Mathematical problem posing: conceptual considerations and empirical investigations for understanding the process of problem posing
Saved in:
| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Wiesbaden
Springer Spektrum
[2022]
|
| Series: | Kölner Beiträge zur Didaktik der Mathematik
Research |
| Subjects: | |
| Online Access: | Inhaltstext http://www.springer.com/ Inhaltsverzeichnis Inhaltsverzeichnis |
| Physical Description: | xv, 301 Seiten Illustrationen, Diagramme 21 cm, 422 g |
| ISBN: | 9783658399160 3658399163 |
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MARC
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| 245 | 1 | 0 | |a Mathematical problem posing |b conceptual considerations and empirical investigations for understanding the process of problem posing |c Lukas Baumanns |
| 264 | 1 | |a Wiesbaden |b Springer Spektrum |c [2022] | |
| 300 | |a xv, 301 Seiten |b Illustrationen, Diagramme |c 21 cm, 422 g | ||
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| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Kölner Beiträge zur Didaktik der Mathematik | |
| 490 | 0 | |a Research | |
| 502 | |b Dissertation |c Universität zu Köln |d 2022 | ||
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| 650 | 0 | 7 | |a Problemlösen |0 (DE-588)4076358-4 |2 gnd |9 rswk-swf |
| 653 | |a Problem Solving | ||
| 653 | |a Problem Posing | ||
| 653 | |a Metacognition | ||
| 653 | |a Processes | ||
| 653 | |a Review | ||
| 653 | |a Phase model | ||
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| 776 | 0 | 8 | |i Erscheint auch als |n Online-Ausgabe |a Baumanns, Lukas |t Mathematical Problem Posing |b 1st edition 2022 |d Wiesbaden : Springer Fachmedien Wiesbaden, 2022 |h Online-Ressource |
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Record in the Search Index
| _version_ | 1804185923339943936 |
|---|---|
| adam_text | CONTENTS
I
INTRODUCTION
1
1
MOTIVATION
............................
3
2
OBJECTIVES
...........................................................
7
3
THESIS
STRUCTURE
...................................................................
13
II
THEORETICAL
FRAME
17
4
PROBLEM
POSING
FROM
A
SUBJECT-MATTER
DIDACTICS
PER
SPECTIVE
...................................................................................
21
4.1
ILLUSTRATION
WITH
A
GEOMETRIC
EXAMPLE
......................
21
4.2
CONCEPTIONS
OF
PROBLEM
POSING
-
FOUR
MATHEMATICAL
MINIATURES
....................................................................
35
4.2.1
PROBLEM
POSING
AS
GENERATING
NEW
PROBLEMS
50
4.2.2
PROBLEM
POSING
AS
REFORMULATING
A
GIVEN
PROB
LEM
FOR
PROBLEM
SOLVING
..................................
54
4.2.3
PROBLEM
POSING
AS
REFORMULATING
A
GIVEN
PROB
LEM
FOR
INVESTIGATION
.....................................
57
4.2.4
PROBLEM
POSING
AS
CONSTRUCTING
TASKS
FOR
OTHERS
61
5
PROBLEM
POSING
AND
ITS
CONNECTION
TO
RELATED
CONSTRUCTS
IN
MATHEMATICS
EDUCATION
.............................................
67
5.1
MODELLING
....................................................................
68
5.2
PROVING
...........................................................................
70
5.2.1
PROVING
THROUGH
PROBLEM
POSING
...................
72
5.2.2
PROBLEM
POSING
THROUGH
PROVING
....................
72
5.3
PROBLEM
SOLVING
...........................................................
73
5.3.1
PROBLEM
POSING
AS
A
SUBSET
OF
PROBLEM
SOLVING
76
5.3.2
PROBLEM
SOLVING
AS
A
SUBSET
OF
PROBLEM
POSING
78
5.3.3
PROBLEM
POSING
AND
PROBLEM
SOLVING
AS
COM
PLEMENTARY,
BUT
DIFFERENT
IN
NATURE
.............
