an adaptive e-learning system based on users' learning styles author: phạm quang dũng

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AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Page 1: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES

Author: Phạm Quang Dũng

Page 2: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Outline

Introduction

Learning objects and Learning styles

Ontologies and intelligent agents in education

Incorporation of learning styles in a learning management system

Automatic detection of learning styles in LMSs

Conception of an adaptive e-learning system

POLCA – Implementation and results

Conclusion

Page 3: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

3

Outline

Introduction

Learning objects and Learning styles

Ontologies and intelligent agents in education

Incorporation of learning styles in a learning management system

Automatic detection of learning styles in LMSs

Conception of an adaptive e-learning system

POLCA – Implementation and results

Conclusion

Page 4: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Introduction

Motivation and problem statement

Each learner has his own individual needs and characteristics

Most of LMSs do not consider learners’ needs and preferences

the need for providing learners with adaptive courses

While adaptive systems support adaptivity, they support only few functions of web-enhanced education, and the content of courses is not available for reuse.

In contrast, LMSs focus on supporting teachers and help to make online teaching as easy as possible.

use an adaptive learning management system

Page 5: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Introduction

Research issues

1. How can learning styles be identified?

Find a literature-based method for automatic identifying learners’ learning styles based on their behaviour and actions on learning objects in

online courses using LMSs

suitable for LMSs in general

2. How can adaptive courses be provided in LMSs?

which types of learning objects

their order

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Outline

Introduction

Learning objects and Learning styles

Ontologies and intelligent agents in education

Incorporation of learning styles in a learning management system

Automatic detection of learning styles in LMSs

Conception of an adaptive e-learning system

POLCA – Implementation and results

Conclusion

Page 7: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Learning object?

any digital resource that can be reused to support learning (D.A. Wiley, 2000) digital images or photos, video or audio snippets, small bits

of text, animations, a web page

Characterstics Share and reuse

Digital

Metadata-tagged Description information: title, author, format, content

description, instructional function

Instructional and Target-Oriented

Page 8: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Learning style models

To classify and characterise how students receive and process information.

Refer to fundamental aspects:

cognitive style

learning strategy

Well-known models: Myers-Briggs, Kolb, Felder-Silverman

Page 9: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Learning style models

Felder–Silverman Learning Style Model

Each learner has a preference on each of the four dimensions: Active – Reflective

learning by doing – learning by thinking group work – work alone

Sensing – Intuitive concrete material – abstract material more practical – more innovative and creative patient / not patient with details standard procedures – challenges

Visual – Verbal learning from pictures – learning from words

Sequential – Global learn in linear steps – learn in large leaps good in using partial knowledge – need “big picture”

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Learning style models - FSLSM (cont’)

Types of combination of LS dimensions

1. active/sensing/visual/sequential

2. active/sensing/visual/global

3. active/sensing/verbal/sequential

4. active/sensing/verbal/global

5. active/intuitive/visual/sequential

6. active/intuitive/visual/global

7. active/intuitive/verbal/sequential

8. active/intuitive/verbal/global

9. reflective/sensing/visual/sequential

10. reflective/sensing/visual/global

11. reflective/sensing/verbal/sequential

12. reflective/sensing/verbal/global

13. reflective/intuitive/visual/sequential

14. reflective/intuitive/visual/global

15. reflective/intuitive/verbal/sequential

16. reflective/intuitive/verbal/global

Page 11: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Index of Learning Style (ILS) questionnaire

44 questions, 11 for each LS dimensions

Scales of the dimensions:

FSLSM (cont’)

Page 12: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

A reductive questionnaire

Based on FSLSM To be used for collecting initial learning style

information of students Aims at saving time for students to answer Contains of 20 questions

some from the ILS questionnaire, the rest from us 5 questions for each LS dimension

The questionnaire Graphical presentation: VIS

ACT

SNSGLO

SEQ

REF

INT

VRB0 1 2 3 4 5-1-2-3-4-5

1

2

3

4

5

-1

-2

-3

-4

-5

Page 13: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Implications of LSs in education

make learners aware of their learning styles

and show them their individual strengths

and weaknesses

students can be supported by matching the

teaching style with their learning styles

Page 14: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Outline

Introduction Learning objects and Learning styles Ontologies and intelligent agents in

education Incorporation of learning styles in a learning

management system Automatic detection of learning styles in LMSs Conception of an adaptive e-learning system POLCA – Implementation and results Conclusion

Page 15: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Ontology in education

Ontology represents domain knowledge by defining terminology, concepts, relations, and hierarchies

