In This Presentation Software in Math learning DALESTElica

In This Presentation … • Software in Math learning • DALEST/Elica project • Implemented applications • Demonstrations

Solids with Solid Edges Leonardo da Vinci’s “The Divine Proportion” (1509) • The 1 st illustrations of polyhedra ever in the form of solid edges • Readers can see through to the structure of the rear surface • Illustrations in pairs: models with solid faces and solid edges • A new form of insightful geometric illustration 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 Drawing solids Making paper models … or wooden Studying Solids

Studying Solids First degree UFOconic encounter Traditional methods – textbooks – hand-made drawings – real models Modern methods – on-line textbooks – 3 D software, virtual models – interractive, dynamic content 3 D Software

3 D Software • A large amount of 3 D software – Industry / Scientific – Artistic – Scientific / Educational • Educational 3 D software – – Virtualizing static content (ritualizing) Interraction and manipulation Animations, dynamic modification Hundreds of microapplications DALEST/Elica

DALEST Project • Acronym: Developing an Active Learning Environment 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 3 D 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 for Creative 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 3 D 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 Eucli 3 D – A set of separate Elica applications • Main Challenges – Unique problems – To rationalize use of computers – Attractive visualization

Possible Elica Applications Playing Archimedes • Ideas about 20+ different applications • Submerging solids in bath-tubes • New ideas are added all the time • Various shapes of solids • Ideas various topics: • Various shapescover of bath-tubes – Volumes of solids • Measuring water levels – 3 D structures and space relations Bottle Factory – Nets • Designing bottles – Art and Nature • Using basic/composite solids • Four(designing) ideas implemented • Measuring volume 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 3 D 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