Difficulty Analysis for Learners in Problem Solving Process based on the Knowledge Map Speaker: Rita...

Difficulty Analysis for Difficulty Analysis for Learners in Problem Solving Learners in Problem Solving

Process Process based on the Knowledge Mapbased on the Knowledge Map

Speaker: Rita KuoSpeaker: Rita Kuo

Rita Kuo, Wei-Peng Lien, Maiga Chang, Jia-Sheng Heh

Multimedia Communication System LaboratoryMultimedia Communication System LaboratoryDept. of Information and Computer EngineeringDept. of Information and Computer Engineering

Chung-Yuan Christian Univ., Chung-Li, 320, TaiwanChung-Yuan Christian Univ., Chung-Li, 320, Taiwan

ICALT 2003ICALT 20032002/06/272002/06/27 To Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated KnowledgeTo Develop an Item Generating System with Analyzing the Problem Model in the Inter-Correlated Knowledge 22

OutlinesOutlines

►Basic DefinitionBasic Definition Basic Problem ModelBasic Problem Model Problem Construction StepsProblem Construction Steps Knowledge and Problem StructureKnowledge and Problem Structure

►Problem Difficulty AnalysisProblem Difficulty Analysis Difficulty FeaturesDifficulty Features Difficulty DimensionsDifficulty Dimensions

►Demonstration of Item Generating Demonstration of Item Generating SystemSystem

►Brief ConclusionBrief Conclusion


Basic Problem ModelBasic Problem Model► Inter-correlated KnowledgeInter-correlated Knowledge

Manipulation of inter-correlation among knowledge Manipulation of inter-correlation among knowledge Ex. Physics, Chemistry, and MathematicsEx. Physics, Chemistry, and Mathematics

► Knowledge ObjectKnowledge Object Way to analyze Way to analyze

Inter-correlated KnowledgeInter-correlated Knowledge Basic concept of a specific domain Basic concept of a specific domain

► Basic Problem DefinitionBasic Problem Definition One Core Knowledge ObjectOne Core Knowledge Object Example in Physics: Example in Physics:

Physics PhenomenonPhysics Phenomenon► Basic Problem ModelBasic Problem Model

Corresponding Corresponding ConceptsConcepts

ExampleExample

Basic Basic ProbleProblem m ModelModel

Sub-Problem Flag Sub-Problem Flag AttributeAttribute

Free FallFree Fall Phenomena Phenomena

Given AttributesGiven Attributes Given value of Given value of DistanceDistance and and VelocityVelocity AttributesAttributes

Unknown AttributesUnknown Attributes Ask for Ask for TimeTime Attribute Attribute

Object PhysicsPhenomenon

PhysicsQuantity

Physics Law

Proceed

Then / Equal

AssociateCompose

Influence

Has Has

Influence

Associate


Problem ConstructionProblem Construction

► Knowledge BaseKnowledge Base Knowledge MapKnowledge Map

1.1. Concept SelectionConcept Selection Knowledge MapKnowledge Map

2.2. Unknown DesignationUnknown Designation Problem MatrixProblem Matrix

3.3. Proposition ConstructioProposition Constructionn

Unknow nDesignation

ProblemProposition

Construction

ProblemMatrix

Knowledge Map

ProblemConstruction

ConceptSelection


Knowledge MapKnowledge Map

► Concept HierarchyConcept Hierarchy Hierarchical structure of concepts Hierarchical structure of concepts Concept Concept

MapMap

► Concept SchemaConcept Schema Attributes Attributes SchemaSchema Definitions, Ability (Can-Fly), Property (Age) etc.Definitions, Ability (Can-Fly), Property (Age) etc.


Example of Knowledge MapExample of Knowledge Map

Physics Mechanics

Kinematics

1-DimensionMotion

2 or moreDimension

Motion

Motion with ConstantVelocity

Def: a branchof dynamicsthat . . .Attr: has position has velocity has acce.

Def: motionalone . . .Attr: has position has velocity has acce.

