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IS4IS VIENNA (2015) KETCindy supporting tool to convert students findings into knowledge Masataka Kaneko Satoshi Yamashita Hideyo Makishita Yoshifumi Maeda Naoki Hamaguchi Shigeki Kobayashi Setsuo Takato KAKENHI 15K01037 CONTENTS

  1. IS4IS VIENNA (2015) KETCindy supporting tool to convert students’ findings into knowledge Masataka Kaneko Satoshi Yamashita Hideyo Makishita Yoshifumi Maeda Naoki Hamaguchi Shigeki Kobayashi Setsuo Takato KAKENHI 15K01037

  2. CONTENTS 1. Activities in math classroom 2. ICT support in math classroom 3. Linkage to T EX edition 4. Problem of T EX edition 5. Approach using CAS (KETpic) 6. Approach using DGS (KETCindy)

  3. 1. Activities in math classroom Inductive Reasoning Deductive Reasoning Establishment of Knowledge Application of Knowledge

  4. 1. Activities in math classroom Inductive Reasoning Simulation, Observation, Conjecture Deductive Reasoning Establishment of Knowledge Application of Knowledge

  5. 1. Activities in math classroom Inductive Reasoning Simulation, Observation, Conjecture Deductive Reasoning Calculation, Interpretation, Proof Establishment of Knowledge Application of Knowledge

  6. 1. Activities in math classroom Inductive Reasoning Simulation, Observation, Conjecture Deductive Reasoning Calculation, Interpretation, Proof Establishment of Knowledge Memorization, Exercise Application of Knowledge

  7. 1. Activities in math classroom Inductive Reasoning Simulation, Observation, Conjecture Deductive Reasoning Calculation, Interpretation, Proof Establishment of Knowledge Memorization, Exercise, Reflection Application of Knowledge Application to other situations

  8. 2. ICT support in math classroom Inductive Reasoning Simulation with CAS/DGS Deductive Reasoning Establishment of Knowledge Application of Knowledge

  9. 2. ICT support in math classroom Inductive Reasoning Deductive Reasoning Calculation and Proof with the aid of CAS/DGS Establishment of Knowledge Application of Knowledge

  10. 2. ICT support in math classroom Inductive Reasoning Deductive Reasoning Establishment of Knowledge Web based Training Application of Knowledge

  11. 2. ICT support in math classroom Inductive Reasoning Deductive Reasoning Establishment of Knowledge Application of Knowledge Materials accumulated on the Web

  12. 2. ICT support in math classroom Inductive Reasoning Paper and Pencil based learning is Deductive Reasoning indispensable Establishment of Knowledge Application of Knowledge

  13. 3. Linkage to T EX edition From CAS to T EX y 1 x Π Π 2 � 1

  14. 3. Linkage to T EX edition From CAS to T EX y 1 x π π O 2 − 1

  15. 3. Linkage to T EX edition From DGS to T EX Simulation via DGS screen calculation via T EX document

  16. 3. Linkage to T EX edition y x

  17. 3. Linkage to T EX edition y y = x 2 α − 1 x α − 2 y = x 2 − 4 y = 2 αx − α 2 y = 2( α + 1) x − ( α + 1) 2

  18. 3. Linkage to T EX edition y x

  19. 4. Problem of T EX edition Characteristics of edition via T EX 1. high quality in graphics 2. limitation in computing and programming capability 3. generated table tends to be inappropriate 4. page layout can not be set flexibly

  20. 4. Problem of T EX edition Characteristics of edition via T EX 1. high quality in graphics 2. limitation in computing and programming capability 3. generated table tends to be inappropri- ate 4. page layout can not be set flexibly

  21. 4. Problem of T EX edition 5 π π 0 · · · · · · · · · 2 π x 6 6 y ′ + 0 − 0 + √ √ 5 π π 2 ↗ 6 + 3 ↘ 6 − 3 ↗ 2 + 2 π y

  22. 4. Problem of T EX edition 5 π · · · · · · · · · 0 2 π x 6 π 6 + − + y ′ 0 0 √ √ 5 π 6 + 3 ↗ ↘ ↗ 2 + 2 π 2 6 π − 3 y

  23. 4. Problem of T EX edition y f ( x ) π x O π g ( x ) 2 ↗ ↘ f ( x ) ↗ ↗ g ( x ) ↗ ↘

  24. 4. Problem of T EX edition Characteristics of edition via T EX 1. high quality in graphics 2. limitation in computing and programming capability 3. generated table tends to be inappropriate 4. page layout can not be set flexibly

  25. 4. Problem of T EX edition y x

  26. 4. Problem of T EX edition y x

  27. 4. Problem of T EX edition y x

  28. 4. Problem of T EX edition

  29. 4. Problem of T EX edition Crossing

  30. 4. Problem of T EX edition Crossing Bezier curves can be generated via KETCindy.

