History in mathematics education: the ICMI study
Gespeichert in:
| Weitere Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Dordrecht [u.a.]
Kluwer Acad. Publ.
2000
|
| Schriftenreihe: | New ICMI study series
6 |
| Schlagworte: | |
| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVIII, 437 Seiten Illustrationen, Digramme |
| ISBN: | 1402009429 079236399X |
Internformat
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Datensatz im Suchindex
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Contents Introduction. . xi 1. The political context 1 1.1 1.2 Introduction. —.—.—. —------ .—1 What part does history of mathematics currently occupy in national curricula? .2 1.2.1 1.2.2 1.2.3 1.2.4 1.2.5 1.2.6 1.2.7 1.2.8 1.2.9 1.2.10 1.2.11 1.2.12 1.2.13 1.2.14 1.2.15 1.2.16 Argentina. 2 Austria. . 3 Brazil. 3 China. 4 Denmark. 5 France.;. 7 Greece. 8 Israel. 9
Italy. 9 Japan. . 10 Netherlands. 11 New Zealand. .12 Norway . 14 Poland . 15 United Kingdom. 16 United States of America. 18 1.3 History of mathematics in curriculaand schoolbooks: a case study of Poland._ ._ .— _ _ .19 1.3.1 1.3.2 1.3.3 History of mathematics in mathematicscurricula. 20 History of mathematics in mathematicsschool-books. 21 Final
remarks.28 1.4 Policy and politics in the advocacy of ahistorical component .29 1.4.1 1.4.2 1.4.3 1.4.4 1.4.5 1.4.6 Political authorities (at all levels). 31 Teacher associations. 31 Professional mathematics associations. 32 Tertiary teachers. 32 Parents . 33 Textbook authors.33 1.5 Quotations on the use of history of mathematics in mathematics teaching and learning. 33
vi 2. Philosophical, multicultural and interdisciplinary issues 39 2.1 Introduction .39 2.2 Philosophical issues._ .----- ------------ .40 2.2.1 2.2.2 2.2.3 Historical investigation, evidence and interpretation.40 Philosophy of mathematics, old and new. 42 The ends of the spectrum. 44 2.3 Multicultural issues._ .—.46 2.3.1 2.3.2 2.3.3 Introduction. 46 Multiculturalism inside the history of mathematics. 47 Mathematics as a human enterprise. 50 2.4 Interdisciplinary issues. ---------.---------------------- ---------- ----- 52 2.4.1 2.4.2 2.4.3 2.4.4 Introduction. 52 History of mathematics and the study of history. 53 History of mathematics linking topics within mathematics. 53 History of mathematics
linking mathematics with other disciplines. 55 2.5 Conclusion.61 3. Integrating history: research perspectives 63 3.1 3.2 Introduction .63 The historical dimension: from teacher to learner .66 3.3 3.4 The indirect genetic approach to calculus--------- ------- ._ .71 Stochastics teaching and cognitive development.--------- ._.74 3.5 3.6 Ancient problems for the development of strategic thinking. 78 Difficulties with series in history and in the classroom —.-----82 3.7 On potentialities, limits and risks. 86 3.8 Suggestions for future research.—. . 90 4. History of Mathematics for Trainee Teachers 91 4.1 Earlier views on history in teacher education .91 4.2 4.3 International overview. .93 Examples of current practice.H0 4.3.1 Current practice in initial teacher training. 110 4.3.2 Current practice in in-service training. 131 4.4 Issues of
Concern. 140
vii 5. Historical formation and student understanding of mathematics. 143 5.1 Introduction. 143 5.2 The role of historical analysis in predicting and interpreting students’ difficulties in mathematics. 149 5.3 The relevance of historical studies in designing and analysing classroom activities. 154 5.3.1 5.3.2 Bringing historical texts into the classroom: the ‘voices and echoes’ games.155 Indirect use of historical and epistemological studies in the design of activities for students. 156 The example of linear algebra. 157 The example of calculus. 159 Research on the methodology of history-based design of activities for students. 160 5.3.3 5.3.4 5.3.5 5.4 Epistemological assumptions framing interpretations ofstudents understanding of mathematics. 162 5.4.1 5.4.2 5.4.3 The ‘epistemological obstacles’ perspective. 162 A socio-cultural
perspective. 163 The ‘voices and echoes’ perspective. 165 5.5 Conclusions: guidelines and suggestions for future research. 168 6. History in support of diverse educational requirements — opportunities for change. 171 6.1 Introduction. 171 6.2 Educational, cultural, social andeconomicdiversity in primary, secondary and tertiary settings. .172 6.2.1 6.2.2 6.2.3 6.2.4 6.25 6.2.6 Primary education and the use of mathematics history in the classroom. 172 Under-served (limited resources) students. 174 Alternative educational pathways: adult learnersreturning to mathematics education, vocational education and training. 179 Minority school populations. 184 Students having educational challenges. 187 Mathematically gifted and talented students. . 188 6.3 Opportunities for
change. 195 6.3.1 Teacher education.195 6.4 Conclusion. 199 7. Integrating history of mathematics in the classroom:an analytic survey. . . 201 7.1 Introduction. 201 7.2 Why should history of mathematics beintegratedin mathematics education?. . 202
viii 7.3 How may history of mathematics be integrated in mathematics education?._.----- -—.—.----- .—.—.------ 208 7.3.1 7.3.2 7.3.3 Direct historical information. 208 A teaching approach inspired by history. 208 Mathematical awareness.211 7.4 Ideas and examples for classroom implementation. .213 7.4.1 7.4.2 7.4.3 7.4.4 7.4.5 7.4.6 Historical Snippets. 214 Student research projects based on history texts. 215 PrimarySources. -. 216 Worksheets. 216 Historical packages. 217 Taking advantage of errors, alternative conceptions, change of perspective, revision of implicit assumptions, intuitive arguments etc. 219 Historical problems. 224 Mechanical
