Explanation and proof in mathematics: philosophical and educational perspectives
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
New York [u.a.]
Springer
2010
|
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | VIII, 294 S. Ill., graph. Darst. |
| ISBN: | 9781441905758 1441905758 |
Internformat
MARC
| LEADER | 00000nam a2200000 c 4500 | ||
|---|---|---|---|
| 001 | BV035986705 | ||
| 003 | DE-604 | ||
| 005 | 20200812 | ||
| 007 | t | ||
| 008 | 100129s2010 ad|| |||| 00||| eng d | ||
| 020 | |a 9781441905758 |9 978-1-4419-0575-8 | ||
| 020 | |a 1441905758 |9 1-4419-0575-8 | ||
| 035 | |a (OCoLC)502399282 | ||
| 035 | |a (DE-599)BVBBV035986705 | ||
| 040 | |a DE-604 |b ger |e rakwb | ||
| 041 | 0 | |a eng | |
| 049 | |a DE-12 |a DE-11 |a DE-91 |a DE-384 | ||
| 050 | 0 | |a QA9.54 | |
| 082 | 0 | |a 510.1 |2 22 | |
| 084 | |a SM 603 |0 (DE-625)143291: |2 rvk | ||
| 084 | |a MAT 036f |2 stub | ||
| 084 | |a EDU 730f |2 stub | ||
| 245 | 1 | 0 | |a Explanation and proof in mathematics |b philosophical and educational perspectives |c Gila Hanna ... eds. |
| 264 | 1 | |a New York [u.a.] |b Springer |c 2010 | |
| 300 | |a VIII, 294 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 650 | 4 | |a Mathematics / Philosophy | |
| 650 | 4 | |a Proof theory | |
| 650 | 4 | |a Mathematik | |
| 650 | 4 | |a Philosophie | |
| 650 | 4 | |a Mathematics |x Philosophy | |
| 650 | 4 | |a Proof theory | |
| 650 | 0 | 7 | |a Beweistheorie |0 (DE-588)4145177-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Philosophie |0 (DE-588)4045791-6 |2 gnd |9 rswk-swf |
| 689 | 0 | 0 | |a Beweistheorie |0 (DE-588)4145177-6 |D s |
| 689 | 0 | 1 | |a Philosophie |0 (DE-588)4045791-6 |D s |
| 689 | 0 | |C b |5 DE-604 | |
| 700 | 1 | |a Hanna, Gila |d 1934- |0 (DE-588)172124794 |4 edt | |
| 856 | 4 | 2 | |m HBZ Datenaustausch |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018879505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-018879505 | ||
Datensatz im Suchindex
| _version_ | 1804141008721543168 |
|---|---|
| adam_text | Titel: Explanation and Proof in Mathematics
Autor: Hanna, Gila
Jahr: 2010
Contents
1 Introduction............................................................................................... 1
Part I Reflections on the Nature and Teaching of Proof
2 The Conjoint Origin of Proof and Theoretical Physics......................... 17
Hans Niels Jahnke
3 Lakatos, Lakoff and Nunez: Towards a Satisfactory
Definition of Continuity............................................................................ 33
Teun Koetsier
4 Preaxiomatic Mathematical Reasoning:
An Algebraic Approach............................................................................ 47
Mary Leng
5 Completions, Constructions, and Corollaries......................................... 59
Thomas Mormann
6 Authoritarian Versus Authoritative Teaching:
Polyaand Lakatos..................................................................................... 71
Brendan Larvor
7 Proofs as Bearers of Mathematical Knowledge...................................... 85
Gila Hanna and Ed Barbeau
8 Mathematicians Individual Criteria for Accepting
Theorems and Proofs: An Empirical Approach..................................... 101
Aiso Heinze
v¡ Contents
Part II Proof and Cognitive Development
9 Bridging Knowing and Proving in Mathematics:
A Didactical Perspective......................................................................... 115
Nicolas Balacheff
10 The Long-Term Cognitive Development of Reasoning
and Proof.................................................................................................. 137
David Tall and Juan Pablo Mejia-Ramos
11 Historical Artefacts, Semiotic Mediation and Teaching Proof........... 151
Maria G. Bartolini Bussi
12 Proofs, Semiotics and Artefacts of Information Technologies............ 169
Maria Alessandra Mariotti
Part HI Experiments, Diagrams and Proofs
13 Proof as Experiment in Wittgenstein.................................................... 191
Alfred Nordmann
14 Experimentation and Proof in Mathematics........................................ 205
Michael de Villiers