Motion with ConstantAcceleration

Def: acce. is constantAttr: has position has velocity has acce. rule vt=v0+a*t

Def: basicallythe study ofthe motion ofmaterial object


Problem MatrixProblem Matrix

► Manipulating conceptsManipulating concepts Example in Physics: Physics QuantityExample in Physics: Physics Quantity {“Displacement”, “Time”, “Velocity”, {“Displacement”, “Time”, “Velocity”,

“Acceleration”}“Acceleration”}

► Manipulating relationsManipulating relations Example in Physics: Physics LawExample in Physics: Physics Law {“Displacement = 0.5 * Acceleration * Time ^ {“Displacement = 0.5 * Acceleration * Time ^

2”,2”, “Velocity = Acceleration * Time”} “Velocity = Acceleration * Time”}DisplacemeDisplaceme

ntntTimTimee

VelocitVelocityy

AcceleratioAccelerationn

Displacement = 0.5 * Acceleration * Displacement = 0.5 * Acceleration * Time ^ 2Time ^ 2

11 11 00 11

Velocity = Acceleration * TimeVelocity = Acceleration * Time 00 11 11 11


Example of Problem Example of Problem ConstructionConstruction

► Physics PhenomenonPhysics Phenomenon Motion with constant velocityMotion with constant velocity

► Problem Matrix Problem Matrix tf:tf: final time; final time; si:si: initial position; initial position; ti:ti: initial time; initial time;

vi:vi: initial velocity; initial velocity; sf:sf: final position; final position; d:d: distance distance tftf sisi titi vivi sfsf dd

sf – si = (vf – vi) * (tf – ti)sf – si = (vf – vi) * (tf – ti) 11 11 11 11 11 00

d = sf – sid = sf – si 00 11 00 00 11 11


Unknown DesignerUnknown Designer

►Select Physics LawSelect Physics Law

►Set AttributesSet Attributes

tftf sisi titi vivi sfsf dd


d = sf – sid = sf – si 00 11 00 00 11 11

tftf sisi titi vivi sfsf dd

5252 UnknowUnknownn

88 1.11.1 6060


d = sf – sid = sf – si 00 11 00 00 11 11


Problem Constructor (cont.)Problem Constructor (cont.)

ModelModel Corresponding Corresponding ConceptsConcepts ExampleExample

# Sub-# Sub-ProblemsProblems

# Unknowns# Unknowns

Basic Problem Basic Problem ModelModel

Sub-Problem Sub-Problem Flag AttributeFlag Attribute

The elevator of the building proceeds The elevator of the building proceeds motion with constant velocitymotion with constant velocity. .

Given AttributesGiven Attributes The The velocityvelocity of the elevator is of the elevator is 1.1 1.1 meter/secondmeter/second. .

The The initial timeinitial time of the elevator is of the elevator is 88thth secondsecond. .

The The final timefinal time of the elevator is of the elevator is 5252ndnd secondsecond. .

The The final positionfinal position of the elevator is of the elevator is 60 60 metermeter. .

Unknown Unknown AttributesAttributes

Ask for the Ask for the initial positioninitial position of the elevator of the elevator


Difficulty AnalysisDifficulty Analysis

► Difficulty FeaturesDifficulty FeaturesAccording to the problem construction processAccording to the problem construction process1.1. Selected ConceptsSelected Concepts

Knowledge MapKnowledge Map

2.2. Attributes SettingAttributes Setting Problem MatrixProblem Matrix

► Difficulty DimensionsDifficulty DimensionsAccording to the problem solving stepsAccording to the problem solving steps1.1. Problem IdentificationProblem Identification2.2. Problem ElaborationProblem Elaboration3.3. Problem PlanningProblem Planning4.4. Problem ExecutionProblem Execution


Difficulty FeaturesDifficulty Features

UnknownDesignation

ProblemProposition

Construction

ProblemMatrix

Knowledge Map

ProblemConstruction

ConceptSelection

ElementElement Difficulty FeatureDifficulty Feature DenotatioDenotationn

Number of Sub-ProblemsNumber of Sub-Problems sub_prob

SelectedSelected Number of Needed AttributesNumber of Needed Attributes need_attr

