Teaching Boolean Logic with augmented reality and boundary logic
Upcoming SlideShare
Loading in...5
×
 

Like this? Share it with your network

Share

Teaching Boolean Logic with augmented reality and boundary logic

on

  • 1,587 views

Presentation delivered as part of course IE 543, virtual interface technology.

Presentation delivered as part of course IE 543, virtual interface technology.

Associated full paper available for download (contact me via Slideshare for URL)

Statistics

Views

Total Views
1,587
Views on SlideShare
1,585
Embed Views
2

Actions

Likes
0
Downloads
18
Comments
0

1 Embed 2

http://www.slideshare.net 2

Accessibility

Categories

Upload Details

Uploaded via as Microsoft PowerPoint

Usage Rights

© All Rights Reserved

Report content

Flagged as inappropriate Flag as inappropriate
Flag as inappropriate

Select your reason for flagging this presentation as inappropriate.

Cancel
  • Full Name Full Name Comment goes here.
    Are you sure you want to
    Your message goes here
    Processing…
Post Comment
Edit your comment

Teaching Boolean Logic with augmented reality and boundary logic Presentation Transcript

  • 1. Teaching Boolean Logic with augmented reality and boundary logic IE 543 – Virtual Interface Design Trond Nilsen IE 543 - Trond Nilsen 06/06/09
  • 2. Introduction
    • The Problem
    • Background
      • Augmented Reality
      • Boundary Logic
    • The Application
      • Visualization
      • Interaction
    • Justifications
    • Conclusion & Future Work
    IE 543 - Trond Nilsen 06/06/09
  • 3. The Problem
    • Propositional / Boolean logic is fundamental to reason
      • Necessary for rational argument
      • Not well practiced or understood
      • Abstract and verbal
      • Normally taught formally in university
    • Intuitively understood even by children
      • Should be taught earlier
      • Important for decision making
      • Can be understood visually
    06/06/09 IE 543 - Trond Nilsen
  • 4. Augmented Reality
    • Overlaying virtual imagery on real world
    • Tangible User Interface
      • Physical objects mapped to virtual objects
      • Particularly suitable for augmented reality
    • Caveat : Today’s AR often is not perfect
      • The system described could be implemented with AR today
      • But it would likely face significant difficulties in deployment
      • Assumes hypothetical ‘ideal’ head mounted AR
    06/06/09 IE 543 - Trond Nilsen
  • 5. Background – Boundary Logic 1
    • Symbolic algebra based on division of space
    • Fundamental symbol – enclosure ()
      • An enclosure divides space into ‘inside’ and ‘outside’
      • No cardinality or uniqueness.
    • Somewhat counter-intuitive when read symbolically
    06/06/09 IE 543 - Trond Nilsen ()() = () Calling (()) = <void> Crossing ((a)) = a Involution (() a) = <void> Occlusion a (b a) = a (b) Pervasion
  • 6. Background – Boundary Logic 2
    • Expressions in Boolean logic map to expressions in boundary logic
    06/06/09 IE 543 - Trond Nilsen <void> = FALSE () = TRUE (a) = NOT a a b = a OR b ((a) (b)) = a AND b (a) b = IF a THEN b ((a) b) (a (b)) = a XOR b (a b) ((a) (b)) = a IFF b
  • 7. Visualizing Boundary Logic
    • Due to strong nesting rules, boundary logic is hierarchical in form and can be visualized as a tree of ‘pipes’
      • Truth of expression at left
      • A, B, C are truth variables
      • <void> is still false
    06/06/09 IE 543 - Trond Nilsen TRUE = () = A OR B = () () = A AND B = ((A) (B)) = IF (A OR B) THEN (B AND C) = (A B) ((B) (C)) =
  • 8. Visualizing Boundary Logic – AR
    • One marker per element
      • Marker for each variable
      • Marker for root
      • Marker for crossing
      • Markers for branch base and branch
    • Reference orientation from root
    • Linking determined by placement
    06/06/09 IE 543 - Trond Nilsen
  • 9. Visualizing Boundary Logic – AR
    • Display symbolic representations alongside AR
    • Valid marker placement shown through highlighting
    • Activities:
      • Manual truth resolution
      • Walk through a proof (inductive)
      • Interactive proofs (deductive)
    06/06/09 IE 543 - Trond Nilsen
  • 10. Justification – Motivation
    • Novelty
      • Novelty may break despondency
      • ‘ Wow!’ effect
      • Varied content and learning activity
    • Less Formal
      • Assume: Similarity to fun tasks = easier to motivate
      • Less de-motivating than classroom teaching
    • Flow
      • Requires dynamic activity with cycle of action & feedback
      • Intensely motivating
    06/06/09 IE 543 - Trond Nilsen
  • 11. Justification – Inductive Learning
    • Two forms of reasoning:
      • Deductive: learn by taking rules & facts, then extending
      • Inductive: learn by generalizing rules from examples
    • Most mathematical teaching is deductive
      • Can lead to a focus on syntactic application
    • Most students learn best with combo
    • Inductive reasoning is often under-developed
    06/06/09 IE 543 - Trond Nilsen
  • 12. Justification – Experiential Anchoring
    • Correlation between strong experience and memory
      • Richness, intensity, meaning
      • Knowledge contextualize with experience is better recalled
    • Novelty of activity
      • ‘ Wow!’ effect
    • Interactivity supports student participation and ownership
      • Social context
      • Increased motivation
    06/06/09 IE 543 - Trond Nilsen
  • 13. Justification – Active & Spatial Learning
    • Direct mapped interaction
      • Movement of marker tags directly affects expressions
      • Reduces cognitive load, freeing attention
    • Supports active exploration of system
      • Explore symbol combinations / expression configuration by moving tags (similar to jigsaw puzzle)
      • Particularly important for learning of spatial / configurational knowledge
    06/06/09 IE 543 - Trond Nilsen
  • 14. Justification – Sensory Integration
    • Mayer’s Multimedia theory
      • The more senses that are employed, the stronger the learning
      • Applies for combinations of all ‘five’ senses
    • Tangible UI affords greater sensory integration
      • Learning is stronger when multiple senses are engaged
      • Particularly important for spatial learning.
      • Supports kinaesthetic learners
    06/06/09 IE 543 - Trond Nilsen
  • 15. Justification – Learning Styles
    • Students utilize different learning styles
      • Generally not exclusive
      • The more learning styles supported, the better
      • Many schemes
        • Verbal / Visual
        • Global / Sequential
        • Active / Passive
        • Intuitive / Sensing
    • Particular teaching styles map to particular learning styles
      • Traditional classroom mathematics tends to be visual, sequential, passive, and intuitive
      • System supports visual, global, active, sensing learners.
    06/06/09 IE 543 - Trond Nilsen
  • 16. Conclusion
    • AR system for teaching Boolean logic using visualization and manipulation of boundary logic
    • Justifications:
      • Motivation
      • Inductive Learning
      • Experiential Anchoring
      • Active & Spatial Learning
      • Sensory Integration
      • Learning Styles
    06/06/09 IE 543 - Trond Nilsen
  • 17. Future Work
    • Implement
      • Hoped to, but unable to fit this into time available
      • Suitable for implementation with ARToolkit
    • Evaluate
      • vs traditional classroom teaching
      • vs visual classroom teaching
      • vs desktop PC equivalent
    • Improved theoretical basis for AR in education
    • Apply to more complex algebras
      • Predicate logic, tense logic, etc
      • Number theory
    06/06/09 IE 543 - Trond Nilsen