Educations with Dynamic Mathematical Software

Tatsuyoshi Hamada, Sep 1, 2015

RIMS研究集会「数学ソフトウェアとその効果的教育利用に関する研究」

Table of Contents

  1. Preliminaries
    1. Brief History of IGS/DGS
    2. Mathemataical Software
    3. Dynamic Mathematical Software
  2. GeoGebra - Dynamic Mathematical Software -
    1. Euclidean Geometry
    2. Graphs of functions
    3. SlopeField
    4. Fourier series
    5. Spreadsheet
    6. CAS (Computer Algebra System)
    7. Complex series
    8. 3D graphics view
    9. Export image formats
    10. Export TeX formats
    11. GeoGebraTube
  3. Dynamic vs Static
    1. Vector Analysis
    2. A Polynomial Curve of Constant Width
    3. Frenet-serret frame
    4. Gradient Vector Field
    5. Drawing parabola from data
    6. Measureing trigonometric function
    7. Table of logarithmic function
    8. Drawing curve
    9. PGF/TikZ
    10. Lua
    11. TeX environments
    12. Auto Multiple Choice
  4. Conclusion
    1. Dynamic mathematical(geometry) software is
    2. What is mathematical software?
    3. Imaginations (delusion?) on our education.
  5. Appendix
    1. Mathematical Software and Free Documents XXI
    2. JSSAC: Japan Society for Symbolic and Algebraic Computation
    3. 日本数式処理学会第25回大会 2015年福岡県

1.

Preliminaries

  • 1. Brief History of IGS/DGS
  • 2. Mathemataical Software
  • 3. Dynamic Mathematical Software

1.1.

Brief History of IGS/DGS

The earliest Geometry Software?
The earliest IGS was the [color=red]Geometric Supposer[/color], which was developed in the early 1980s.[br][br][list][*] Schwartz; Yerushalmy and Wilson (1993). The Geometric Supposer: What is it a Case of?. Hillsdale, NJ: Lawrence Erlbaum Associates.[/list]
Interactive Geometry Software
[list][*][color=red][url=http://www.cabri.com/]Cabri[/url] (Jean-Marie Laborde, 1986-)[/color][*][color=purple][url=http://www.cinderella.de/]Cinderella[/url] (Jürgen Richter-Gebert and Ulrich Kortenkamp, 1998-)[/color][/list]
Dynamic Geometry Software
[list][*][color=red][url=http://www.dynamicgeometry.com/]Geometer's Sketchpad[/url] (Nicholas Jackiw, 1986-)[/color][*][color=blue][url=http://www.mit.edu/~ibaran/kseg.html]KSEG[/url] (Ilya Baran, 1996-2007)[/color][/list]
Construction Tool? （作図ツール）
[list][br][*] [color=purple][url=http://yiijima.sakura.ne.jp/wiki/e01/]GC[/url] (Yasuyuki Iijima, 1989)[/color][br][/list]
– Tatsuyoshi Hamada

1.2.

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1.3.

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2.

GeoGebra - Dynamic Mathematical Software -

  • 1. Euclidean Geometry
  • 2. Graphs of functions
  • 3. SlopeField
  • 4. Fourier series
  • 5. Spreadsheet
  • 6. CAS (Computer Algebra System)
  • 7. Complex series
  • 8. 3D graphics view
  • 9. Export image formats
  • 10. Export TeX formats
  • 11. GeoGebraTube

2.1.

Euclidean Geometry

– Tatsuyoshi Hamada

2.2.

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2.3.

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2.4.

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2.5.

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2.6.

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2.7.

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2.8.

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2.9.

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2.10.

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2.11.

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3.

Dynamic vs Static

  • 1. Vector Analysis
  • 2. A Polynomial Curve of Constant Width
  • 3. Frenet-serret frame
  • 4. Gradient Vector Field
  • 5. Drawing parabola from data
  • 6. Measureing trigonometric function
  • 7. Table of logarithmic function
  • 8. Drawing curve
  • 9. PGF/TikZ
  • 10. Lua
  • 11. TeX environments
  • 12. Auto Multiple Choice

3.1.

Vector Analysis

Arclength Parameter of Cycloid
– Tatsuyoshi Hamada

3.2.

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3.3.

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3.4.

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3.5.

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3.6.

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3.7.

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3.8.

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3.9.

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3.10.

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3.11.

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3.12.

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4.

Conclusion

  • 1. Dynamic mathematical(geometry) software is
  • 2. What is mathematical software?
  • 3. Imaginations (delusion?) on our education.

4.1.

Dynamic mathematical(geometry) software is

[list][*]not only for elementary geometry.[*]It's an environment for describing mathematics with your own idea.[*]Please don't restrict your ideas and knowledge to small area.[*]We can find various connections of various mathematical fields, but it's a small subset of very enormous field of mathematics.[*]Please suspect "This software is bla bla bla."[/list]
– Tatsuyoshi Hamada

4.2.

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4.3.

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5.

Appendix

  • 1. Mathematical Software and Free Documents XXI
  • 2. JSSAC: Japan Society for Symbolic and Algebraic Computation
  • 3. 日本数式処理学会第25回大会 2015年福岡県

5.1.

Mathematical Software and Free Documents XXI

数学ソフトウェアとフリードキュメント XXI
[list][*][url=http://www.mathlibre.org/msfd/21-ja.html]http://www.mathlibre.org/msfd/21-ja.html[/url][/*][*]2015年9月12日(土)13:00–18:00[/*][*][url=http://www.kyoto-su.ac.jp/access.html]京都産業大学[/url] [url=http://mathsoc.jp/meeting/kyoto-sangyo15sept/program/prog15sept_ja_20150825.pdf#page=42]11号館 11408教室[/url][/*][*]京都市北区上賀茂本山 [/*][*]地下鉄で「国際会館駅」下車→京都バス（40系統）で京都産業大学前下車[/*][*]地下鉄で「北大路駅」下車→市バス（北3号系統）または京都バスで京都産大前下車[/*][*]入場無料[/*][*]終了後に講演者を囲んで懇親会を企画しています。[/*][*]懇親会参加を希望される方は、9/4までに濱田 (hamada at fukuoka-u.ac.jp) まで連絡いただければ幸いです。[/*][/list][br]組織委員会[list][*]野呂正行 (立教大学)[/*][*]高山信毅 (神戸大学)[/*][*]濱田龍義 (福岡大学/OCAMI)[/*][*]横山俊一 (九州大学)[/*][/list]後援[list][*]日本数学会情報システム運用委員会[/*][/list][br]キーワード[list][*]レコメンデーションシステム, WebMathematica, Math on Web, TeX, PSTricks, TikZ, ポリオミノ，ポリイアモンド, CafeObj, Coq[/*][/list][br]プログラム[list][*]13:00-13:50 川添 充（大阪府立大学），吉冨 賢太郎（大阪府立大学）[/*][*]14:00-14:50 Norbert Preining （北陸先端科学技術大学院大学）[/*][*]15:00-15:50 溝口 佳寛（九州大学IMI）[/*][*]16:00-16:50 川辺 治之（日本ユニシス）[/*][*]17:00-17:50 加藤 公一（シルバーエッグ・テクノロジー）[/*][/list]
– Tatsuyoshi Hamada

5.2.

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5.3.

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