Geometria A tool for interactive geometry modules with response analysis

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Geometria A tool for interactive geometry
modules with response analysis

• Timo Ehmke
• University of Kiel, Germany

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Introduction

• Geometria is designed to develop interactive
  learning modules on web-pages
• The development was based on the Geometry-Applet
  by David Joyce
• Geometria-worksheets are used in the ZERO -
  Mathematik online-project at Flensburg
  University, Germany
• Virtual University of Eastern Finland /
  JoensuuDiscrete Math examples

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Components of a Learning Module

• Special functions
• An extend class of dragable figures
• Interfaces to Java JavaScript
• Response analysis

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The class of dragable figures

• Euclidean constructions and transformation
  geometry (points, lines, circles, polygons,
  reflection, translation, rotation).
• Analytically defined objects (point objects
  depending on user defined functions, parametric
  curve objects).
• Term evaluation (evaluating user defined term
  objects, defining term objects for a response
  analysis).
• Controll elements like buttons, checkboxes,
  controllers.

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Software-Interfaces

• Java interface for specific curve-objects(calcula
  tion of the curve is done by a user-defined
  Java-class).
• Java interface for user-defined
  functions(calculation of an arbitrary Java
  function).
• JavaScript interface (1. including user-defined
  functions, 2. using HTML- JavaScript-elements,
  3. Connecting two or more Applets together).
• Examples Zero of Parabola

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Response analysis

• Judges and comments on the current state of the
  figure.
• Gives feedback on solutions which are right,
  partly right, or even wrong.
• Is defined in a GeoScript-file.
• Examples Algebra of Sets, Relation 1, Relation
  2, Relation 3
• External classes functioning to achieve extensive
  and complex response analysis.
• Example Problem of the eight queens

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Further Information...

• to develop interactive worksheets,
• about syntax of GeoScript- and GeoStyle-files,
• about interfaces and response analysis,
• and examples are downloadable at
• http//www.geometria.de.