ConceptsConcepts Learning SequenceLearning Sequence learn_seq

Concept DepthConcept Depth cpt_depth

Number of UnknownsNumber of Unknowns unknown

AttributeAttributess

Number of Giving AttributesNumber of Giving Attributes given_attr

SettingSetting Number of Elaborating Number of Elaborating AttributesAttributes

elb_attr

Mathematical ComplexityMathematical Complexity math_cpx


Attributes DefinitionAttributes Definition► Basic DefinitionBasic Definition

rootroot: the root of Knowledge Ma: the root of Knowledge Mapp

ii: ith concept: ith concept► Knowledge MapKnowledge Map

heightheight((ii)): the height of sub-tre: the height of sub-tree from e from iith conceptth concept

CSCS((ii)): Concept Schema of : Concept Schema of iith th conceptconcept

sizesize((CSCS((ii)))): number of attribut: number of attributes in concept from full Concept es in concept from full Concept SchemaSchema

attrattrLSLS((CSCS((ii)))): learning sequenc: learning sequence attribute stored in Concept Sce attribute stored in Concept Schemahema

► Problem MatrixProblem Matrix #given_attr#given_attr: number of given at: number of given at

tributes in the problemtributes in the problem #unknown#unknown: number of unknown : number of unknown

attributes in the problemattributes in the problem attrattrmanip_cptmanip_cpt((ii)): attributes extract: attributes extract

ed to manipulating concepts in ed to manipulating concepts in Problem MatrixProblem Matrix

sizesize((attrattrmanip_cptmanip_cpt((ii)))): number of : number of manipulating concepts in Problmanipulating concepts in Problem Matrixem Matrix

attrattrmax_unknownmax_unknown((ii)): maximum num: maximum number of unknown in ber of unknown in iith conceptth concept


ExampleExample

► In sky, raindrop proceeds In sky, raindrop proceeds the motion of constant accelerthe motion of constant accelerationation. The . The initial velocity (vi)initial velocity (vi) is 0 m/s. is 0 m/s. Acceleration (a)Acceleration (a) is is 5 m/s^2. 5 m/s^2. The final time (tf)The final time (tf) is 5 s. Ask for the value of is 5 s. Ask for the value of fin final velocity (vf)al velocity (vf)..

► Selected ConceptSelected Concept The motion of constant accelerationThe motion of constant acceleration

► Attributes SettingAttributes Settingdidi dfdf vivi vfvf titi tftf aa

00 unknowunknownn

55 55

vf = vi + a * (tf – ti)vf = vi + a * (tf – ti) 00 00 11 11 11 11 11

df = di + vi * (tf – ti) + 0.5 *a * (tf – ti)^2df = di + vi * (tf – ti) + 0.5 *a * (tf – ti)^2 11 11 11 00 11 11 11

vf ^2 = vi ^ 2 + 2 * a * (df – di)vf ^2 = vi ^ 2 + 2 * a * (df – di) 11 11 11 11 00 00 11


Attributes Definition – Knowledge Attributes Definition – Knowledge MapMap

► size size ((CS CS (“Motion with Constant Acceleration”) ) = 11(“Motion with Constant Acceleration”) ) = 11► size size ((CS CS (“Free Fall”) ) = 13(“Free Fall”) ) = 13► heightheight (“Physics”) = 4 (“Physics”) = 4► heightheight (“Motion with Constant Acceleration”) = 2 (“Motion with Constant Acceleration”) = 2

► attrattrLSLS(“Motion with Constant Acceleration”) = 2(“Motion with Constant Acceleration”) = 2Physics