15 Proof, Mathematical Problem-Solving, and Explanation
in Mathematics Teaching........................................................................ 223
Kazuhiko Nunokawa
16 Evolving Geometric Proofs in the Seventeenth Century:
From Icons to Symbols........................................................................... 237
Evelyne Barbin
17 Proof in the Wording: Two Modalities from Ancient
Chinese Algorithms................................................................................. 253
Karine Chemla
Index................................................................................................................. 287
|
| any_adam_object | 1 |
| author2 | Hanna, Gila 1934- |
| author2_role | edt |
| author2_variant | g h gh |
| author_GND | (DE-588)172124794 |
| author_facet | Hanna, Gila 1934- |
| building | Verbundindex |
| bvnumber | BV035986705 |
| callnumber-first | Q - Science |
| callnumber-label | QA9 |
| callnumber-raw | QA9.54 |
| callnumber-search | QA9.54 |
| callnumber-sort | QA 19.54 |
| callnumber-subject | QA - Mathematics |
| classification_rvk | SM 603 |
| classification_tum | MAT 036f EDU 730f |
| ctrlnum | (OCoLC)502399282 (DE-599)BVBBV035986705 |
| dewey-full | 510.1 |
| dewey-hundreds | 500 - Natural sciences and mathematics |
| dewey-ones | 510 - Mathematics |
| dewey-raw | 510.1 |
| dewey-search | 510.1 |
| dewey-sort | 3510.1 |
| dewey-tens | 510 - Mathematics |
| discipline | Pädagogik Mathematik |
| format | Book |
| fullrecord | <?xml version="1.0" encoding="UTF-8"?><collection xmlns="http://www.loc.gov/MARC21/slim"><record><leader>01695nam a2200469 c 4500</leader><controlfield tag="001">BV035986705</controlfield><controlfield tag="003">DE-604</controlfield><controlfield tag="005">20200812 </controlfield><controlfield tag="007">t</controlfield><controlfield tag="008">100129s2010 ad|| |||| 00||| eng d</controlfield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">9781441905758</subfield><subfield code="9">978-1-4419-0575-8</subfield></datafield><datafield tag="020" ind1=" " ind2=" "><subfield code="a">1441905758</subfield><subfield code="9">1-4419-0575-8</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(OCoLC)502399282</subfield></datafield><datafield tag="035" ind1=" " ind2=" "><subfield code="a">(DE-599)BVBBV035986705</subfield></datafield><datafield tag="040" ind1=" " ind2=" "><subfield code="a">DE-604</subfield><subfield code="b">ger</subfield><subfield code="e">rakwb</subfield></datafield><datafield tag="041" ind1="0" ind2=" "><subfield code="a">eng</subfield></datafield><datafield tag="049" ind1=" " ind2=" "><subfield code="a">DE-12</subfield><subfield code="a">DE-11</subfield><subfield code="a">DE-91</subfield><subfield code="a">DE-384</subfield></datafield><datafield tag="050" ind1=" " ind2="0"><subfield code="a">QA9.54</subfield></datafield><datafield tag="082" ind1="0" ind2=" "><subfield code="a">510.1</subfield><subfield code="2">22</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">SM 603</subfield><subfield code="0">(DE-625)143291:</subfield><subfield code="2">rvk</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">MAT 036f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="084" ind1=" " ind2=" "><subfield code="a">EDU 730f</subfield><subfield code="2">stub</subfield></datafield><datafield tag="245" ind1="1" ind2="0"><subfield code="a">Explanation and proof in mathematics</subfield><subfield code="b">philosophical and educational perspectives</subfield><subfield code="c">Gila Hanna ... eds.</subfield></datafield><datafield tag="264" ind1=" " ind2="1"><subfield code="a">New York [u.a.]</subfield><subfield code="b">Springer</subfield><subfield code="c">2010</subfield></datafield><datafield tag="300" ind1=" " ind2=" "><subfield code="a">VIII, 294 S.</subfield><subfield code="b">Ill., graph. Darst.