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

4. 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 Illustrations in pairs: models with solid faces and solid edges A new form of insightful geometric illustration Leonardo da Vinci’s “The Divine Proportion” (1509) Stereometry

5. 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

6. Hands-on Activities With Solids Making paper models… or wooden Drawing solids Studying Solids

7. 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

8. 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

10. 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.

11. 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

12. 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)

13. 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

14. 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

15. 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

16. 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

18. 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

19. Cubix Snapshot

20. Cubix Problems

21. 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

22. Slider Snapshot

23. Slider Conical Sections

24. 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

25. Stuffed Toys Snapshot

26. Other Stuffed Toys and Nets

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

28. Scissors Snapshot

29. Ribbons Set