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In This Presentation …. Software in Math learning DALEST/Elica project Implemented applications Demonstrations. Solids with Solid Edges. The 1 st illustrations of polyhedra ever in the form of solid edges Readers can see through to the structure of the rear surface

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in this presentation
In This Presentation …
  • Software in Math learning
  • DALEST/Elica project
  • Implemented applications
  • Demonstrations
solids with solid edges
Solids with Solid Edges
  • The 1st illustrations of polyhedra ever in the form of solid edges
  • Readers can see through to the structure ofthe rear surface
  • Illustrationsin pairs:modelswith solidfacesand solid edges
  • A new form of insightful geometricillustration

Leonardo da Vinci’s “The Divine Proportion” (1509)

Stereometry

stereometry
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

hands on activities with solids
Hands-on Activities With Solids

Drawing solids

Making paper models

… or wooden

Studying Solids

studying solids
First degree UFOconic encounter

Traditional methods

textbooks

hand-made drawings

real models

Studying Solids

Modern methods

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

3D Software

3d software
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

dalest project
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.
dalest objectives
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

elica project
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)
elica features
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
dalest elica project
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
possible elica applications
Possible Elica Applications

Playing Archimedes

  • Submerging solids in bath-tubes
  • Various shapes of solids
  • Various shapes of bath-tubes
  • Measuring water levels

Bottle Factory

  • Designing bottles
  • Using basic/composite solids
  • Measuring (designing) volume
  • 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
possible elica applications16
Possible Elica Applications

Free-form Shadow

  • Solids on a table, light turned off
  • Guessing the solid by examining the silhouettes (skyline)
  • Table can be rotated

Stereometry Puzzle

  • Structures of solids
  • Some measurements are given
  • Others should be guessed or calculated
cubix
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
slider
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
stuffed toys
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
scissors
Scissors
  • The true reverse problem of net folding
  • Available are three sets including ribbons
  • Based on Stuffed Toys
  • Animation of unfolding