1-DimensionMotion

2 or moreDimension

Motion



QTY

LS

QTY

QTY

QTY

QTY

QTY

QTY

LAW

LAW

LAW

2

Init. Position

Final Position

Init. Velocity

Final Velocity

Init. Time

Final Time

Acceleration

Vel-Acce Law

Pos-Acce Law

Pos-Vel Law

Free Fall

QTY

LS

QTY

QTY

QTY

QTY

QTY

QTY

LAW

LAW

LAW

2

Init. Position

Final Position

Init. Velocity

Final Velocity

Init. Time

Final Time

Acceleration

Vel-Acce Law

Pos-Acce Law

Pos-Vel Law

COND

Def Free Fall is an phenomenon with constantacceleration of 9.8

Acceleration = 9.8


Attributes Definition – Problem Attributes Definition – Problem MatrixMatrix

► #given_attr#given_attr = 3 = 3► #unknown#unknown = 1 = 1

► sizesize((attrattrmanip_cptmanip_cpt((ii)) = 7)) = 7

► attrattrmax_unknownmax_unknown((ii) = 2) = 2

didi ddff

vivi vfvf titi tftf aa

00 unknowunknownn

55 55





Difficulty Features Calculation (1)Difficulty Features Calculation (1)► need_attrneed_attr = = sizesize((CSCS((ii)) / arg max)) / arg maxjjKMKM sizesize((CSCS((jj))))

= = sizesize((CSCS(“Motion with Constant Acceleration”)) (“Motion with Constant Acceleration”)) / / sizesize((CSCS(“Free Fall”)) (“Free Fall”)) = 11 / 13 = 0.8 = 11 / 13 = 0.8

Physics1-Dimension

Motion

2 or moreDimension

Motion



QTY

LS

QTY

QTY

QTY

QTY

QTY

QTY

LAW

LAW

LAW

2

Init. Position

Final Position

Init. Velocity

Final Velocity

Init. Time

Final Time

Acceleration

Vel-Acce Law

Pos-Acce Law

Pos-Vel Law

Free Fall

QTY

LS

QTY

QTY

QTY

QTY

QTY

QTY

LAW

LAW

LAW

2

Init. Position

Final Position

Init. Velocity

Final Velocity

Init. Time

Final Time

Acceleration

Vel-Acce Law

Pos-Acce Law

Pos-Vel Law

COND


Acceleration = 9.8


Difficulty Features Calculation (2)Difficulty Features Calculation (2)► learn_seq learn_seq = = attrattrLSLS((ii) / arg max) / arg maxjjsiblingsibling((ii) ) attrattrLSLS((jj))

= = attrattrLSLS(“Motion with Constant Acceleration”) (“Motion with Constant Acceleration”)

/ / attrattrLSLS(“Motion with Constant Acceleration”)(“Motion with Constant Acceleration”)

= 2 / 2 = 1 = 2 / 2 = 1Physics

1-DimensionMotion

2 or moreDimension

Motion



QTY

LS

QTY

QTY

QTY

QTY

QTY

QTY

LAW

LAW

LAW

2

Init. Position

Final Position

Init. Velocity

Final Velocity

Init. Time

Final Time

Acceleration

Vel-Acce Law

Pos-Acce Law

Pos-Vel Law

Free Fall

QTY

LS

QTY

QTY

QTY

QTY

QTY

QTY

LAW

LAW

LAW

2

Init. Position

Final Position

Init. Velocity

Final Velocity

Init. Time

Final Time

Acceleration

Vel-Acce Law

Pos-Acce Law

Pos-Vel Law

COND


Acceleration = 9.8


Difficulty Features Calculation (3)Difficulty Features Calculation (3)► cpt_depth cpt_depth = (= (heightheight((rootroot) – ) – heightheight ( (ii)) / )) / heightheight((rootroot))

= ( = (heightheight(“Physics”) – (“Physics”) – heightheight (“Motion with Constant Acceleration”)) (“Motion with Constant Acceleration”))

/ / heightheight(“Physics”)(“Physics”) = ( 4 – 2 ) / 4 = 0.5 = ( 4 – 2 ) / 4 = 0.5Physics

1-DimensionMotion

2 or moreDimension

Motion



QTY

LS

QTY

QTY

QTY

QTY

QTY

QTY

LAW

LAW

LAW

2

Init. Position

Final Position

Init. Velocity

Final Velocity

Init. Time

Final Time

Acceleration

Vel-Acce Law

Pos-Acce Law

Pos-Vel Law

Free Fall

QTY

LS

QTY

QTY

QTY

QTY

QTY

QTY

LAW

LAW

LAW

2

Init. Position

Final Position

Init. Velocity

Final Velocity

Init. Time

Final Time

Acceleration

Vel-Acce Law

Pos-Acce Law

Pos-Vel Law

COND


Acceleration = 9.8


Difficulty Features Calculation Difficulty Features Calculation (4)(4)

