icce2008 invited talk 1 error-visualization for metacognitive awareness tsukasa hirashima hiroshima...

ICCE2008 　 Invited Talk

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Error-Visualization for Metacognitive Awareness

Tsukasa　HIRASHIMA　Hiroshima　University


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Concept　and　Method

Concept: Error -Visualization Method: Error-Based Simulation

• Error-Based Simulation: a simulation is generated based on a student’s error.

• The generated simulation usually shows unusual behavior reflecting the error.

• By showing such unusual behavior, let the student to be aware of the error by himself and motivate to correct it.

Not only to be aware of the error but also to be aware of how unusual the error is

Metacogntive Awareness


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Demonstration　of　Error-Visualization

Table

BlockNormal Reaction

Gravity


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Contents Learning from Errors

Theoretical Framework of EBS• Using mechanical problems and errors in equations.

Applications of EBS• Pencil Drawing• English composition

Practical Use of EBS in Junior High School• Primitive mechanical concept


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Learning　from　Errors Errors are inevitable event in learning

• Someone who does not make any mistakes, does not need to learn neither.• If someone makes some mistakes, it is necessary to learn to overcome

the errors. Errors as Learning Opportunity

An error does not always motivate a student to learn.• The student may not notice the error• The student may accept teacher’s indication as it is.

• Be aware of the error but don't know how unusual the error is.

It is necessary for students not only to be aware of the error, but also to be aware of how unusual the error is.

Metacogntive Awareness


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Ideal　Story　of　EBS

•Indirect feedback for student’s error•Show what would happen if the answer were correct .•Doesn’t say “it is wrong”•Let the student indicate his error by himself

Ideal interactionSystem: Based on your answer, this event will be happen.

Is it OK ?Student: No. It's wrong. So, my answer may be wrong.

I have to reconsider the answer.


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Behavior

difference in behavior

Equation

Correct equation

difference in equation

EBS　in　Mechanical　Problems

Problem of dynamics

erroneous equation

Correct behavior

student's prediction

EBS

Error-Mapping


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An Example of EBS

m1 x a = m1g - T ...(1) m2 x (a-b) = T ...(2) m1 x b = N ...(3) m3 x b = T - N ...(4)

Formulate equations of motion for each block.

Problem-1

m2

m1

m3 Block-1

Block-2

Block-3ab

a-b

N

T

Normal equations

Typical Error : m2 * a = T


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Error-Based Simulation

EBS

Normal Simulation

Block-1

Block-2

Block-3

• In EBS, the acceleration of Block-2 is calculated by the erroneous equation.• So, Block-2 in EBS moves faster than in the normal simulation.• Other blocks move normally.• As the result, the distance between Block-2 and Block-1 is reduced.

Error-Visualization with EBS

Error-Visualization with EBS


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Management　of　EBS

Problem of dynamics

Equation

erroneous equation

Behavior

Correct behavior

EBS

Error-Mapping

Correct equation

Visibility

Reliability

Suggestiveness


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An Example of EBS

Ø

Make motion equation of the block along the slope.

Equation-1: ma = mg sinØEquation-2: ma = - mg sinØEquation-3: ma = mg cosØEquation-4: ma cosØ = mg


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An Example of EBS

Ø



Moving up positive acceleration

EBS


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An Example of EBS

Ø



Moving down positive acceleration

EBS


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An Example of EBS

Ø



By changing Ø,unnatural behavior is generated


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Conditions of Visibility

(QD-1) Qualitative Difference-1:• difference in qualitative value of velocity: { plus, minus, zero }ex. Normal simulation: moving down [+] EBS for Equation-2: moving up [-]

(QD-2) Qualitative Difference-2 :• difference in qualitative value in the ratio of velocity change

for a parameter's changeex. the ratio of velocity change for time: acceleration

the ratio of velocity change for Ø : Equation-3

QD-1&QD-2 > QD-1 > QD-2 (Preference in visibility)

(QD-1) Qualitative Difference-1:• difference in qualitative value of velocity: { plus, minus, zero }ex. Normal simulation: moving down [+] EBS for Equation-2: moving up [-]

(QD-2) Qualitative Difference-2 :• difference in qualitative value in the ratio of velocity change

for a parameter's changeex. the ratio of velocity change for time: acceleration

the ratio of velocity change for Ø : Equation-3

QD-1&QD-2 > QD-1 > QD-2 (Preference in visibility)


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Diagnosis of Visibility

Diagnosis by using Qualitative Reasoning Techniques

(A) QSIM (by Kuipers)• Qualitative difference in velocity and acceleration

(B) DQ-analysis (by Weld)• Qualitative difference in the ratio of velocity change

with parameters (without time)

Diagnosis by using Qualitative Reasoning Techniques

(A) QSIM (by Kuipers)• Qualitative difference in velocity and acceleration

(B) DQ-analysis (by Weld)• Qualitative difference in the ratio of velocity change

with parameters (without time)


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Problem of dynamics

Equation

erroneous equation

Behavior

Correct behavior

EBS

Error-Mapping

Correct equation

Visibility

Reliability

Suggestiveness


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Reliability

ma = mg sinØ ma = mg cosØ

V=[↑]V=[↑] Ｖ=[↓]Ｖ=[↓]

perturbation of Øperturbation of Ø

Ø = 0boundary value

Ø = 0boundary value

A=　[0]A=　[0]

V=[0]V=[0]

A=　[+]A=　[+]

V=[+]V=[+]