79
5.4
CREATIVITY
AND
GIFTEDNESS
...........................................
81
III
JOURNAL
ARTICLES
85
6
RETHINKING
PROBLEM-POSING
SITUATIONS:
A
REVIEW
....
87
6.1
INTRODUCTION
......................................................
88
6.2
THEORETICAL
BACKGROUND
...................................
91
6.2.1
WHAT
IS
PROBLEM
POSING?
...............................
92
6.2.2
WHAT
IS
POSING?
...............................................
93
6.2.3
WHAT
IS
A
PROBLEM?
........................................
93
6.2.4
OPENNESS
OF
PROBLEMS
.....................................
96
6.2.5
CATEGORISATIONS
OF
PROBLEM-POSING
SITUATIONS
97
6.2.6
RESEARCH
QUESTIONS
............................................
100
6.3
DESIGN
...............................................................
101
6.3.1
DATA
SAMPLING
..................................................
101
6.3.2
DATA
ANALYSIS
......................................................
104
6.4
ANALYSIS
1:
IS
IT
POSING?
............................................
105
6.4.1
DISCUSSION
OF
ANALYSIS
1:
MATHEMATICAL
PROB
LEM
POSING
...............................................
108
6.5
ANALYSIS
2:
IS
IT
FREE,
SEMI-STRUCTURED,
OR
STRUCTURED?
110
6.5.1
DISCUSSION
OF
ANALYSIS
2:
UNSTRUCTURED
SITUA
TIONS
.................................................................
ILL
6.6
ANALYSIS
3:
IS
IT
A
ROUTINE
OR
A
NON-ROUTINE
PROBLEM?
114
6.6.1
DISCUSSION
OF
ANALYSIS
3:
ROUTINE
AND
NON
ROUTINE
INITIAL
PROBLEMS
......................................
114
6.7
CONCLUSION
.........................................................................
116
6.7.1
IMPLICATIONS
FOR
PRACTICE
...................................
119
6.7.2
IMPLICATIONS
FOR
RESEARCH
...................................
119
7
DEVELOPING
A
FRAMEWORK
FOR
CHARACTERISING
PROBLEM
POSING
ACTIVITIES:
A
REVIEW
..................................................
123
7.1
INTRODUCTION
......................................................................
124
7.2
WHAT
IS
PROBLEM
POSING?
................................................
128
7.2.1
DEFINITION
OF
PROBLEM
POSING
.............................
128
7.2.2
NON-POSING
ACTIVITIES
.........................................
129
7.3
THE
PROPOSED
FRAMEWORK
................................................
132
7.3.1
DIMENSION
1:
GENERATING
AND
REFORMULATING
132
7.3.2
DIMENSION
2:
ROUTINE
AND
NON-ROUTINE
PROB
LEMS
.....................................................................
134
7.3.3
DIMENSION
3:
METACOGNITIVE
BEHAVIOUR
...
136
7.4
PROCEDURE
OF
THE
LITERATURE
REVIEW
.................................
137
7.5
QUALITATIVE
APPLICATION
OF
THE
FRAMEWORK
....................
142
7.5.1
DIMENSION
1:
GENERATING
AND
REFORMULATING
143
7.5.2
DIMENSION
2:
ROUTINE
AND
NON-ROUTINE
PROB
LEMS
.....................................................................
144
7.5.3
DIMENSION
3:
METACOGNITIVE
BEHAVIOUR
...
148
7.6
QUANTITATIVE
APPLICATION
OF
THE
FRAMEWORK
.............
151
7.7
CONCLUSION
AND
DISCUSSION
.............................................
153
8
THE
PROCESS
OF
PROBLEM
POSING:
DEVELOPMENT
OF
A
DESCRIPTIVE
PROCESS
MODEL
OF
PROBLEM
POSING
..................