► given_attr given_attr = (= (sizesize((attrattrmanip_cptmanip_cpt((ii)) - #)) - #given_attrgiven_attr + 1) / + 1) / sizesize((attrattrmanip_cptmanip_cpt((ii))))

= ( = (sizesize((attrattrmanip_cptmanip_cpt(“Motion with Constant Acceleration”)) - #(“Motion with Constant Acceleration”)) - #given_attrgiven_attr + 1) + 1)

/ / sizesize((attrattrmanip_cptmanip_cpt(“Motion with Constant Acceleration”))(“Motion with Constant Acceleration”))

= (7 – 3 + 1) / 7 = 0.7 = (7 – 3 + 1) / 7 = 0.7

didi dfdf vvii

vfvf titi tftf aa

00 unknownunknown 55 55






► unknown unknown = #= #unknownunknown / / attrattrmax_unknownmax_unknown((ii) )

= # = #unknownunknown / / attrattrmax_unknownmax_unknown(“Motion with Constant Acceleration”)(“Motion with Constant Acceleration”)

= 1 / 2 = 0.5 = 1 / 2 = 0.5

didi dfdf vivi vfvf titi tftf aa

00 unknowunknownn

55 55






► elb_attrelb_attr = (= (sizesize((attrattrmanip_cptmanip_cpt((ii)) - #)) - #given_attrgiven_attr - # - #unknownunknown + 1) / + 1) / sizesize((attrattrmanip_cptmanip_cpt((ii)) ))

= ( = (sizesize((attrattrmanip_cptmanip_cpt(“Motion with Constant Acceleration”)) (“Motion with Constant Acceleration”))

- # - #given_attrgiven_attr - # - #unknownunknown + 1) + 1) / / sizesize((attrattrmanip_cptmanip_cpt(“Motion with Constant Acceleration”))(“Motion with Constant Acceleration”))

= ( 7 – 3 – 1 + 1) / 7 = 0.4 = ( 7 – 3 – 1 + 1) / 7 = 0.4

didi dfdf vivi vfvf titi tftf aa

00 unknowunknownn

55 55





Difficulty DimensionsDifficulty Dimensions

► According to four steps of problem solvingAccording to four steps of problem solving

Identification Difficulty (Identification Difficulty (idfidf))

Elaboration Difficulty (Elaboration Difficulty (elbelb))

Planning Difficulty (Planning Difficulty (plnpln))

Execution Difficulty (Execution Difficulty (excexc))

ProblemIdentification

ProblemElaboration

ProblemPlanning

ProblemExecution

STM

ProblemLoading

Knowledge BaseLTM

Result

Problem Matrix Problem Graph


Difficulty Dimensions (cont.)Difficulty Dimensions (cont.)

► Identification Difficulty (Identification Difficulty (idfidf)) Position in Knowledge MapPosition in Knowledge Map

► Elaboration Difficulty (Elaboration Difficulty (elbelb)) Size of Concept Schema in Knowledge MapSize of Concept Schema in Knowledge Map

► Planning Difficulty (Planning Difficulty (plnpln)) Number of Manipulating ConceptsNumber of Manipulating Concepts

► Execution Difficulty (Execution Difficulty (excexc)) Number of UnknownsNumber of Unknowns


Difficulty Dimension TransformatioDifficulty Dimension Transformationn

► idfidf = = ww2121 * * learn_seqlearn_seq + + ww3131 * * cpt_depthcpt_depth

= = 0.50.5 * * learn_seqlearn_seq + + 0.50.5 * * cpt_depth cpt_depth

= 0.5 * 1 + 0.5 * 0.5 = 0.75 = 0.5 * 1 + 0.5 * 0.5 = 0.75

► elbelb = = ww1212 * * need_attrneed_attr + + ww4242 * * given_attrgiven_attr + + ww6262 * * elb_attrelb_attr