instruments.227 Experiential mathematical activities. 228 Plays. 229 Films and other visual means. 230 Outdoor experiences. 231 The WWW. 232 7.4.7 7.4.8 7.4.9 7.4.10 7.4.11 7.4.12 7.4.13 8. Historical support for particular subjects 241 8.1 8.2 Introduction. 241 Teaching projects inspired by history.—.--------- .243 8.2.1 8.2.2 8.2.3 8.2.4 Examples from algebra and analysis.243 A heuristic introduction to analysis implicitly inspired by its historical development. 245 How may history help the teaching of probabilistic concepts?. 248 Trigonometry in the historical order.252 8.3 Cultural aspects of mathematics
in a historical perspective .253 8.3.1 8.3.2 8.3.3 Number systems and their representations. . 253 The Pythagorean theorem in different cultures. 258 Measuring distances: Heron vs. Liu Hui. 262 8.4 Detailed treatment of particular examples .264 8.4.1 8.4.2 8.4.3 8.4.4 8.4.5 8.4.6 8.4.7 8.4.8 Introducing complex numbers: an experiment. 264 Intertwining a mathematical topic with other (non-) mathematical topics.265 Surveyors’ problems.273 Theory of proportion and the geometry of areas. 276 Deductive vs intuitive thinking: an example from the calculus. 279 Tracing the root of the abstract concept of a set. 281 Discrete mathematics: an example. 282 The relation between geometry and physics: an example. 283
ix 8.5 Improving mathematical awareness through the history of mathematics 286 8.5.1 History of mathematics education. .—.—.286 8.5.2 Teaching secondary mathematics in a historical perspective. 288 8.5.3 Adults’ mathematics educational histories. 289 9. The use of original sources in the mathematics classroom ········*·«·*········*··········«···«··«·«·*·««····*······*··*········*·············*······*·*··········· 9.1 Introduction .291 9.2 Motivations, aims and uses.—.—.292 9.2.1 The specific value and quality of primary sources. 292 9.2.2 Understanding the evolution of ideas. 294 9.2.3 Experiencing the relativity of truth and the human dimension of mathematical activity. 295 9.2.4 Relations between mathematics and philosophy.296 9.25 Simplicity, motivation and didactics. 297 9.2. 6 Perspectives on mathematics education.297 9.2. 7
Local Mathematics. 298 93 Sources, hermeneutics and language .298 9.4 Integrating original sources in pre-service teacher education .299 9.4.1 Example 1: Egyptian measures of angles.299 9.4.2 Example 2: complex numbers in geometry and algebra. 303 9.5 Integrating Original Sources in the Classroom.307 9.5.1 Example 1: Greek surveying: the tunnel of Samos. 307 9.5.2 Example 2: An 18th century treatise on conic sections. 310 9.6 Didactical strategies for integrating sources._—.--------- .313 9.6.1 The triad: text - context - reader. 313 9.6.2 Classroom strategies. 313 9.7 Evaluation, research questions and issues of concern .316 10. Non-standard media and other resources 329 10.1 Introduction .329 10.1.1 10.1.2 10.1.3 10.1.4 10.1.5 Why other
media?. 329 And which media?. 330 Affect and effect.331 Media and cognitive aspects of learning. 333 Media and assessment. 334 10.2 Learning through history and non-standard media-------------------- .335 10.2.1 Mathematical Dramatisation. 335 10.2.2 Ancient instruments in the modem classroom.343
X 10.2.3 Inquiring mathematics with history and software.351 10.3 Resources for history of mathematics on the World Wide Web.358 10.3.1 Teachers, learners and the World Wide Web.358 10.3.2 Web historical resources for the mathematics teacher. 362 11. Bibliography for further work in the area 371 11.1 Introduction. 371 11.2 11.3 11.4 Chinese. 373 Danish. 383 Dutch. 386 11.5 11.6 11.7 11.8 English. 389 French. 404 German. 405 Greek. 411 11.9 Italian. 414 11.10 Collections of articles
(special issues). 416 11.10 11.10 .1 Journals (special issues). 416 .2 Books. 417 Notes on contributors. 419 Index. 429 |
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| spelling | History in mathematics education the ICMI study ed. by John Fauvel ... Dordrecht [u.a.] Kluwer Acad. Publ. 2000 XVIII, 437 Seiten Illustrationen, Digramme txt rdacontent n rdamedia nc rdacarrier New ICMI study series 6 Geschichte gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 gnd rswk-swf Mathematikunterricht (DE-588)4037949-8 s Geschichte z DE-604 Fauvel, John 1947-2001 (DE-588)124238971 edt International Commission on Mathematical Instruction New ICMI study series 6 (DE-604)BV011532615 6 Digitalisierung UB Passau - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=020316030&sequence=000001&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | History in mathematics education the ICMI study Mathematikunterricht (DE-588)4037949-8 gnd |
| subject_GND | (DE-588)4037949-8 |
| title | History in mathematics education the ICMI study |
| title_auth | History in mathematics education the ICMI study |
| title_exact_search | History in mathematics education the ICMI study |
| title_full | History in mathematics education the ICMI study ed. by John Fauvel ... |
| title_fullStr | History in mathematics education the ICMI study ed. by John Fauvel ... |
| title_full_unstemmed | History in mathematics education the ICMI study ed. by John Fauvel ... |
| title_short | History in mathematics education |
| title_sort | history in mathematics education the icmi study |
| title_sub | the ICMI study |
| topic | Mathematikunterricht (DE-588)4037949-8 gnd |
| topic_facet | Mathematikunterricht |
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