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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

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 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

First degree UFOconic encounter

Traditional methods

textbooks

hand-made drawings

real models

Studying SolidsModern methods

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

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

- 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

- 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

- 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

- 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: 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

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 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

- 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

- 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

- 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

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

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