159
8.1
INTRODUCTION
.....................................................................
160
8.2
THEORETICAL
BACKGROUND
...................................................
162
8.2.1
PROBLEM
POSING
..................................................
162
8.2.2
PROCESS
OF
PROBLEM
POSING
-
STATE
OF
RESEARCH
164
8.2.3
RESEARCH
QUESTIONS
....................................
169
8.3
THE
STUDY
.......................................................................
169
8.3.1
DATA
COLLECTION
...................................................
169
8.3.2
DATA
EVALUATION
........................................
171
8.4
RESULTS
.............................................................................
173
8.4.1
CATEGORY
DEVELOPMENT
OF
EPISODE
TYPES
IN
PROBLEM
POSING
.........................................
176
8.4.2
DERIVATION
OF
A
DESCRIPTIVE
PHASE
MODEL
FOR
PROBLEM
POSING
.........................................
183
8.5
DISCUSSION
.......................................................................
185
9
IDENTIFYING
METACOGNITIVE
BEHAVIOR
IN
PROBLEM-POSING
PROCESSES.
DEVELOPMENT
OF
A
FRAMEWORK
AND
A
PROOF
OF
CONCEPT
................................................................................
189
9.1
INTRODUCTION
......................................................................
190
9.2
THEORETICAL
BACKGROUND
...................................................
192
9.2.1
PROBLEM
POSING
..................................................
192
9.2.2
METACOGNITION
......................................................
193
9.2.3
RESEARCH
ON
METACOGNITION
IN
MATHEMATICS
EDUCATION
........................................................
197
9.2.4
RESEARCH
ON
METACOGNITION
IN
PROBLEM
POSING
198
9.3
RESEARCH
OBJECTIVES
.........................................................
200
9.4
METHODS
........................................................................
201
9.4.1
RESEARCH
DESIGN
FOR
DATA
COLLECTION
............
201
9.4.2
DATA
ANALYSIS
-
ASSESSMENT
OF
METACOGNITIVE
BEHAVIOR
...............................................................
203
9.5
RESULTS
..............................................................................
205
9.5.1
DEVELOPMENT
OF
A
FRAMEWORK
FOR
IDENTIFYING
PROBLEM-POSING-SPECIFIC
ASPECTS
OF
METACOG
NITIVE
BEHAVIOR
.....................................................
205
9.5.2
PROOF
OF
CONCEPT:
THE
CASES
OF
TINO
&
ULRICH
AND
VALERIE
&
WENKE
.........................................
208
9.6
DISCUSSION
........................................................................
218
9.7
CONCLUSION
........................................................................
220
IV
DISCUSSION
&
OUTLOOK
225
10
SUMMARY
..................................................................................
229
11
POTENTIAL
FOR
FURTHER
RESEARCH
.................................................
233
V
LISTINGS
237
BIBLIOGRAPHY
..................................................................................
239
LIST
OF
TABLES
...............................................................................
269
LIST
OF
FIGURES
...............................................................................
273
VI
APPENDIX 275
A
ONLINE
SUPPLEMENT
OF
JOURNAL
ARTICLE
2
.................................
277
A.1
LIST
OF
ALL
47
INCLUDED
ARTICLES
INCLUDED
IN
THE
REVIEW
277
A.
2
CATEGORISATION
OF
ALL
47
ARTICLES
WITHIN
THE
DEVELOPED
FRAMEWORK
...............................................................
284
B
ONLINE
SUPPLEMENT
OF
JOURNAL
ARTICLE
3
...............................
287
|
| adam_txt |
CONTENTS
I
INTRODUCTION
1
1
MOTIVATION
.
3
2
OBJECTIVES
.
7
3
THESIS
STRUCTURE
.
13
II
THEORETICAL
FRAME
17
4
PROBLEM
POSING
FROM
A
SUBJECT-MATTER
DIDACTICS
PER
SPECTIVE
.
