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 of the rear surface

• Illustrations in pairs: modelswith solid faces and solid edges

• A new form of insightful geometric illustration

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

Hands-on Activities With Solids

Making paper models … or wooden

Drawing solids

Studying Solids

Studying Solids

First degree UFOconic encounter

Traditional methods– textbooks

– hand-made drawings

– real models

3D Software

Modern methods– on-line textbooks

– 3D software, virtual models

– interractive, dynamic content

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

1. To analyze the existing stereometry curricula and teachers’ requirements

2. To develop a dynamic 3D software and teaching scenarios for stereometry

3. To provide in-service training

4. 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

Cubix Snapshot

Cubix Problems

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

Slider Snapshot

Slider Conical Sections

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

Stuffed Toys Snapshot

Other Stuffed Toys and Nets

Scissors

• The true reverse problem of net folding

• Available are three sets including ribbons

• Based on Stuffed Toys• Animation of unfolding

Scissors Snapshot

Ribbons Set