Understanding versus Procedure Analytic Geometry    Martin Zacharias
Understanding?  Comprehension?
Everyday life in school <ul><li>Given are to lines   and   </li></ul><ul><ul><li>a) Which situation do they have? Find the...
Everyday life in school?
<ul><li>The exercise isn’t to bad. You have to argue, you have do draw.  </li></ul><ul><li>But the finding of terms and eq...
Vertical lines
Distance
Circle (0|0) with radius 4
Descartes Dictionary
<ul><li>We need activities for the pupils. </li></ul>
Concept by Objects <ul><li>From doing to thinking in three steps   </li></ul><ul><li>to comprehend the real model  (situat...
Crossing section on a cube
Diagonals
2D of real objects
Forms of a roof
Read out the point
S is the summit of a pyramid
half of a cube
Cross-sections by liquids
Cross-section of a regular Hexagon
Werkzeug -CD F:VortragKiel_100922CD_AnaGeostart.htm
Schrägbilddarstellungen
Corner of a cube C=(8|3|6), F=(2|9|6), G=(4|5|10), H=(0|1|8)
Vector
Vectors in objects
Vectors in objects
Regular Hexagon in a cube
Regular Hexagon in an Oktaeder
Rectangle in a cube Center of the cube – center of the rectangle.
Cross-section
Diagonals in the space
Mittendreieck
Lines in the space
Lagebeziehung von Geraden im Raum
Area in a roof  (Walmdach) Describe the blue area with lines.
Line segments in a Pyramid
„ Haus des Nikolaus“
Cube with a cut off corner
Cut off cube (Kuboktaeder)
Position of lines
Point of intersection? No, it doesn’t exist a point of intersection.
Lagebeziehung mit GTR
Lagebeziehung und GTR
Ebenen im Raum
experiment - search
Ebene - experimentell
Objektstudie
What happens, when …  ? <ul><li>… B  goes towards F with the angle beta?  </li></ul>
111020 analytic geometry
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111020 analytic geometry

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111020 analytic geometry

  1. 1. Understanding versus Procedure Analytic Geometry Martin Zacharias
  2. 2. Understanding? Comprehension?
  3. 3. Everyday life in school <ul><li>Given are to lines and </li></ul><ul><ul><li>a) Which situation do they have? Find the points of intersection. </li></ul></ul><ul><ul><li>b) Describe the plane E, which includes the lines g and h. </li></ul></ul><ul><ul><li>c) Find a line, which has no points of intersection with g and h. Give the reason for your choice. </li></ul></ul><ul><ul><li>d) Find the points of intersection to the basic-planes (xy-plane, xz-plane and yz-plane) and draw the lines g and h. </li></ul></ul><ul><ul><li>Draw the point of intersection of both lines. </li></ul></ul><ul><ul><li>e) Find the angle between g and h. </li></ul></ul><ul><ul><li>f) Find the angle between the basic-planes. </li></ul></ul><ul><ul><li>… </li></ul></ul>
  4. 4. Everyday life in school?
  5. 5. <ul><li>The exercise isn’t to bad. You have to argue, you have do draw. </li></ul><ul><li>But the finding of terms and equations and the calculation with equations is dominant. </li></ul><ul><li>Geometry and basis ideas don’t exist. </li></ul>
  6. 6.
  7. 7. Vertical lines
  8. 8. Distance
  9. 9. Circle (0|0) with radius 4
  10. 10. Descartes Dictionary
  11. 11. <ul><li>We need activities for the pupils. </li></ul>
  12. 12. Concept by Objects <ul><li>From doing to thinking in three steps </li></ul><ul><li>to comprehend the real model (situation) </li></ul><ul><li>to represent und describe it in a drawing </li></ul><ul><li>to represent and describe it in the analytic model </li></ul>
  13. 13. Crossing section on a cube
  14. 14. Diagonals
  15. 15.
  16. 16. 2D of real objects
  17. 17. Forms of a roof
  18. 18. Read out the point
  19. 19. S is the summit of a pyramid
  20. 20. half of a cube
  21. 21.
  22. 22.
  23. 23. Cross-sections by liquids
  24. 24. Cross-section of a regular Hexagon
  25. 25. Werkzeug -CD F:VortragKiel_100922CD_AnaGeostart.htm
  26. 26. Schrägbilddarstellungen
  27. 27. Corner of a cube C=(8|3|6), F=(2|9|6), G=(4|5|10), H=(0|1|8)
  28. 28. Vector
  29. 29. Vectors in objects
  30. 30. Vectors in objects
  31. 31. Regular Hexagon in a cube
  32. 32. Regular Hexagon in an Oktaeder
  33. 33. Rectangle in a cube Center of the cube – center of the rectangle.
  34. 34. Cross-section
  35. 35. Diagonals in the space
  36. 36. Mittendreieck
  37. 37.
  38. 38.
  39. 39. Lines in the space
  40. 40. Lagebeziehung von Geraden im Raum
  41. 41.
  42. 42. Area in a roof (Walmdach) Describe the blue area with lines.
  43. 43. Line segments in a Pyramid
  44. 44. „ Haus des Nikolaus“
  45. 45. Cube with a cut off corner
  46. 46. Cut off cube (Kuboktaeder)
  47. 47. Position of lines
  48. 48. Point of intersection? No, it doesn’t exist a point of intersection.
  49. 49. Lagebeziehung mit GTR
  50. 50. Lagebeziehung und GTR
  51. 51. Ebenen im Raum
  52. 52. experiment - search
  53. 53.
  54. 54. Ebene - experimentell
  55. 55. Objektstudie
  56. 56.
  57. 57. What happens, when … ? <ul><li>… B goes towards F with the angle beta? </li></ul>

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