== 0.30.3 * * need_attrneed_attr + + 0.30.3 * * given_attrgiven_attr + + 0.30.3 * * elb_attrelb_attr

= = 0.3 * 0.8 + 0.3 * 0.7 + 0.4 * 0.4 = 0.610.3 * 0.8 + 0.3 * 0.7 + 0.4 * 0.4 = 0.61

► plnpln = = ww5353 * * unknownunknown + + ww6363 * * elb_attrelb_attr

= 0.5 = 0.5 * * unknownunknown + + 0.50.5 * * elb_attrelb_attr

= 0.5 * 0.5 + 0.5 * 0.4 = 0.45 = 0.5 * 0.5 + 0.5 * 0.4 = 0.45

► excexc = = ww5454 * * unknownunknown

= 1 = 1 * * unknownunknown

= 1 * 0.5 = 0.5 = 1 * 0.5 = 0.5


DemonstrationDemonstration


Brief ConclusionsBrief Conclusions

►Problem Construction StepsProblem Construction Steps Concept SelectionConcept Selection Unknown DesignationUnknown Designation Proposition ConstructionProposition Construction

►Problem DifficultiesProblem Difficulties Difficulty FeaturesDifficulty Features Difficulty DimensionsDifficulty Dimensions

► Item Generating SystemItem Generating System Physics DomainPhysics Domain


Future WorksFuture Works

► Complex problemComplex problem construction construction

► Mathematical complexityMathematical complexity analysis analysis

► Answer of the learners Answer of the learners diagnosisdiagnosis

Thank YouThank You




Presentations of KnowledgePresentations of Knowledge

► ConceptConcept Basic element of knowledgeBasic element of knowledge A atomic unit of knowledge piecesA atomic unit of knowledge pieces Ex. “Ex. “Free FallFree Fall”, “”, “Constant Acceleration MotionConstant Acceleration Motion” ” etc.etc.

► RelationRelation The aggregation of conceptsThe aggregation of concepts Ex. Ex. Is-AIs-A, , Has-AHas-A etc.etc.

► PropositionProposition An integration of concepts and relationAn integration of concepts and relation One relation with at least two conceptsOne relation with at least two concepts Ex. “Ex. “Free FallFree Fall” ” Is-AIs-A “ “Constant Acceleration MotionConstant Acceleration Motion””


Inter-correlated KnowledgeInter-correlated Knowledge► Inter-correlated KnowledgeInter-correlated Knowledge

Manipulation of inter-correlation among knowledge Manipulation of inter-correlation among knowledge Ex. Physics, Chemistry, and MathematicsEx. Physics, Chemistry, and Mathematics

► Knowledge ObjectKnowledge Object Way to Analysis Inter-correlated KnowledgeWay to Analysis Inter-correlated Knowledge Basic concept of a specific domainBasic concept of a specific domain

► Relations between Knowledge ObjectsRelations between Knowledge Objects Ten types in The Frame Game Ten types in The Frame Game

[Clifford, 1981][Clifford, 1981]

Object PhysicsPhenomenon

PhysicsQuantity

Physics Law

Proceed

Then / Equal

AssociateCompose

Influence

Has Has

Influence

Associate

PropositionProposition RelatioRelation Typen Type

[OBJ]<Proceed>[PHE][OBJ]<Proceed>[PHE] PWPW

[PHE]<Has>[LAW][PHE]<Has>[LAW] PWPW

[PHE]<Influence>[QTY][PHE]<Influence>[QTY] INFINF

[LAW]<Influence>[QTY][LAW]<Influence>[QTY] INFINF

[OBJ]<Has>[QTY][OBJ]<Has>[QTY] PWPW

[QTY][QTY]1~n1~n<Compose>[LA<Compose>[LAW]W]

