Teaching Boolean Logic with augmented reality and boundary logic IE 543 – Virtual Interface Design Trond Nilsen IE 543 - Trond Nilsen 06/06/09

Introduction The Problem Background Augmented Reality Boundary Logic The Application Visualization Interaction Justifications Conclusion & Future Work IE 543 - Trond Nilsen 06/06/09

The Problem

Background

Augmented Reality

Boundary Logic

The Application

Visualization

Interaction

Justifications

Conclusion & Future Work

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

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

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

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

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

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

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

Expressions in Boolean logic map to expressions in boundary logic

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)) =

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

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

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

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

Display symbolic representations alongside AR

Valid marker placement shown through highlighting

Activities:

Manual truth resolution

Walk through a proof (inductive)

Interactive proofs (deductive)

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

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

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

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

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

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

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

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

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

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

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

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.

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

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

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

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