Teaching Boolean Logic with augmented reality and boundary logic IE 543 – Virtual Interface Design Trond Nilsen IE 543 - T...
Introduction <ul><li>The Problem </li></ul><ul><li>Background </li></ul><ul><ul><li>Augmented Reality </li></ul></ul><ul><...
The Problem <ul><li>Propositional / Boolean logic is fundamental to reason </li></ul><ul><ul><li>Necessary for rational ar...
Augmented Reality <ul><li>Overlaying virtual imagery on real world </li></ul><ul><li>Tangible User Interface </li></ul><ul...
Background – Boundary Logic 1 <ul><li>Symbolic algebra based on division of space </li></ul><ul><li>Fundamental symbol – e...
Background – Boundary Logic 2 <ul><li>Expressions in Boolean logic map to expressions in boundary logic </li></ul>06/06/09...
Visualizing Boundary Logic <ul><li>Due to strong nesting rules, boundary logic is hierarchical in form and can be visualiz...
Visualizing Boundary Logic – AR <ul><li>One marker per element </li></ul><ul><ul><li>Marker for each variable </li></ul></...
Visualizing Boundary Logic – AR <ul><li>Display symbolic representations alongside AR </li></ul><ul><li>Valid marker place...
Justification – Motivation  <ul><li>Novelty </li></ul><ul><ul><li>Novelty may break despondency </li></ul></ul><ul><ul><li...
Justification – Inductive Learning <ul><li>Two forms of reasoning: </li></ul><ul><ul><li>Deductive:  learn by taking rules...
Justification – Experiential Anchoring <ul><li>Correlation between strong experience and memory </li></ul><ul><ul><li>Rich...
Justification – Active & Spatial Learning <ul><li>Direct mapped interaction </li></ul><ul><ul><li>Movement of marker tags ...
Justification – Sensory Integration <ul><li>Mayer’s Multimedia theory </li></ul><ul><ul><li>The more senses that are emplo...
Justification – Learning Styles <ul><li>Students utilize different learning styles </li></ul><ul><ul><li>Generally not exc...
Conclusion <ul><li>AR system for teaching Boolean logic using visualization and manipulation of boundary logic </li></ul><...
Future Work <ul><li>Implement </li></ul><ul><ul><li>Hoped to, but unable to fit this into time available </li></ul></ul><u...
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Teaching Boolean Logic with augmented reality and boundary logic

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

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Teaching Boolean Logic with augmented reality and boundary logic

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

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