  31. 5. CAS+KETpic CAS PDF file Mod. Compile K ETpic T EXfile Plot Data \ input Tpic code http://ketpic.com

  32. 5. CAS+KETpic y dx  dt = x ( t ) · (1 − y ( t ))  dy dt = 0 . 5 · y ( t ) · ( x ( t ) − 1)  x O

  33. 5. CAS+KETpic CAS PDF file Mod. Compile K ETpic T EXfile Plot Data \ input Tpic code

  34. 5. CAS+KETpic S1=NDSolve[{x’(t)==x[t]*(1-y[t]),y’[t]==0.5*y[t]*(x[t]-1), x[0]==**,y[0]==**},{x,y},{t,10}]; PS1=ParametricPlot[Evaluate[{x[t],y[t]}/.S1],{t,0,10}]; y x O

  35. 5. CAS+KETpic CAS PDF file Mod. Compile K ETpic T EXfile Plot Data \ input Tpic code

  36. 5. CAS+KETpic Openfile(’’fig.tex’’,’’1cm’’); Drwline(PS1); Closefile(’’1’’); y x O

  37. 5. CAS+KETpic y ketlayer x O

  38. 0 5. CAS+KETpic 10 \usepackage{ketpic, ketlayer} 20 \begin{layer}{160}{90} 30 \end{layer} 40 50 60 70 80 900 10 20 30 40 50 60 70 80 90 100 110 120 130

  39. 0 5. CAS+KETpic 10 \usepackage{ketpic, ketlayer} 20 y \begin{layer}{160}{90} \putnotese{5}{20}{\input{fig.tex}} 30 \end{layer} 40 50 60 70 80 x O 900 10 20 30 40 50 60 70 80 90 100 110 120 130

  40. 0 5. CAS+KETpic 10 \usepackage{ketpic, ketlayer} 20 y \begin{layer}{160}{90} \putnotese{5}{20}{\input{fig.tex}} 30 \arrowlineseg{40}{61}{40}{25} \end{layer} 40 50 60 70 80 x O 900 10 20 30 40 50 60 70 80 90 100 110 120 130

  41. 5. CAS+KETpic \usepackage{ketpic, ketlayer} y \begin{layer}{160}{0} \putnotese{5}{20}{\input{fig.tex}} \arrowlineseg{40}{61}{40}{25} \end{layer} x O

  42. 6. DGS+KETCindy From CAS to DGS 1. DGS may be inferior to CAS in computation and programming capability. 2. Interactive drawing of T EX graphics (while checking the final output) should be helpful. 3. It is desirable that the burden of writing com- mand is reduced.

  43. 6. DGS+KETCindy DGS PDF file KETCindy CAS TeX file K ETpic Tpic code Plot Data https://sites.google.com/sites/ketcindy/home

  44. 6. DGS+KETCindy DGS PDF file KETCindy CAS TeX file batch processing K ETpic Tpic code Plot Data

  45. 6. DGS+KETCindy y x

  46. 6. DGS+KETCindy Animation

  47. 6. DGS+KETCindy DGS PDF file KETCindy CAS TeX file K ETpic Tpic code Plot Data

  48. 6.DGS+KETCindy Start End

  49. 6.DGS+KETCindy Start End

  50. 6.DGS+KETCindy Start End

  51. 6.DGS+KETCindy Start End

  52. 6.DGS+KETCindy Start End

  53. 6.DGS+KETCindy Start End

  54. 6.DGS+KETCindy Start End

  55. 6.DGS+KETCindy Start End

  56. 6.DGS+KETCindy Start End

  57. 6.DGS+KETCindy Start End

  58. 6.DGS+KETCindy Start End

  59. 6.DGS+KETCindy Start End

  60. 6.DGS+KETCindy Start End

  61. 6.DGS+KETCindy Start End

  62. 6.DGS+KETCindy Start End

  63. 6.DGS+KETCindy Start End

  64. 6.DGS+KETCindy Start End

  65. 6.DGS+KETCindy Start End

  66. 6.DGS+KETCindy Start End

  67. 6.DGS+KETCindy Start End

  68. 6.DGS+KETCindy Start End

  69. Tnank you very much for your attentions!!

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