Ex. of educational ontology: OntoEdu

It enables education applications to share and reuse educational content

Ontology is machine-readable and reasonable: Suitable for description of learning objects

It will be faster and more convenient to query and retrieval educational material

Page 16: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Intelligent agents in education

how to provide adaptive teaching which is suitable to each student?

the use of Artificial Intelligence (AI) techniques such as Multi Agents or Agent Society-based architectures intelligence may be applied through user models to

make assumptions about the user’s state of knowledge, which may in turn help determine the user’s learning needs

may enable the system to dynamically personalise applications and services to meet user preferences, goals and desires

Page 17: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Outline

Introduction

Learning objects and Learning styles

Ontologies and intelligent agents in education

Incorporation of learning styles in a learning management system

Automatic detection of learning styles in LMSs

Conception of an adaptive e-learning system

POLCA – Implementation and results

Conclusion

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Developed for teachers to create and manage their courses.

Can be built based on pedagogical strategies: more learner-centered or more teacher-centered

The applied strategies focus mainly on how to teach learners from a general point of view, without considering the individual needs of learners.

Introduction to LMSs

Page 19: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Adaptivity in LMSs

Adaptivity indicates all kinds of automatic adaptation to individual learners’ needs. Course’s content

Personal annotations

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Benefits from using the Felder-Silverman learning style model in LMSs

FSLSM describes learning style in more detail, represents also balanced preferences

allows providing more accurate adaptivity

FSLSM considers learning styles as “flexibly stable”

LSs might change over time. An adaptive system can

adjust to the change.

FSLSM considers learning styles as tendencies

a student might act differently from his LS tendency. An

adaptive system should consider also exceptions and extraordinary situations.

Page 21: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Behaviour of learners in LMSs with respect to learning styles

Active/Reflective dimension

Active learners: do exercise first then look at examples

perform more self-assessment questions

Reflective learners: visit examples first then perform exercises

spend more time on examples and outlines

performed better on questions about interpreting

predefined solutions

Page 22: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Behaviour of learners

Benefits

Make teachers and course developers aware of the different needs, different ways of learning of their students.

Should provide courses with many different learning materials that support different learning styles.

Might present learning materials in different orders corresponding to different preference for LSs.

Page 23: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Providing adaptive courses in LMSs

Course elements

Adaptation features

Page 24: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Providing adaptive courses in LMSs

Course elements

A course consists of several chapters, where for each chapter, adaptivity can be provided.

Each chapter includes: An outline Content objects

definitions, algorithms, graphics, etc. Examples Self-assessment tests Exercises A summary

Page 25: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Providing adaptive courses in LMSs Adaptation features

Indicate how a course can change for students with different learning styles.

Include:

the sequence of LOs and their positions.

the number of presented examples and

exercises

Page 26: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Adaptation features (cont’)

For active learners: outlines are only presented once before the content

objects the number of exercises is increased

a small number of examples is presented

self-assessment tests are presented at the beginning

and at the end of a chapter a final summary is provided in order to conclude the

chapter

Page 27: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Adaptation features (cont’)

For reflective learners: the number of exercises and self-assessment tests is

decreased content objects are presented before examples

outlines are additionally provided between the topics

a conclusion is presented straight after all content objects

Page 28: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Methodology of incorporating LSs in a LMS

Creating adaptive course Course structure Learning objects with learning style properties

enough interchangeable LO?

Student modelling A LS questionnaire for initialising An automatic approach for revising

Providing adaptive course Combination of selecting and ordering learning

objects

Page 29: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Outline

Introduction Learning objects and Learning styles Ontologies and intelligent agents in education Incorporation of learning styles in a learning

management system Automatic detection of learning styles in

LMSs Conception of an adaptive e-learning system POLCA – Implementation and results Conclusion

Page 30: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Problems with collaborative student modelling that use a questionnaire

Uncertainty because of: a lack of students’ motivation

a lack of self-awareness about their learning preferences

the influence of expectations from others Questionnaires are static and describe the

learning style of a student at a specific point of time The result depends much on students’ mood

Page 31: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Benefits of using automatic student modelling

does not require additional effort from students

is free of uncertainty

can be more fault-tolerant due to information

gathering over a longer period of time

can recognise and update the change of

students’ learning preferences

Page 32: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Automatic student modelling approaches

