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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 …

  • Software in Math learning

  • DALEST/Elica project

  • Implemented applications

  • Demonstrations

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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)


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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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First degree UFOconic encounter

Traditional methods


hand-made drawings

real models

Studying Solids

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


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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.


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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

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

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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

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  • 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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  • 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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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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  • The true reverse problem of net folding

  • Available are three sets including ribbons

  • Based on Stuffed Toys

  • Animation of unfolding