PhD Student:Lai Danbo, School of Computer EngineeringSupervisors:Assoc Prof. Alexei Sourin, School of Computer EngineeringAssoc Prof. Zhao Dong Sheng, National Institute of Education

Cyberlearning: classification and applications

Problems of teaching subjects rich with geometry

Research focus

Feasibility study

Conclusion

2

Cyberlearning: Computer-based techniques for learning-related purposes

Different types of e-learning systems:

Learning Management System (LMS)

Intelligent Tutoring Systems (ITS)

Simulation-based Cyberworlds

LMS: Software platform for the administration, documentation, tracking, and reporting of training programs, classroom and online events, e-learning programs and training contents.

Trends:

Automated assessment

Integration with social media;

Integration with 3D shared virtual worlds

…

ITS: computer system that provides direct customized instruction of feedback to students.

Classified by interaction modalities: Form-based tutoring system Text-based dialogue system Spoken dialogue system Multi-modal system

Trends: Discourse planning Emotion Animated pedagogical agents …

Simulation-based educational cyberworlds: computer generated simulations for educational purpose

Advantages:

Time and physical location: historical exhibition, geology

Constructivism theory

Being safe and economy: virtual laboratories

Avoid illegal: medical students training

…..

Simulation of real classes

Being a replacement model for real world experience

Simulation of imaginary world

http://www3.ntu.edu.sg/home/assourin

/VirCampus.html

Virtual Campus of NTU K. Johnsen, et.al, "Experiences in Using

Immersive Virtual Characters to Educate

Medical Communication Skills," in

Proceedings of the IEEE Conference 2005 on

Virtual Reality, , pp. 179-186,324,

Washington, DC, March 2005

Learning about cell structure within

a 3D cell model

http://slurl.com/secondlife/Genome/1

28/130/48

Retrieved from Genome Island in

Second Life

Problems with teaching and learning geometry-rich

subjects

3D spatial visualization and stereovision in particular are

undeveloped in modern urban society

In Singapore schools only 2D geometry is taught

Imaging and mental manipulating three-dimensional objects is

neither natural nor easy

Insufficient interaction with 3D objects

Students lack a visual vocabulary pertaining to spatial geometry

There is a lack of attention paid to verbal processes involved in

learning 3D geometry

Computer programs which allow user to create and then manipulate geometric constructions

Key feature:

User can explore the dynamic behavior of a construction by moving its defining parts, and adding an extra part.

Overcome the limitations of static textbook images and the misconceptions students can develop from seeing only a few cases

Interactive Geometry Software (or Dynamic Geometry Environment)

A Screenshot of Cabri3D (one of the

popular IGSs). Shows the result of a

construction with points and faces which

can be dragged and moved.Retrieved from:

http://www.chartwellyorke.com/cabri3d/flash/d

odecahedron.swf

More information about interactive

geometry software: http://en.wikipedia.org/wiki/Dynamic_geom

etry_environment

Immersive shared virtual environment CyberMath-Taxen, G. and A. Naeve, CyberMath: A System for Exploring Open Issues in

VR-based Education, in SIGGRAPH- Educator's Program. 2001.

Features Allow physical distributed users

Collaboration: audio-based discussion, share experience of mathematical objects with lacer pointing

Virtual lecture hall: simulation of real classes

Exhibition Hall: allow collaboratively explore mathematical objects

http://www.nada.kth.se/~gustavt/cy

bermath/

Augmented virtual reality Construct3D - Kaufmann, H. and D. Schmalstieg. Designing Immersive Virtual Reality

for Geometry Education. in IEEE virtual reality conference. 2006.

Feature Augmented reality:

▪ allow combination of real and virtual environment▪ apply traditional pedagogies

Construction and manipulation of 3D geometry objects like normal Interactive Geometry Software

Construct3D allows

exploratory construction of

geometric tasks. Shown is

a collaborative attempt to

construct a proof task

Schematic

overview of the

Augmented

Classroom

From: Mag. Hannes

Kaufmann, ”Geometry Education with

Augmented Reality”, PhD thesis, Institute

for Software Technology and Interactive

Systems, Vienna University of Technology

Mixed reality both visual and haptic representation Nikolakis, G., et al., A Mixed Reality Learning Environment for Geometry Education in

Methods and Applications of Artificial Intelligence, G.A. Vouros and T. Panayiopulos, Editors. 2004, Springer Berlin/ Heidelberg. p. 93-102.