Determining relevant behaviour

Selecting features and patterns

Classifying the occurance of

behaviour

Defining patterns for each dimentions

Inferring learning styles from behaviour

Preparing input data

Data-driven approach Literature-based approachOR

Predicted learning style preferences

LMS database

Page 33: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Automatic student modelling approaches

data-driven vs. literature-based

Felder-Silverman learning style model

Index of Learning Style questionnaire

Literature-based approach

Data-driven approach

Page 34: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Automatic student modelling

The data-driven approach

uses sample data in order to build a model for identifying learning styles from the behaviour of learners

aims at building a model that imitates the ILS questionnaire

Advantage: the model can be very accurate due to the use of real data

Disadvantage: the approach strictly depends on the available data and is developed for specific systems

Page 35: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Automatic student modelling

The literature-based approach

uses the behaviour of students in order to get

hints about their learning style preferences then applies a rule-based method to calculate

LSs from the number of matching hints

Advantage: generic and applicable for data gathered from any course

Disadvantage: might have problems in estimating the importance of the different hints

Page 36: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Outline

Introduction Learning objects and Learning styles Ontologies and intelligent agents in education Incorporation of learning styles in a learning

management system Automatic detection of learning styles in LMSs Conception of an adaptive e-learning

system POLCA – Implementation and results Conclusion

Page 37: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Methodology for implementing adaptation

Annotating learning objects

Estimating learning styles

Providing adaptivity

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Page 38: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Methodology

Annotating learning objects

Each learning object is annotated with one subtype of any element in the set of 16 types of

combination E.g: Annotation of an example LO is RefSen

38

Active Reflective Sensing Intuitive Visual Verbal Sequential Global

Self-assessment exercises, multiple-question-guessing exercises

Examples, outlines, summaries, result pages

Examples, explanation, facts, practical material

Definitions, algorithms

Images, graphics, charts, animations, videos

Text, audio

Step-by-step exercises, constrict link pages

Outlines, summaries, all-link pages

Page 39: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

MethodologyEstimating learning styles

Expected time spent on each learning object, Timeexpected_stay, is determined.

The time that a learner actually spent on each learning object, Timespent, is recorded.

Ratios for number of visits with respect to each LS element

39

stayectedexp

spentelementLS Time

TimeRT

__

LOs

LOsRV visited

elementLS _

Page 40: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Methodology

Estimating learning styles (cont’)

An example

Learning style: moderate Active/Reflective, and strong Visual.

40

Ravg LS Preference

0 – 0.3 Weak

0.3 – 0.7 Moderate

0.7 – 1 Strong

  ACT REF SNS INT VIS VRB SEQ GLO

Ravg 0.5 0.6 0.25 0.2 0.8 0.15 0.8 0.9

Page 41: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Methodology Providing adaptivity

Assumption: interchangeable learning objects are sufficient for each learning content.

The LMS automatically delivers suitable LOs for each learner based on: What learning content he choses

His learning style that has been identified

Previous example: only LOs with Act/Ref/Vis annotations.

Combined with changing their appearance order

41

Page 42: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

System’s adaptation

LO 1_1

Course

Learner 1

Topic 1

Topic 2

Topic n

Reflective

Active

Sensing

Intuitive

Visual

Verbal

Sequential

Global

Learner 2

Learner n

LO 1_2

LO n_1

LO n_2

LO n_3

LO 2_1

LO 2_2

x

Learning stylesLearning objects

Page 43: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

System’s domain ontology

lnHasObjective

isSupportedBy

supports

nextConceptpreviousConcept

hasRequisiteisPrequisiteFor

consistsOfsimilarTo

oppositeOfabHasObjective

helpsToAchieveAbility

abBelongsTo

csHasObjective

hasAbility

isDescribedBydescribes

hasConcept

hasDescription

ccBelongsTo

lnHasLearningStyle

takes

helpsToAchieveKnowledge

rdHasLearningStyle

ccHasObjective

includedInhasResource

Concept (Knowledge)

conceptName: StringccBelongsTo: CourseccHasObjective: CompetenceconsistOf: ConceptsimilarTo: ConceptoppositeOf: ConceptnextConcept: ConceptpreviousConcept: ConcepthasRequisite: ConceptisPrerequisiteFor: ConceptisDescribedBy: Resource

Learning Style

activeReflective: IntegersensingIntuitive: IntegervisualVerbal: IntegersequaltialGlobal: Integer

Ability

abilityName: StringabBelongsTo: CourseabHasObjective: CompetenceisSupportedBy: Resource

Learner

fullName: StringdateOfBirth: Datesex: Booleanphone#: Stringemail: StringlevelOfStudy: StringyearOfStudy: IntegerworkStatus: Stringperformance: StringlnHasObjective: Competencetakes: CourselnHasLearningStyle: LearningStyle

