Transcript Slide 1

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 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: models
with solid faces and solid edges
• A new form of insightful
geometric illustration
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
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
– 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
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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 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 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
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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
• 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
– 3D 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 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