Features Visual Geometry

Haptic Interaction: Feeling the 3D object by hand touching

Screenshot of the application ,

show is a construction of

sphere and changing its size

Touching geometry objects

with a glove-”Cybertouch”

Intelligent Tutoring System

Geometry explanation Tutor - Popescu, O., V. Aleven, and K. Koedinger. Understanding

Students' Explanations in Geometry Tutoring. in the 20th International Conference on Computational Linguistics. 2004. Geneva, Switzerland: Association for Computational Linguistics.

AutoTutor - Graesser, A., et al., AutoTutor: Learning through Natural Language Dialogue that

Adapts to the Cognitive and Affective States of the Learner, in Recent innovations in educational technology that facilitate student learning. 2008. p. 95-125.

Feature

Emphasizing the importance of one-to-one tutoring

Focus on verbal process involved in learning geometry,

Self-explanation: deep understanding of the concepts An Interaction example of “Geometry explanation

Tutor”

IMAGINARY exhibition Organizer: MFO (Mathematisches Forschungsinstitut Oberwolfach)

An attempt to promote geometry education

Image Gallery Interactive Software: Surfer

Videos & Films Surfaces as Sculptures

Interactive Software Surfer: visualize, create algebraic surfaces

in a simple and intuitive way jReality: a visualization and sonification

java library focus on mathematical and scientific content

3D-XplorMath: visualization different types of mathematical objects and related processes

Morenaments: paint symmetrical patterns Cinderella: dynamic geometry software-

chaos theory, symmetries Retrieved from http://www.imaginary2008.de/

Cyberlearning is actively used and commonly accepted 3D visualization ability is significant Previous work: ITS: only considering language interaction

IGS: perform visualization, only able to see images

CyberMath, Construct3D: restrict to a limited class of geometric objects

Imaginary Exhibition: an attempt to promote geometry education, inspirations that geometry education can be interesting, full of beauties

Research gap: Immersive visualization of mathematical formulas

New ways of interaction with the scene

Collaborative learning

Visual Immersive Haptic Mathematics Emphasizing how complex geometry, appearance, and physical

properties can be defined by mathematical formulas and algorithms

Using various forms of mathematical functions to represent object models

Addition of various media (sound/music) and interaction forms (haptic) as well as artificial intelligence to geometric models and to the learning environment

Computational Environment:

Shared virtual space implemented using VRML or X3D with server-client model of communication

Various forms of mathematical formulas are used to represent object models, to define geometry, appearance and physical properties:

▪ Implicit functions: – surface geometry

▪ Explicit functions: –solid object geometry, CSG, physical properties, components of colors, geometric textures

▪ Parametric functions: – curves, surfaces, solid objects, colors, physical properties (force vectors)

0),,,( tzyxf

0),,,( tzyxfg

)|,|,|,( twvufP

Encouraging interactively creation of beautiful Algebraic surfaces with polynomial formulas (implicit functions)

Coefficient changes in real time and the influence on object can be observed immediately

X^4*y^2+y^4*x^2-x^2*y^2+z^6=0x^2+y^2+z^3-z^2=0

Rendering Geometric properties by various ways: e.g. rendered by color

Example:

FShape {

appearance FAppearance {

material FMaterial {

diffuseColor "sqrt(x*x+y*y+z*z)“

patternColor [0 0 1 0 1 0 1 0 0]

patternKey [1 2 3]

}}

geometry FGeometry {

resolution [50 50]

definition "(2-sqrt(x*x+y*y))^2+z^2-1^2“

}}

height function

“z”

distance function

“sqrt(x*x+y*y+z*z)”

Provide haptic representation by adding a tension force to the surface

Intelligent cyber-instructor can be involved any time for consultation

Add a tension force to the surface

Consult the intelligent cyber-instructor

Touching Curves: by adding a force field around the curve.

More complex cases need to be analyzed

A general method should be investigated and provided

Forces at the points near the curve is pointed to the

nearest curve point

Conclusion: Shared virtual space with server-client model of communication – able

to easily apply collaborative learning

We propose Visual Immersive Haptic Mathematics

Future Work Using media(sound/music) to add more information to geometric

objects, providing new interaction method

▪ Music has its own geometry: numbers, geomtrization

Realistic haptic solution for touching mathematical objects

Guided learning: Instructor initiated discussion and task oriented learning

Cyberlearning is actively used and commonly accepted Teaching geometry-rich subjects in cyberspace requires new

paradigms We propose visual immersive haptic mathematics