In This Presentation

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In This Presentation

• Software in Math learning
• DALEST/Elica project
• Implemented applications
• Demonstrations

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Solids with Solid Edges
Leonardo da Vincis The Divine Proportion (1509)

• The 1st illustrations of polyhedra ever in the
  form of solid edges
• Readers can see through to the structure of the
  rear surface
• Illustrations in pairs modelswith solid faces
  and solid edges
• A new form of insightful geometric illustration

Stereometry
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Stereometry

• Stereometry deals with the measurements of
  volumes of various solid figures cylinder,
  circular cone, truncated cone, sphere, prisms,
  blades, wine casks.
• Pythagoreans sphere and regular solids
• Platonists pyramid, prism, cone and cylinder
• from Wikipedia

Hands-on Activities
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Hands-on Activities With Solids
Drawing solids

• Making paper models

or wooden
Studying Solids
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Studying Solids

• First degree UFOconic encounter

• Traditional methods
• textbooks
• hand-made drawings
• real models

• Modern methods
• on-line textbooks
• 3D software, virtual models
• interractive, dynamic content

3D Software
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3D Software

• A large amount of 3D software
• Industry / Scientific
• Artistic
• Scientific / Educational

• Educational 3D software
• Virtualizing static content (ritualizing)
• Interraction and manipulation
• Animations, dynamic modification
• Hundreds of microapplications

DALEST/Elica
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DALEST Project

• Acronym Developing an Active LearningEnvironment
  for STereometry
• Partners Universities of Cyprus, Southampton,
  Lisbon, Sofia, Athens N.K.M Netmasters and
  Cyprus Mathematics Teachers Association
• Co-funded by the European Union under the
  Socrates Program, MINERVA, 2005 Selection.

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DALEST Objectives

• To analyze the existing stereometry curricula and
  teachers requirements
• To develop a dynamic 3D software and teaching
  scenarios for stereometry
• To provide in-service training
• To test the software and the teaching approaches
  in different schools and evaluate their
  effectiveness.

Elica
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Elica Project

• Acronym Educational Logo Interface forCreative
  Activities
• First steps Initial development supported by a
  Grant Award by Best Practices in Education
• Usage In schools and universities all over the
  world (except for Antarctica)

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Elica Features

• Free
• Core language is a dialect of Logo
• Natural Object-oriented Programming
• 3D graphics and animations
• Flexible, extendable
• Suitable for building Microworlds
• Already used to build educational software

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DALEST/Elica Project

• DALEST Two software streams
• A monolith application Eucli3D
• A set of separate Elica applications

• Main Challenges
• Unique problems
• To rationalize use of computers
• Attractive visualization

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Possible Elica Applications

• Ideas about 20 different applications
• New ideas are added all the time
• Ideas cover various topics
• Volumes of solids
• 3D structures and space relations
• Nets
• Art and Nature
• Four ideas implemented so far

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Possible Elica Applications
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Cubix

• A structure made of unit-size cubes. Users have
  to calculate the volume and the surface of the
  structure
• Possible methods of solving
• calculation (counting)
• splitting the structure into simpler structures
• complementing the structure to a bigger structure
• Functionalities
• to rotate the structure
• to color stucture elements

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Cubix Snapshot
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Cubix Problems
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Slider

• An invisible 3D solid (cube, sphere, cone, ...)
• Cutting with a magic plane, only the intersection
  becomes visible
• By moving and rotating the cutting plane students
  are supposed to analyze the changes in the
  intersection and find out the solid

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Slider Snapshot
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Slider Conical Sections
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Stuffed Toys

• A stuffed cube is ripped off
• What net will come out when unfolded?
• Two sets of toys
• simple white cubes
• coloured toys of various shapes cubes, round
  balls, rugby balls, sharp and soft octahedrons,
  eggs, pebbles, etc.
• Animation of ripping off

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Stuffed Toys Snapshot
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Other Stuffed Toys and Nets
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Scissors

• The true reverse problem of net folding
• Available are three sets including ribbons
• Based on Stuffed Toys
• Animation of unfolding

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Scissors Snapshot
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Ribbons Set
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