PWPW

[LAW][LAW]1~n1~n<Associate>[LA<Associate>[LAW]W]00

ASOASO

[PHE][PHE]22<Then>[PHE]<Then>[PHE]11 SQNSQN

[PHE][PHE]11<Equal>[PHE]<Equal>[PHE]22 EQLEQL

[QTY][QTY]11<Associate>[QTY]<Associate>[QTY]22 ASOASO


Problem Structure 1: Problem Problem Structure 1: Problem GraphGraph

► A graph composed with A graph composed with propositionproposition Relation among concepts Relation among concepts

in the problemin the problem► ExampleExample

Concept SetConcept Set{"Object", "Free Fall", {"Object", "Free Fall", Displacement", "Time",Displacement", "Time","19.6", "unknown"}"19.6", "unknown"}

PropositionsPropositionsObject <proceeds> Free Object <proceeds> Free Fall,Fall,Object <has> Object <has> Displacement,Displacement,Object <has> Time, Object <has> Time, Displacement <is> 19.6, Displacement <is> 19.6, Time <is> UnknownTime <is> Unknown

An object proceeds Free Fall. An object proceeds Free Fall. After the phenomenon, the After the phenomenon, the displacement of the object is displacement of the object is 19.6. Ask for the procedure 19.6. Ask for the procedure time of the object.time of the object.Object Free Fall

Displacement19.6TimeUnknown

Proceed

Has

Is

Is

ObjecObjectt

FreFree e FallFall

DisplacDisplace-mente-ment

TimTimee

19.19.66

Un-Un-knowknownn

ProceeProceedd

11 11 00 00 00 00

HasHas 11 00 11 00 00 00

HasHas 11 00 00 11 00 00

IsIs 00 00 11 00 11 00

IsIs 00 00 00 11 00 11


Problem ConstructionProblem Construction

►Basic Problem ModelBasic Problem Model►Problem Construction StepsProblem Construction Steps►Essential Data StructuresEssential Data Structures


Problem Matrix for Item Problem Matrix for Item GenerationGeneration

► Extract manipulating concepts and Extract manipulating concepts and attributesattributes

► Set Given and Unknown AttributesSet Given and Unknown AttributesDisplacemeDisplacementnt

TimTimee

VelocitVelocityy

AcceleratioAccelerationn

unknownunknown 55 1010 22

Displacement = 0.5 * Acceleration * Displacement = 0.5 * Acceleration * Time ^ 2Time ^ 2

11 11 00 11

Velocity = Acceleration * TimeVelocity = Acceleration * Time 00 11 11 11

Corresponding ConceptsCorresponding Concepts ExampleExample


Sub-Problem Flag Sub-Problem Flag AttributeAttribute Free FallFree Fall Phenomena Phenomena

Given AttributesGiven Attributes Given value of Given value of TimeTime, , VelocityVelocity, and , and AccelerationAcceleration Attributes Attributes

Unknown AttributesUnknown Attributes Ask for Ask for DisplacementDisplacement Attribute Attribute


Problem TemplateProblem Template► Problem FormatProblem Format

Description SequenceDescription Sequence Possible SentencesPossible Sentences

ModelModel ParameterParameterAvailable Available PropositioPropositio

nnPhysics ExamplePhysics Example

No. of Sub-ProblemsNo. of Sub-Problems 11

No. of UnknownsNo. of Unknowns 11


Sub-Sub-Problem Problem Flag Flag AttributeAttribute

PW-1PW-1 Object proceeds Free FallObject proceeds Free Fall

Given Given AttributesAttributes

EQL-1EQL-1

EQL-2EQL-2The Velocity of Object is 3The Velocity of Object is 3

Unknown Unknown AttributesAttributes PWQ-1PWQ-1 Ask for the Acceleration of the Ask for the Acceleration of the

ObjectObject


Proposition TableProposition Table

►Possible Sentences in problemsPossible Sentences in problems Corresponding syntaxCorresponding syntax

Proposition IDProposition ID Syntax PatternSyntax Pattern ExampleExample

PropositioProposition n Transform Transform UnitUnit

Relation Type Relation Type with identify with identify nono

Syntactic ruleSyntactic rule

Example Example in Physicsin Physics

PW-1PW-1[Object] [Object] <<ProceedProceed> > [Phenomena][Phenomena]