21
4.1
ILLUSTRATION
WITH
A
GEOMETRIC
EXAMPLE
.
21
4.2
CONCEPTIONS
OF
PROBLEM
POSING
-
FOUR
MATHEMATICAL
MINIATURES
.
35
4.2.1
PROBLEM
POSING
AS
GENERATING
NEW
PROBLEMS
50
4.2.2
PROBLEM
POSING
AS
REFORMULATING
A
GIVEN
PROB
LEM
FOR
PROBLEM
SOLVING
.
54
4.2.3
PROBLEM
POSING
AS
REFORMULATING
A
GIVEN
PROB
LEM
FOR
INVESTIGATION
.
57
4.2.4
PROBLEM
POSING
AS
CONSTRUCTING
TASKS
FOR
OTHERS
61
5
PROBLEM
POSING
AND
ITS
CONNECTION
TO
RELATED
CONSTRUCTS
IN
MATHEMATICS
EDUCATION
.
67
5.1
MODELLING
.
68
5.2
PROVING
.
70
5.2.1
PROVING
THROUGH
PROBLEM
POSING
.
72
5.2.2
PROBLEM
POSING
THROUGH
PROVING
.
72
5.3
PROBLEM
SOLVING
.
73
5.3.1
PROBLEM
POSING
AS
A
SUBSET
OF
PROBLEM
SOLVING
76
5.3.2
PROBLEM
SOLVING
AS
A
SUBSET
OF
PROBLEM
POSING
78
5.3.3
PROBLEM
POSING
AND
PROBLEM
SOLVING
AS
COM
PLEMENTARY,
BUT
DIFFERENT
IN
NATURE
.
79
5.4
CREATIVITY
AND
GIFTEDNESS
.
81
III
JOURNAL
ARTICLES
85
6
RETHINKING
PROBLEM-POSING
SITUATIONS:
A
REVIEW
.
87
6.1
INTRODUCTION
.
88
6.2
THEORETICAL
BACKGROUND
.
91
6.2.1
WHAT
IS
PROBLEM
POSING?
.
92
6.2.2
WHAT
IS
POSING?
.
93
6.2.3
WHAT
IS
A
PROBLEM?
.
93
6.2.4
OPENNESS
OF
PROBLEMS
.
96
6.2.5
CATEGORISATIONS
OF
PROBLEM-POSING
SITUATIONS
97
6.2.6
RESEARCH
QUESTIONS
.
100
6.3
DESIGN
.
101
6.3.1
DATA
SAMPLING
.
101
6.3.2
DATA
ANALYSIS
.
104
6.4
ANALYSIS
1:
IS
IT
POSING?
.
105
6.4.1
DISCUSSION
OF
ANALYSIS
1:
MATHEMATICAL
PROB
LEM
POSING
.
108
6.5
ANALYSIS
2:
IS
IT
FREE,
SEMI-STRUCTURED,
OR
STRUCTURED?
110
6.5.1
DISCUSSION
OF
ANALYSIS
2:
UNSTRUCTURED
SITUA
TIONS
.
ILL
6.6
ANALYSIS
3:
IS
IT
A
ROUTINE
OR
A
NON-ROUTINE
PROBLEM?
114
6.6.1
DISCUSSION
OF
ANALYSIS
3:
ROUTINE
AND
NON
ROUTINE
INITIAL
PROBLEMS
.
114
6.7
CONCLUSION
.
116
6.7.1
IMPLICATIONS
FOR
PRACTICE
.
119
6.7.2
IMPLICATIONS
FOR
RESEARCH
.
119
7
DEVELOPING
A
FRAMEWORK
FOR
CHARACTERISING
PROBLEM
POSING
ACTIVITIES:
A
REVIEW
.
123
7.1
INTRODUCTION
.
124
7.2
WHAT
IS
PROBLEM
POSING?
.
128
7.2.1
DEFINITION
OF
PROBLEM
POSING
.
128
7.2.2
NON-POSING
ACTIVITIES
.
