icce2008 invited talk 1 error-visualization for metacognitive awareness tsukasa hirashima hiroshima...
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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
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
Moving up positive acceleration
EBS
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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
Moving down positive acceleration
EBS
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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
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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Management of EBS
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
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=[+]
Qualitative Difference-2
Qualitative Difference-1 Qualitative Difference-2
Ø: [↑]
ma = mg
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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=[+]
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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Management of EBS
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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Pre-, Post-, and Delayed Post-test
(f)
(g) (h) (i)
(j)
F
(k)
F
(l)
Transfer-task Post and delayed post
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Pre-, Post-, and Delayed Post-test
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)