HOWCOULDHIGHSCHOOLALGEBRATEACHERS USEFUNCTIONMACHINESSOFTWARE ? FUNCTION MACHINES&ELICA Thursday, December 5, 2002 Pavel Boytchev, Elica Team E-mail: pavel@elica.net Home site: www.elica.net
The Presentation • About Logo and Elica • Function Machines and Elica • Demonstrations
About Logo and Elica • Elica History • Elica and Its Mission • Elica Logo • The Future of Elica
Elica History • Predecessors and inspirators (1985-87):PGS and Geomland • Early work (1990-1999):TopLogo++, TGS, LGS, LGSW, RLS • Grant award by BPE (1999):Elica 3.0 • Recent work (2000-2002):Elica 4.0, 5.0, 5.1, 5.1.1, 5.1.1a, 5.2, and 5.3 • Future development:AESOP (Advanced Elica SOP)
Elica and Its Mission Elica(Educational Logo Interface for Creative Activities): • Programming language • Educational tool • Research and modeling environment • Mission: • To enrich Logo with FP, OOP, 3D graphics, etc. • To allow easy understanding and use of objects and OOP • To provide flexible environment for learning, researching and modeling • To support both beginners and advanced users
Elica Logo • Elica is a flexible system • Suitable as a base of different models • Elica supports few Logo commands • Logo language is implemented as a library • Turtle Graphics is implemented as a library
The Future of Elica • Support for imperative, object-oriented, functional and logical programming styles • Integration of Logo and AI (Artificial Intelligence) • Subject-oriented programming • Implementation of nice features from other systems like Function Machines and Boxer • OS independent
Function Machines and Elica • Function Machines and Elica Future • A “typical” Word Problem • Some Ideas Pedagogical Issues Software Issues Algebra Function Machines
Function Machines and Elica Future • Two products that can exchange information (texts, images, algorithms) in real-time • A new system that inherits the best from both • Elica transplant into Function Machines • Function Machines transplant into Elica • Two incompatible products (as it is now)
A “Typical” Word Problem ? ? ? ? ? SCHOOL . . . . . 5 pigs walk from NYC to Boston for 37 days. How many pigs will be enough to walk the same distance for 20 days?
Some Ideas • Advanced: • Multiple Interfaces • “Learn by mind, not by heart” • Algebric Interactive Animator • Virtual City • Pedagogically Supported: • WP Rephraser • WP explorer • Function Machines Reverser Non-graphical: • Simple, powerful and flexible language • Rules and reversible constructions Graphical: • Graphical interface • “Follow me” modes • Custom shapes and actions
Simple, power and flexible language • Importance of programming languages in visual environments • Elica core is based on only 10 reserved words • UFO – User Friendly Objects • A single FM as an object • Custom operators • Functional Function Machines (FM as data) • Solves the “too-parallel” problem Example: Elica Help, Languages, Fact, Time, UnitsLogo, UnitsElica
Rules and reversible constructions old data new data Machine machine Old Data New Data • Current FM: active machines, passive data (FP) • Addition: active data, passive machines (OOP) • One-way rules • Two-way reversible constructions Example: TwoWay
Graphical Interface • 3D images instead of 2D ones • Zoom in/out, different view points • More like a game rather than as a textbook • Spatial Function Machines (solves “cross-connections” problem) Examples: Steam, Truss & Truss3D
“Follow-me” Modes • Provide close-up and detailed view of the process • Users identify themselves with the objects that are processed • Ignore other threads and focus on a single datum flow Examples: Follow & Glide
Custom Shapes and Actions • Using various visual forms: shapes, images or animations • User-definable forms • User-constructible forms • Forms for functions and data Examples: Gravity, Spectrophotometer
Multiple interfaces Interfaces: • Textual (a la Logo) for program sources • Graphical (a la FM ) for algorithms • Graphical (a la Boxer) for structures • Textual – natural language descriptions • Free-style – a mixture of any of the above Features: • User-controlled interface selection • Task-specific interfaces Examples: ErrInsp1 & ErrInsp2
“Learn by mind, not by heart” Solution Problem Solution Not a solution thinking Wrong answer Problem Solution Wrong answer guessing • Typical Algebra • Philosophy • Usually only 1 correct solution • Mistakes and wrong answers • Unfriendly domain Typical Logo Philosophy • Several correct solutions • No mistakes and bad programs • Friendly domain
Algebric Interactive Animator • Identify different problems and assign scenarios to each of them • Create interactive animations or simulations • Allow different explorations of the same problem Example: Equation Balance, NavigVect3
Word Problem Rephraser • Converts algebra problems into prealgebra problems • Does not solve the problem for the student, but help him/her to find a solution • Demonstrates how proper rephrasing could make the problem easier to solve • Could be integrated with other WP ideas
Rephraser Example Formalizing the problem (had) – (apples)*(price) = (has) 85–x*25=10 Problem wording contains relation Understanding the problem Does not allow left-to-right calculations Solution John had 85c. He bought some apples at 25c each and 10c left.How many apples did he buy? Problem wording contains algorithm for solving John had 85c, but now has only 10c because he gave 25c per apple to buy some apples. Rephrasing (85–10)/25=x Allows left-to-right calculations John had 85c. He bought 3 apples at 25c each. How many cents he has now? Problem wording contains algorithm for solving Understanding the problem Allows left-to-right calculations (had) – (apples)*(price) = (has) 85–3*25=x Formalizing the problem
Word Problem Explorer • Allows covertion of word problems into equations • … and equations into word problems • Experiments with problem variants • Blurs the differences between algebra and prealgebra problems • Could be integrated with the rephraser
Explorer Examples John had 85c. He bought 3 apples at 25c each. How many cents has he got now? Core of Problem Domain (had)-(apples)*(price)=(left) 85-3*25=x John had 85c. He bought some apples at 25c each and had 10c left. How many apples did he buy? John had 85c. He bought 3 apples and had 10c left. How many cents does cost an apple? 85-3*x=10 85-x*25=10 Inner ring of equations x-3*25=10 Outer ring word problems John bought 3 apples at 25c each and had 10c left. How many cents had he got initially?
Function Machine Reverser • Demonstrates connection between a function machine and its “opposite” machine • Experiments with “black-boxes” problem • Provides tools for building reversed function machines that find input from output
Virtual City-1 • Facts from different domains in unified way • Methods/algorithms from different domains • Modifying knowledge • Applying methods from one domain onto data from abother domain • Represent different domains in a cross-domain view • Interactive work with any aspect of the knowledge base
Virtual City-2 Structure • City – the whole knowledgebase • Boroughs – different domains in the city • Buildings – facts, methods, algorithms, etc Roles • Visitors – they are new to the city, can only look around and visit museums, galleries • Citizens – interact with each othe, share information, organize meetings and clubs, create new facilities in one or more domains • Government – responsible to governs the city, have right to design new boroughs, change infrastructure and facilities