Competence (Objective)

objective: String

Resource (Learning Object)

includedIn: Coursedescribes: Conceptsupports: AbilityhasDescription: ResourceDescription

Course

courseName: StringcourseDescription: StringcsHasObjective: CompetencehasConcept: ConcepthasAbility: AbilityhasResoure: Resource

ResourceDescription

createdBy: StringhasKeyword: StringhelpsToAchieveKnowledge: ConcepthelpsToAchieveAbility: Abilitytype: Stringlanguage: StringdifficultLevel: StringrdHasLearningStyle: LearningStyle

Page 44: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Outline

Introduction Learning objects Learning styles Ontologies and intelligent agents in education Incorporation of learning styles in a learning

management system Automatic detection of learning styles in LMSs Conception of an adaptive e-learning system POLCA – Implementation and results Conclusion

Page 45: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

System architecture

A multi-agent one with artificial agents

45

Adaptive content agent

Learning style monitoring agent

Login service

TutorAdaptive delivery

service

Learning style testing service

Advice agent

Content management service Learning content

database

Personal agent of tutor

Learners withdifferent learning styles

User profile database

Chat/Analyse

Chat/ Analyse

Inter-agent communication

Personal agents of learners

Other services

Page 46: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

System interface and functionality

Administrator: updates personal information of teachers

and students,

views statistics about each individual or all of students' behaviour with respect to FSLSM

other management tasks

Page 47: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng
Page 48: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

System interface and functionality

Teachers

update list of his courses: subjects, chapters, sections

update his learning objects: outlines, definitions, algorithms, graphics, examples, exercises, summaries, etc.

set up tests and see participated students' results

accept application requests for his course from students

view statistics of students' behaviour related to their learning styles

Page 49: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Annotating the learning object

with LS properties

Choosing the topic that learning

object belongs to

Editing learning object’s contentControl menu for

teachers

Page 50: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

System interface and functionality

Students

register for a course

take registered courses

do the tests

see the test results

Page 51: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

System interface and functionality

System’s agents

Learning style monitoring agent keeps track on every student's number of and

his visit spent time on learning objects of the courses

stores students' learning styles and updates new estimated ones

Adaptive content agent chooses and orders the learning objects to

present for each student

Page 52: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

LS detection result

Experiment:

an Artificial Intelligence course – 9 weeks

204 learning objects – test of LS properties

44 participated students – were asked to fill in

the Index of Learning Style (ILS) questionnaire

Precision: (72,73%, 70.15%, 79.54%, 65.91%) for

Act/Ref, Sen/Int, Vis/Vrb, and Seq/Glo

52

n

LSLSSimecisionPr

ILS

n

determined ),(1

Page 53: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

53

Outline

Introduction

Learning objects and Learning styles

Ontologies and intelligent agents in education

Incorporation of learning styles in a learning management system

Automatic detection of learning styles in LMSs

Conception of an adaptive e-learning system

POLCA – Implementation and results

Conclusion

Page 54: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Contributions

Develop a reductive questionnaire for detecting learning styles

Make a survey of students' learning styles based on the Felder-Silver learning style model

Develop an agent-based architecture for building adaptive LMSs in general

Propose an annotation of learning objects and a mixture method to provide adaptivity in LMSs according to users' learning styles

Page 55: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Contributions

Propose a new automatic and dynamic approach based on literature for identifying students’ learning styles in LMSs has a promising detection result,

is simpler than existing ones,

and can be applied for LMSs in general

Develop an adaptive e-learning system incorporating above architecture and methodologies.

Page 56: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Limitations

no incorporated communication channel

among students

the short testing time and the restricted

pools of testing students

Page 57: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

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Future work

develop more system’s functions

have more accurate results in LS detection: include more students’ behaviour patterns

examine more exceptions of student behaviour

consider the ability of including the relationship between learning styles and cognitive skills

focus on providing better adaptivity find whether there are adaptation features which have more

impact than others

monitoring agent will track also their learning performance

Page 58: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Thanks for your attention!

Page 59: AN ADAPTIVE E-LEARNING SYSTEM BASED ON USERS' LEARNING STYLES Author: Phạm Quang Dũng

Summarise the most contributions - Section 10.1

Add the reasons why to use those appendices

Add our own citations - Sections 8.1, 8.2, 9.1, 9.3.1

Explain more clearly about literature-based approach and Graf's method (including Figure 7.2 and Table 7.1) - Section 7.2

Make the comparison between our method with the others more clearly - Section 9.3.1