Object Object proceedsproceeds Free Free FallFall

EQL-1EQL-1[Quantity] <[Quantity] <ofof> > [Object] <[Object] <isis> > [Value][Value]

The Velocity The Velocity ofof Object Object isis 33


Item Generating SystemItem Generating System

UnknownDesigner

ProblemTemplate

ItemProblem

Constructor

DeclarativeKnowledge

ProblemMatrix

Knowledge Map

Item GeneratingSystem

PropositionTable

ConceptSelector


Problem ConstructorProblem Constructor► Finding suitable Problem TemplateFinding suitable Problem Template► Finding related propositionFinding related proposition

ModelModel ParameterParameterAvailable Available PropositioPropositio

nnSyntax PatternSyntax Pattern

# Sub-# Sub-ProblemsProblems 11

# Unknowns# Unknowns 11

Basic Problem Basic Problem ModelModel

Sub-Sub-Problem Problem Flag Flag AttributeAttribute

PW1PW1[Object] [Object] <proceed> <proceed> [Phenomena][Phenomena]

Given Given AttributesAttributes

EQL1EQL1 [Physics [Physics Quantity] <Is> Quantity] <Is> [Value][Value]

Unknown Unknown AttributesAttributes PWQ1PWQ1

<Ask for> <Ask for> [Physics [Physics Quantity] <of> Quantity] <of> [Object][Object]


Item Generating SystemItem Generating System


Conception SelectionConception Selection


Problem Matrix ConstructionProblem Matrix Construction


Physics Law SelectionPhysics Law Selection


Physics Quantity Setting / Physics Quantity Setting / Item ConstructionItem Construction


Knowledge CategoriesKnowledge Categories

► Grammatical KnowledgeGrammatical Knowledge usually has syntax, which has rules and formats in usually has syntax, which has rules and formats in

it. it. Ex. Courses of Chinese, English, Music, and ArtEx. Courses of Chinese, English, Music, and Art

► Positioning KnowledgePositioning Knowledge lays stress on the location and direction among lays stress on the location and direction among

objects. objects. Ex. History and geographyEx. History and geography

► Inter-Correlated KnowledgeInter-Correlated Knowledge attaches more importance to the manipulation of attaches more importance to the manipulation of

inter-correlation among knowledge. inter-correlation among knowledge. Ex. Physics, Chemistry, and MathematicsEx. Physics, Chemistry, and Mathematics


Complex Problem ModelComplex Problem Model

Corresponding ConceptsCorresponding Concepts ExampleExample

Basic Basic Problem Problem Model 1Model 1

Sub-Problem Flag AttributeSub-Problem Flag Attribute Free FallFree Fall Phenomena Phenomena

Given AttributesGiven Attributes Given value of Given value of DistanceDistance,, Time Time and and VelocityVelocity AttributesAttributes

Unknown AttributesUnknown Attributes

Sub-Sub-Problems Problems ConnectioConnectionn

Related Basic Problem 1 Related Basic Problem 1 AttributesAttributes

Final PositionFinal Position, , Final VelocityFinal Velocity, , Final AccelerationFinal Acceleration, , Final TimeFinal Time

Related Basic Problem 2 Related Basic Problem 2 AttributesAttributes

Initial PositionInitial Position, , Initial VelocityInitial Velocity, , Initial Initial AccelerationAcceleration, , Initial TimeInitial Time

Relation between AttributesRelation between Attributes EqualEqual

Basic Basic Problem Problem Model 2Model 2

Sub-Problem Flag AttributeSub-Problem Flag Attribute Motion of Constant AccelerationMotion of Constant Acceleration Phenomena Phenomena

Given AttributesGiven Attributes Given value of Given value of DistanceDistance,, Acceleration Acceleration and and VelocityVelocity Attributes Attributes

Unknown AttributesUnknown Attributes Ask for Ask for TimeTime Attribute Attribute

Date post:	20-Jan-2016
Category:	Documents
Upload:	ernest-jefferson
View:	214 times
Download:	0 times

Difficulty Analysis for Learners in Problem Solving Process based on the Knowledge Map Speaker: Rita...

Documents