Teaching Boolean Logic with augmented reality and boundary logic
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Transcript of Teaching Boolean Logic with augmented reality and boundary logic
Teaching Boolean Logic with augmented reality and boundary logic
IE 543 – Virtual Interface DesignTrond Nilsen
IE 543 - Trond Nilsen10/04/23 1
Introduction
The Problem Background
Augmented Reality Boundary Logic
The Application Visualization Interaction
Justifications Conclusion & Future Work
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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
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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
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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
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()() = () Calling
(()) = <void> Crossing
((a)) = a Involution
(() a) = <void> Occlusion
a (b a) = a (b) Pervasion
Background – Boundary Logic 2
Expressions in Boolean logic map to expressions in boundary logic
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<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
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
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TRUE = () =
A OR B = () () =
A AND B = ((A) (B)) =
IF (A OR B) THEN (B AND C) = (A B) ((B) (C)) =
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
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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)
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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
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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
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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
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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
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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
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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.
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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
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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
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