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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 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
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
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