129
7.3
THE
PROPOSED
FRAMEWORK
.
132
7.3.1
DIMENSION
1:
GENERATING
AND
REFORMULATING
132
7.3.2
DIMENSION
2:
ROUTINE
AND
NON-ROUTINE
PROB
LEMS
.
134
7.3.3
DIMENSION
3:
METACOGNITIVE
BEHAVIOUR
.
136
7.4
PROCEDURE
OF
THE
LITERATURE
REVIEW
.
137
7.5
QUALITATIVE
APPLICATION
OF
THE
FRAMEWORK
.
142
7.5.1
DIMENSION
1:
GENERATING
AND
REFORMULATING
143
7.5.2
DIMENSION
2:
ROUTINE
AND
NON-ROUTINE
PROB
LEMS
.
144
7.5.3
DIMENSION
3:
METACOGNITIVE
BEHAVIOUR
.
148
7.6
QUANTITATIVE
APPLICATION
OF
THE
FRAMEWORK
.
151
7.7
CONCLUSION
AND
DISCUSSION
.
153
8
THE
PROCESS
OF
PROBLEM
POSING:
DEVELOPMENT
OF
A
DESCRIPTIVE
PROCESS
MODEL
OF
PROBLEM
POSING
.
159
8.1
INTRODUCTION
.
160
8.2
THEORETICAL
BACKGROUND
.
162
8.2.1
PROBLEM
POSING
.
162
8.2.2
PROCESS
OF
PROBLEM
POSING
-
STATE
OF
RESEARCH
164
8.2.3
RESEARCH
QUESTIONS
.
169
8.3
THE
STUDY
.
169
8.3.1
DATA
COLLECTION
.
169
8.3.2
DATA
EVALUATION
.
171
8.4
RESULTS
.
173
8.4.1
CATEGORY
DEVELOPMENT
OF
EPISODE
TYPES
IN
PROBLEM
POSING
.
176
8.4.2
DERIVATION
OF
A
DESCRIPTIVE
PHASE
MODEL
FOR
PROBLEM
POSING
.
183
8.5
DISCUSSION
.
185
9
IDENTIFYING
METACOGNITIVE
BEHAVIOR
IN
PROBLEM-POSING
PROCESSES.
DEVELOPMENT
OF
A
FRAMEWORK
AND
A
PROOF
OF
CONCEPT
.
189
9.1
INTRODUCTION
.
190
9.2
THEORETICAL
BACKGROUND
.
192
9.2.1
PROBLEM
POSING
.
192
9.2.2
METACOGNITION
.
193
9.2.3
RESEARCH
ON
METACOGNITION
IN
MATHEMATICS
EDUCATION
.
197
9.2.4
RESEARCH
ON
METACOGNITION
IN
PROBLEM
POSING
198
9.3
RESEARCH
OBJECTIVES
.
200
9.4
METHODS
.
201
9.4.1
RESEARCH
DESIGN
FOR
DATA
COLLECTION
.
201
9.4.2
DATA
ANALYSIS
-
ASSESSMENT
OF
METACOGNITIVE
BEHAVIOR
.
203
9.5
RESULTS
.
205
9.5.1
DEVELOPMENT
OF
A
FRAMEWORK
FOR
IDENTIFYING
PROBLEM-POSING-SPECIFIC
ASPECTS
OF
METACOG
NITIVE
BEHAVIOR
.
205
9.5.2
PROOF
OF
CONCEPT:
THE
CASES
OF
TINO
&
ULRICH
AND
VALERIE
&
WENKE
.
208
9.6
DISCUSSION
.
218
9.7
CONCLUSION
.
220
IV
DISCUSSION
&
OUTLOOK
225
10
SUMMARY
.
229
11
POTENTIAL
FOR
FURTHER
RESEARCH
.
233
V
LISTINGS
237
BIBLIOGRAPHY
.
239
LIST
OF
TABLES
.
