Learner Modelling and Adaptation in Math-Bridge Sergey Sosnovsky!

Saarland University

Learning Content Presentation: Dashboard

Learning Content Presentation: Main View

Personalised Course Generation

1 2

3

4

Adaptive Link Annotation

Micro-course generation

Intelligent Adaptive e-Learning System:Main Components

Instructional Content

Interaction

0..1..1..0..1..1..

DomainModel !!!

Learner Model

PedagogicalModel

Adaptation

Me t a d a t a

Learning Events of Math-Bridge

0..1..1..0..1..1..

Rich continuos stream of learning data ❖ Any interaction of the student with Math-Bridge causes

an event in the system logs;!

❖ More than 30 types of events (e.g., system login/logout, course started/finished, exercise started/finished, etc.);!

❖ More than 50 attributes (e.g., for the exerciseStep event: time, user, session, courseId, successRate, metadataText, userInputDelay, userInputText,…);

Content and knowledge modelling in Math-Bridge

Instructional Content

DomainModel !!!

Me t a d a t a

Knowledge Items

Abstract Concepts

Concepts with content

Content

Metadata❖ Descriptive!

❖ author!❖ date…!

❖ Pedagogical!❖ difficulty!❖ competency!❖ educational level…!

❖ Semantic!❖ is prerequisite for!❖ is exercise for!❖ is introduction for…

Ontology❖ 536 symbols!

❖ will, probably, need to be extended

Martin Homik 5th Sakai Conference 2006, Vancouver !14

Knowledge Representation

D

S

EX

P

T

S S

S

isA

D

D T

XE

Definition

E

Symbol

Example

Theorem

ProofExercise

X

forfor

forforfor

D D

for counter

P

for

S S

for depends on

depends on

Abstract Layer

Content Layer

Satellite Layer

OMDoc❖ All content and its metadata, are

represented in OMDoc!

❖ OMDoc is an XML dialect developed for math documents !

❖ Formulas are written in OpenMath!

❖ OpenMath is an extensible standard for representing the semantics of mathematical objects

<definition id="c6s1p4_Th2_def_monoid" for="c6s1p4_monoid„ <metadata> <depends-on> <ref theory="cp1_Th3" name="structure" /> </depends-on> <Title xml:lang="en">Definition of a monoid</Title> </metadata> <CMP xml:lang="en" format="omtext"> A monoid is a <ref xref="cp1_Th3_def_structure"> structure </ref> <OMOBJ> <OMS cd="elementary" name="ordered-triple"/> <OMV name="M"/> <OMS cd="cp4_Th2" name="times"/> <OMS cd="cp4_Th2" name="unit"/> </OMOBJ> in which <OMOBJ> <OMS cd="elementary" name="ordered-pair"/> <OMV name="M"/> <OMS cd="cp4_Th2" name="times"/> </OMOBJ> is a semi-group with <ref xref="c6s1p3_Th2_def_unit">e</ref> <OMOBJ xmlns="http://www.openmath.org/OpenMath"> <OMS cd="cp4_Th2" name="unit"/> </OMOBJ>. </CMP> <FMP><OMOBJ> ... </OMOBJ></FMP> </definition>

Definition of a Monoid

Learner Modelling in Math-Bridge

Background

❖ Dynamic Overlay Model with forgetting!

❖ Specific challenges !

❖ Dynamic Domain Model!

❖ Dynamic Content Base and Metadata annotations!

❖ SLM (Eric, Arndt, Salim)

Evidences

❖ (s,e,c,p,l,a)!

❖ Student!

❖ Exercise!

❖ Concept!

❖ Competency!

❖ Achievement

Updates❖ Direct evidence - individual events for 1 concept, 1

process!

❖ Indirect evidence - propagation!

❖ Intra-Concept: across competencies!

❖ Inter-Concept: prerequisite, for

Amplitude of the update❖ IRT:

psychometric theory for testing!

❖ Used successfully since 20+ years

IRT Usage

❖ Pool of calibrated items with known ICC!

❖ Logistic function (difficulty, discrimination, guess)!

❖ Idea: Measure latent trait 𝞱!

❖ Administer sequence of test items!

❖ 𝞱 uncovered by responses to items

IRT vs. MthBridge—IRTPropoer IRT MathBridge—IRT

ICC Empirical Theoretical

Input Item Response Sequence

Sparse Evidences

Answers Dichotomous Continuous

Difficulty Single factor Difficulty/Competency

IndependenceItems are

independent of each other

Exercises are often related

LearningNo learning between

or during assessment

Learning is essential for Math-Bridge

Belief Masses

❖ Round achievement to {1,0}!

❖ if r=1: m(H(b)) = P(correct | 𝞱 =b)!

❖ if r=0: m(H(b)) = 1-P(correct | 𝞱 =b)!

!

❖ restrict updated hypotheses to Information Radius interval: [irtdiff ±δ]

𝞱

p(co

rrec

t)

Mastery inference

Learning Event (Raw evidence)

𝞱

p(co

rrec

t)

Dempster-Shafer Best belief about mastery

Competency Models

❖ Bloom (subset: K / C / A)!

❖ PISA (☈ operationalization)!

❖ Math-Bridge !

❖ TU-D cognitive operators!

❖ Commonality: Multi-dimensional overlays

Exercise

Concept

is For

Competency

Mastery Aggregate❖ Single “mastery” value!

❖ Necessary for Course Generation!

❖ Implemented as (weighted) average of competencies

Adaptation in Math-Bridge

PedagogicalModel Adaptation

Scenario LearnNewIntroduce

Develop

Practice

Connect

Reflect

Scenario LearnNew

Introduce

Develop

Practice

Connect

Reflect

Motivate

Context

Illustrate

Prerequisites

Scenario LearnNew

Introduce

Develop

Practice

Connect

Reflect

Motivate

Context

Illustrate

Prerequisites

(:method (motivate! ?c) ((learnerProperty hasEducationalLevel ?el) (learnerProperty hasAnxiety ?c ?an) (?an <= 2) (GetElement ((class Exercise) (class Introduction) (relation isFor ?c) (property hasLearningContext ?el) (property hasDifficulty very_easy)))) ((insert! ?element)))

IF

THEN

Scenario LearnNew

Introduce

Develop

Practice

Connect

Reflect

Motivate

Context

Illustrate

Prerequisites

(:method (motivate! ?c) ((learnerProperty hasEducationalLevel ?el) !! (GetElement ((class Example) (class Introduction) (relation isFor ?c) (property hasLearningContext ?el) (property hasDifficulty very_easy)))) ! ((insert! ?element)))

IF

THEN

(:method (motivate! ?c) ((learnerProperty hasEducationalLevel ?el) (learnerProperty hasAnxiety ?c ?an) (?an <= 2) (GetElement ((class Exercise) (class Introduction) (relation isFor ?c) (property hasLearningContext ?el) (property hasDifficulty very_easy)))) ((insert! ?element)))