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">[Amsterdam]</subfield><subfield code="b">IOS Press</subfield><subfield code="c">2011</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">Heidelberg</subfield><subfield code="b">AKA</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">XX, 247 S.</subfield><subfield code="b">Ill., graph. Darst.</subfield><subfield code="c">21 cm</subfield></datafield><datafield tag="336" ind1=" " ind2=" "><subfield code="b">txt</subfield><subfield code="2">rdacontent</subfield></datafield><datafield tag="337" ind1=" " ind2=" "><subfield code="b">n</subfield><subfield code="2">rdamedia</subfield></datafield><datafield tag="338" ind1=" " ind2=" "><subfield code="b">nc</subfield><subfield code="2">rdacarrier</subfield></datafield><datafield tag="490" ind1="1" ind2=" "><subfield code="a">Dissertationen zur künstlichen Intelligenz</subfield><subfield code="v">334</subfield></datafield><datafield tag="502" ind1=" " ind2=" "><subfield code="a">Zugl.: Saarbrücken, Univ., Diss., 2010</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Mathematikstudium</subfield><subfield code="0">(DE-588)4037947-4</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Automatisches Beweisverfahren</subfield><subfield code="0">(DE-588)4069034-9</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Beweis</subfield><subfield code="0">(DE-588)4132532-1</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="655" ind1=" " ind2="7"><subfield code="0">(DE-588)4113937-9</subfield><subfield code="a">Hochschulschrift</subfield><subfield code="2">gnd-content</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Beweis</subfield><subfield code="0">(DE-588)4132532-1</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Mathematikstudium</subfield><subfield code="0">(DE-588)4037947-4</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="2"><subfield code="a">Automatisches Beweisverfahren</subfield><subfield code="0">(DE-588)4069034-9</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="5">DE-604</subfield></datafield><datafield tag="830" ind1=" " ind2="0"><subfield code="a">Dissertationen zur künstlichen Intelligenz</subfield><subfield code="v">334</subfield><subfield code="w">(DE-604)BV005345280</subfield><subfield code="9">334</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">DNB Datenaustausch</subfield><subfield code="q">application/pdf</subfield><subfield code="u">http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022488463&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA</subfield><subfield code="3">Inhaltsverzeichnis</subfield></datafield><datafield tag="999" ind1=" " ind2=" "><subfield code="a">oai:aleph.bib-bvb.de:BVB01-022488463</subfield></datafield></record></collection> |
| genre | (DE-588)4113937-9 Hochschulschrift gnd-content |
| genre_facet | Hochschulschrift |
| id | DE-604.BV037334626 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T23:22:19Z |
| institution | BVB |
| isbn | 9783898383349 9781607507192 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-022488463 |
| oclc_num | 712445708 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR |
| physical | XX, 247 S. Ill., graph. Darst. 21 cm |
| publishDate | 2011 |
| publishDateSearch | 2011 |
| publishDateSort | 2011 |
| publisher | IOS Press AKA |
| record_format | marc |
| series | Dissertationen zur künstlichen Intelligenz |
| series2 | Dissertationen zur künstlichen Intelligenz |
| spelling | Schiller, Marvin Verfasser (DE-588)138518769 aut Granularity analysis for tutoring mathematical proofs Marvin R. G. Schiller [Amsterdam] IOS Press 2011 Heidelberg AKA XX, 247 S. Ill., graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Dissertationen zur künstlichen Intelligenz 334 Zugl.: Saarbrücken, Univ., Diss., 2010 Mathematikstudium (DE-588)4037947-4 gnd rswk-swf Automatisches Beweisverfahren (DE-588)4069034-9 gnd rswk-swf Beweis (DE-588)4132532-1 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Beweis (DE-588)4132532-1 s Mathematikstudium (DE-588)4037947-4 s Automatisches Beweisverfahren (DE-588)4069034-9 s DE-604 Dissertationen zur künstlichen Intelligenz 334 (DE-604)BV005345280 334 DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022488463&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schiller, Marvin Granularity analysis for tutoring mathematical proofs Dissertationen zur künstlichen Intelligenz Mathematikstudium (DE-588)4037947-4 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Beweis (DE-588)4132532-1 gnd |
| subject_GND | (DE-588)4037947-4 (DE-588)4069034-9 (DE-588)4132532-1 (DE-588)4113937-9 |
| title | Granularity analysis for tutoring mathematical proofs |
| title_auth | Granularity analysis for tutoring mathematical proofs |
| title_exact_search | Granularity analysis for tutoring mathematical proofs |
| title_full | Granularity analysis for tutoring mathematical proofs Marvin R. G. Schiller |
| title_fullStr | Granularity analysis for tutoring mathematical proofs Marvin R. G. Schiller |
| title_full_unstemmed | Granularity analysis for tutoring mathematical proofs Marvin R. G. Schiller |
| title_short | Granularity analysis for tutoring mathematical proofs |
| title_sort | granularity analysis for tutoring mathematical proofs |
| topic | Mathematikstudium (DE-588)4037947-4 gnd Automatisches Beweisverfahren (DE-588)4069034-9 gnd Beweis (DE-588)4132532-1 gnd |
| topic_facet | Mathematikstudium Automatisches Beweisverfahren Beweis Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=022488463&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV005345280 |
| work_keys_str_mv | AT schillermarvin granularityanalysisfortutoringmathematicalproofs |