269
LIST
OF
FIGURES
.
273
VI
APPENDIX 275
A
ONLINE
SUPPLEMENT
OF
JOURNAL
ARTICLE
2
.
277
A.1
LIST
OF
ALL
47
INCLUDED
ARTICLES
INCLUDED
IN
THE
REVIEW
277
A.
2
CATEGORISATION
OF
ALL
47
ARTICLES
WITHIN
THE
DEVELOPED
FRAMEWORK
.
284
B
ONLINE
SUPPLEMENT
OF
JOURNAL
ARTICLE
3
.
287 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Baumanns, Lukas |
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| bvnumber | BV049374569 |
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| format | Thesis Book |
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| genre_facet | Hochschulschrift |
| id | DE-604.BV049374569 |
| illustrated | Illustrated |
| index_date | 2024-07-03T22:55:30Z |
| indexdate | 2024-07-10T10:02:57Z |
| institution | BVB |
| institution_GND | (DE-588)1043386068 |
| isbn | 9783658399160 3658399163 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-034634458 |
| oclc_num | 1357102877 |
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| physical | xv, 301 Seiten Illustrationen, Diagramme 21 cm, 422 g |
| publishDate | 2022 |
| publishDateSearch | 2022 |
| publishDateSort | 2022 |
| publisher | Springer Spektrum |
| record_format | marc |
| series2 | Kölner Beiträge zur Didaktik der Mathematik Research |
| spelling | Baumanns, Lukas Verfasser (DE-588)1283027275 aut Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing Lukas Baumanns Wiesbaden Springer Spektrum [2022] xv, 301 Seiten Illustrationen, Diagramme 21 cm, 422 g txt rdacontent n rdamedia nc rdacarrier Kölner Beiträge zur Didaktik der Mathematik Research Dissertation Universität zu Köln 2022 Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Problemlösen (DE-588)4076358-4 gnd rswk-swf Problem Solving Problem Posing Metacognition Processes Review Phase model (DE-588)4113937-9 Hochschulschrift gnd-content Problemlösen (DE-588)4076358-4 s Mathematikunterricht (DE-588)4037949-8 s DE-604 Springer Fachmedien Wiesbaden (DE-588)1043386068 pbl Erscheint auch als Online-Ausgabe Baumanns, Lukas Mathematical Problem Posing 1st edition 2022 Wiesbaden : Springer Fachmedien Wiesbaden, 2022 Online-Ressource X:MVB text/html http://deposit.dnb.de/cgi-bin/dokserv?id=72cc6f0d071b458f96353680a4bfa133&prov=M&dok_var=1&dok_ext=htm Inhaltstext X:MVB http://www.springer.com/ B:DE-101 application/pdf https://d-nb.info/1270837591/04 Inhaltsverzeichnis DNB Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=034634458&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p dnb 20230503 DE-101 https://d-nb.info/provenance/plan#dnb |
| spellingShingle | Baumanns, Lukas Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing Mathematikunterricht (DE-588)4037949-8 gnd Problemlösen (DE-588)4076358-4 gnd |
| subject_GND | (DE-588)4037949-8 (DE-588)4076358-4 (DE-588)4113937-9 |
| title | Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing |
| title_auth | Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing |
| title_exact_search | Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing |
| title_exact_search_txtP | Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing |
| title_full | Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing Lukas Baumanns |
| title_fullStr | Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing Lukas Baumanns |
| title_full_unstemmed | Mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing Lukas Baumanns |
| title_short | Mathematical problem posing |
| title_sort | mathematical problem posing conceptual considerations and empirical investigations for understanding the process of problem posing |
| title_sub | conceptual considerations and empirical investigations for understanding the process of problem posing |
| topic | Mathematikunterricht (DE-588)4037949-8 gnd Problemlösen (DE-588)4076358-4 gnd |
| topic_facet | Mathematikunterricht Problemlösen Hochschulschrift |
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