ErrorVisualization for Metacognitive Awareness Tsukasa HIRASHIMA Hiroshima University

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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 students 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.

Metacogntive Awareness
Not only to be aware of the error but also to be
aware of how unusual the error is
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Demonstration of Error-Visualization
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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 teachers 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 students error
• Show what would happen if the answer were correct
  .
• Doesnt say it is wrong
• Let the student indicate his error by himself
• Ideal interaction
• System 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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EBS in Mechanical Problems
Problem of dynamics
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An Example of EBS
Typical Error m2 a T
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Error-Based Simulation

• 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.

EBS
Normal Simulation
Block-2
Error-Visualization with EBS
Block-3
Block-1
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Management of EBS
Equation
Behavior
Correct equation
Correct behavior
Suggestiveness
Visibility
Problem of dynamics
Error-Mapping
erroneous equation
Reliability
EBS
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An Example of EBS
Make motion equation of the block along the slope.
Equation-1 ma mg sinØ Equation-2 ma - mg
sinØ Equation-3 ma mg cosØ Equation-4 ma cosØ
mg
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An Example of EBS
Make motion equation of the block along the slope.
Equation-1 ma mg sinØ Equation-2 ma - mg
sinØ Equation-3 ma mg cosØ Equation-4 ma cosØ
mg
Moving up positive acceleration
EBS
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An Example of EBS
Make motion equation of the block along the slope.
Equation-1 ma mg sinØ Equation-2 ma - mg
sinØ Equation-3 ma mg cosØ Equation-4 ma cosØ
mg
Moving down positive acceleration
EBS
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An Example of EBS
Make motion equation of the block along the slope.
Equation-1 ma mg sinØ Equation-2 ma - mg
sinØ Equation-3 ma mg cosØ Equation-4 ma cosØ
mg
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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 change
• ex. the ratio of velocity change for time
  acceleration
• the ratio of velocity change for Ø
  Equation-3
• QD-1QD-2 gt QD-1 gt 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)

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Management of EBS
Equation
Behavior
Correct equation
Correct behavior
Suggestiveness
Visibility
Problem of dynamics
Error-Mapping
erroneous equation
Reliability
EBS
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Reliability
perturbation of Ø
Ø ?
V?
V?
ma mg sinØ
ma mg cosØ
Ø
Equation-3 ma mg cosØ
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Reliability
perturbation of Ø
Ø ?
V?
V?
Qualitative Difference-2
ma mg sinØ
ma mg cosØ
Qualitative Difference-1 Qualitative Difference-2
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Reliability
perturbation of Ø
Ø ?
V?
V?
Qualitative Difference-2
better in reliability
ma mg sinØ
ma mg cosØ
Qualitative Difference-1 Qualitative Difference-2
better in visibility
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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 gt Perturbation gt Boundary value
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Management of EBS
Equation
Behavior
Correct equation
Correct behavior
Suggestiveness
Visibility
Problem of dynamics
Error-Mapping
erroneous equation
Reliability
EBS
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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.

Error-Based Simulation
Error Mapping
Erroneous equation
Formulation
Problem
Difference in behavior
The way to correct
Suggestiveness
Normal Simulation
Correct equation
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Categorization and Preference
Evaluation of EBS
Reliability
Suggestiveness
Visibility
Direct
Indirect
Visualized Object
Satisfied Conditions
Modified Parameter
Modified Method
Real gt Metaphor
CEV-1 CEV-2 gt CEV-1 gt CEV-2
No modification gt Real gt Metaphor
No modification gt Perturbation gt Boundary value
Suggestive gt 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
Sketch
Motif
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Sketch Drawing
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EBS in Sketch Drawing
3D expression
Sketch
Proper sketch
Proper 3D expression
Visibility
Error-Mapping
Motif
Erroneous sketch
Erroneous 3D expression
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Composition by Animation
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Composition by Animation
Animation
Sentence
Proper sentence
Proper Animation
Visibility
Animation
Error-Mapping
Erroneous sentence
Erroneous animation
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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

• 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

• 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. -gt All
tests
More complex task -gt Post and delayed post
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Pre-, Post-, and Delayed Post-test
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".
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 class 22(in 28) students mentioned of
balance of force. No one indicated behavior
of objects. EBS class 40(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)