Ø: [↑]

Ø

Equation-3: ma = mg cosØ

ma = mg


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Reliability


V=[↑]V=[↑] Ｖ=[↓]Ｖ=[↓]

perturbation　of　Øperturbation　of　Ø

Ø　=　0boundary　value


A=　[0]A=　[0]

V=[0]V=[0]

A=　[+]A=　[+]

V=[+]V=[+]

Qualitative Difference-2

Qualitative Difference-1 Qualitative Difference-2

Ø: [↑]

ma = mg


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Reliability


V=[↑]V=[↑] Ｖ=[↓]Ｖ=[↓]

perturbation　of　Øperturbation　of　Ø



A=　[0]A=　[0]

V=[0]V=[0]

A=　[+]A=　[+]

V=[+]V=[+]

Qualitative Difference-2

Qualitative Difference-1 Qualitative Difference-2

Ø: [↑]

better in visibility

better in reliability

ma = mg


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Preferences in Reliability

• Raw EBS• No modification of parameters

• Perturbation• Change a value of parameter a little in the range

where the equation is valid.

• Boundary value• Specify the boundary value for each parameter in the

range where the equation is valid.

[Raw] > [Perturbation] > [Boundary value]


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Problem of dynamics

Equation

erroneous equation

Behavior

Correct behavior

EBS

Error-Mapping

Correct equation

Visibility

Reliability

Suggestiveness


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Suggestiveness

*Suggestiveness that means whether the visualized difference suggests the way to correct the error or not .

*Opposite acceleration against normal simulation usually suggests a missing correct force or the existence of a wrong one.

Erroneousequation

Correctequation

Problem

Error-BasedSimulation

NormalSimulation

Error Mapping

Difference in behavior

The way to correct

Formulation

Suggestiveness


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Categorization and Preference

Evaluation of EBS

Visibility Reliability Suggestiveness

Visualized Object

SatisfiedConditions

Real> Metaphor

CEV-1 & CEV-2 > CEV-1 > CEV-2

Modified Parameter

Modified Method

No modification> Real > Metaphor

No modification> Perturbation > Boundary value

Direct Indirect

Suggestive> Not suggestive


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Applications

Equations of motion in physics Basic concept of “normal reaction” Sketch drawing Composition by animation Multi-Digit subtraction


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Sketch　Drawing

Motif Sketch


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Sketch　Drawing


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EBS　in　Sketch　Drawing

Motif

Sketch

Erroneous sketch

3D expression

Proper 3D expression

Erroneous 3D expression

Error-Mapping

Proper sketch

Visibility


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Composition　by　Animation


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Composition　by　Animation

Animation

Sentence

Erroneous sentence

Animation

Proper Animation

Erroneous animation

Error-Mapping

Proper sentence

Visibility


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Practical　Use　of　EBS--　EBS　in　classroom　--

Basic concept of “normal reaction”• It is important to understand motion and balance in classical mechanics.

• It is difficult to understand and students often make errors.

Subjects: Junior high school students

Three classes: all classes had a lecture as usual in one class time (45 minutes) and two classes of the three had additional lecture with EBS in one class time.

Usual class: one class(30 students)EBS class: two classes(54 students)


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Additional　Learning　Time　with　EBS

(a) (b)

F

(c)

Each student was required to draw “arrow of force” on the following situations.

Incomplete arrows generated unusual behaviors.


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Additional　Learning　Time　with　EBS

(a) (b)

F

(c)

Each student was required to draw “arrow of force” on the following situations.

Incomplete arrows generated unusual behaviors.


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Additional　Lecture　with　EBS


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Pre-,　Post-,　and　Delayed　Post-test

Learning-task: Problems used in learning. -> All tests

(a) (b)

F

(c)

(d)

F

(e)

More complex task -> Post and delayed post


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(f)

(g) (h) (i)

(j)

F

(k)

F

(l)

Transfer-task Post and delayed post


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Pre-test: (a), (b), (c) : just before the lecture

Post-test: (a)-(l) : just after the lecture Delayed post-test: (a)-(l) : three months later

Scoring method: one correct arrow is plus one point. One wrong arrow is minus one point.


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Statistical　Analysis

Students of EBS classes tended to obtain higher scores in "delayed test"

and "transfer test".

Students in EBS class might obtained abstract and stable criteria to think about "forces".Students in EBS class might obtained abstract and stable criteria to think about "forces".

not only memorize the answer by the impression of EBS


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Interview　for　Students　after　the　Delayed　Post-test

How did you solve this task ?

Usual class22(in 28) students mentioned of “balance of force”.No one indicated “behavior of objects”.

EBS class40(in 48) students mentioned “behavior of objects”."in order to keep it stable, this force is necessary"Students solved the tasks by connecting the forces

and motion.


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Conclusion　Remarks

Error-Visualization by Error-Based Simulation to let students be aware of their errors by themselves.• Framework to manage EBS• Application of EBS• Practical use EBS

Future Works• Extension the applicable domains• Analysis of effect of EBS


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Special　thanks　for　the　EBS　project　members

Tomoya Horiguchi (Kobe University) Noriyuki Matsuda (Wakayama University) Hidenobu Kunichika (Kyushu Institute of Technology) Isao Imai (Shinjyuku Junior High School) Takahito Toumoto (Waseda University) Akihiro Kashihara (University of Electronic-Communication)

icce2008 invited talk 1 error-visualization for metacognitive awareness tsukasa hirashima hiroshima...

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