FUNCTION MACHINES

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FUNCTION MACHINESELICA
HOW COULD HIGH SCHOOL ALGEBRA TEACHERS USE
FUNCTION MACHINES SOFTWARE ?

• Thursday, December 5, 2002

Pavel Boytchev, Elica Team E-mail
pavel_at_elica.net Home site www.elica.net
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The Presentation

• About Logo and Elica
• Function Machines and Elica
• Demonstrations

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About Logo and Elica

• Elica History
• Elica and Its Mission
• Elica Logo
• The Future of Elica

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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 developmentAESOP (Advanced Elica SOP)

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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

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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

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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

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Function Machines and Elica

• Function Machines and Elica Future
• A typical Word Problem
• Some Ideas

Pedagogical Issues
Software Issues
Algebra
Function Machines
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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)

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A Typical Word Problem

• 5 pigs walk from NYC to Boston for 37 days.
• How many pigs will be enough to walk the
• same distance for 20 days?

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Some Ideas

• Non-graphical
• Simple, powerful and flexible language
• Rules and reversible constructions
• Graphical
• Graphical interface
• Follow me modes
• Custom shapes and actions

• Advanced
• Multiple Interfaces
• Learn by mind, not by heart
• Algebric Interactive Animator
• Virtual City
• Pedagogically Supported
• WP Rephraser
• WP explorer
• Function Machines Reverser

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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
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Rules and reversible constructions

• Current FM active machines, passive data (FP)
• Addition active data, passive machines (OOP)

• One-way rules
• Two-way reversible constructions

Example TwoWay
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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
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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
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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
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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
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Learn by mind, not by heart

• 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

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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
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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

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Rephraser Example
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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

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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)(lef
t)
85-325x
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?
85-3x10
85-x2510
Inner ring of equations
x-32510
Outer ring word problems
John bought 3 apples at 25c each and had 10c
left. How many cents had he got initially?
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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

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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

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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