</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="650" ind1=" " ind2="4"><subfield code="a">Mathematics / Philosophy</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proof theory</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematik</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Philosophie</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Mathematics</subfield><subfield code="x">Philosophy</subfield></datafield><datafield tag="650" ind1=" " ind2="4"><subfield code="a">Proof theory</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Beweistheorie</subfield><subfield code="0">(DE-588)4145177-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="650" ind1="0" ind2="7"><subfield code="a">Philosophie</subfield><subfield code="0">(DE-588)4045791-6</subfield><subfield code="2">gnd</subfield><subfield code="9">rswk-swf</subfield></datafield><datafield tag="689" ind1="0" ind2="0"><subfield code="a">Beweistheorie</subfield><subfield code="0">(DE-588)4145177-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2="1"><subfield code="a">Philosophie</subfield><subfield code="0">(DE-588)4045791-6</subfield><subfield code="D">s</subfield></datafield><datafield tag="689" ind1="0" ind2=" "><subfield code="C">b</subfield><subfield code="5">DE-604</subfield></datafield><datafield tag="700" ind1="1" ind2=" "><subfield code="a">Hanna, Gila</subfield><subfield code="d">1934-</subfield><subfield code="0">(DE-588)172124794</subfield><subfield code="4">edt</subfield></datafield><datafield tag="856" ind1="4" ind2="2"><subfield code="m">HBZ 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=018879505&sequence=000002&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:BVB01-018879505</subfield></datafield></record></collection> |
| id | DE-604.BV035986705 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T22:09:03Z |
| institution | BVB |
| isbn | 9781441905758 1441905758 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-018879505 |
| oclc_num | 502399282 |
| open_access_boolean | |
| owner | DE-12 DE-11 DE-91 DE-BY-TUM DE-384 |
| owner_facet | DE-12 DE-11 DE-91 DE-BY-TUM DE-384 |
| physical | VIII, 294 S. Ill., graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | Springer |
| record_format | marc |
| spelling | Explanation and proof in mathematics philosophical and educational perspectives Gila Hanna ... eds. New York [u.a.] Springer 2010 VIII, 294 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Mathematics / Philosophy Proof theory Mathematik Philosophie Mathematics Philosophy Beweistheorie (DE-588)4145177-6 gnd rswk-swf Philosophie (DE-588)4045791-6 gnd rswk-swf Beweistheorie (DE-588)4145177-6 s Philosophie (DE-588)4045791-6 s b DE-604 Hanna, Gila 1934- (DE-588)172124794 edt HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018879505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Explanation and proof in mathematics philosophical and educational perspectives Mathematics / Philosophy Proof theory Mathematik Philosophie Mathematics Philosophy Beweistheorie (DE-588)4145177-6 gnd Philosophie (DE-588)4045791-6 gnd |
| subject_GND | (DE-588)4145177-6 (DE-588)4045791-6 |
| title | Explanation and proof in mathematics philosophical and educational perspectives |
| title_auth | Explanation and proof in mathematics philosophical and educational perspectives |
| title_exact_search | Explanation and proof in mathematics philosophical and educational perspectives |
| title_full | Explanation and proof in mathematics philosophical and educational perspectives Gila Hanna ... eds. |
| title_fullStr | Explanation and proof in mathematics philosophical and educational perspectives Gila Hanna ... eds. |
| title_full_unstemmed | Explanation and proof in mathematics philosophical and educational perspectives Gila Hanna ... eds. |
| title_short | Explanation and proof in mathematics |
| title_sort | explanation and proof in mathematics philosophical and educational perspectives |
| title_sub | philosophical and educational perspectives |
| topic | Mathematics / Philosophy Proof theory Mathematik Philosophie Mathematics Philosophy Beweistheorie (DE-588)4145177-6 gnd Philosophie (DE-588)4045791-6 gnd |
| topic_facet | Mathematics / Philosophy Proof theory Mathematik Philosophie Mathematics Philosophy Beweistheorie |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018879505&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hannagila explanationandproofinmathematicsphilosophicalandeducationalperspectives |