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Error-Visualization for Metacognitive Awareness Tsukasa HIRASHIMA Hiroshima University

Error-Visualization for Metacognitive Awareness Tsukasa HIRASHIMA Hiroshima University. Concept and Method. Concept: Error -Visualization Method: Error-Based Simulation Error-Based Simulation: a simulation is generated based on a student’s error .

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Error-Visualization for Metacognitive Awareness Tsukasa HIRASHIMA Hiroshima University

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  1. ICCE2008　Invited Talk Error-Visualization for Metacognitive AwarenessTsukasa HIRASHIMA Hiroshima University

  2. ICCE2008　Invited Talk 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. Metacogntive Awareness Not only to be aware of the error but also to be aware of how unusual the error is

  3. Block Normal Reaction Table Gravity ICCE2008　Invited Talk Demonstration of Error-Visualization

  4. ICCE2008　Invited Talk 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

  5. ICCE2008　Invited Talk 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

  6. ICCE2008　Invited Talk 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 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.

  7. Equation Behavior Correct equation Correct behavior student's prediction difference in equation difference in behavior Error-Mapping erroneous equation EBS ICCE2008　Invited Talk EBS in Mechanical Problems Problem of dynamics

  8. ICCE2008　Invited Talk An Example of EBS Typical Error : m2 * a = T

  9. ICCE2008　Invited Talk 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

  10. ICCE2008　Invited Talk Management of EBS Equation Behavior Correct equation Correct behavior Suggestiveness Visibility Problem of dynamics Error-Mapping erroneous equation Reliability EBS

  11. Ø ICCE2008　Invited Talk 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

  12. Ø ICCE2008　Invited Talk 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

  13. Ø ICCE2008　Invited Talk 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

  14. Ø By changing Ø, unnatural behavior is generated ICCE2008　Invited Talk 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

  15. ICCE2008　Invited Talk 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 ofvelocitychange for a parameter's change ex. 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)

  16. ICCE2008　Invited Talk 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 ofvelocitychange with parameters (without time)

  17. ICCE2008　Invited Talk Management of EBS Equation Behavior Correct equation Correct behavior Suggestiveness Visibility Problem of dynamics Error-Mapping erroneous equation Reliability EBS

  18. V=[0] V=[+] A= [0] A= [+] ma = mg Ø = 0 boundary value ICCE2008　Invited Talk Reliability perturbation of Ø Ø: [↑] V=[↑] Ｖ=[↓] ma = mg cosØ ma = mg sinØ Ø Equation-3: ma = mg cosØ

  19. V=[0] V=[+] A= [0] A= [+] ma = mg Ø = 0 boundary value ICCE2008　Invited Talk Reliability perturbation of Ø Ø: [↑] V=[↑] Ｖ=[↓] Qualitative Difference-2 ma = mg cosØ ma = mg sinØ Qualitative Difference-1 Qualitative Difference-2

  20. V=[0] V=[+] A= [0] A= [+] ma = mg Ø = 0 boundary value ICCE2008　Invited Talk Reliability perturbation of Ø Ø: [↑] V=[↑] Ｖ=[↓] Qualitative Difference-2 better in reliability ma = mg cosØ ma = mg sinØ Qualitative Difference-1 Qualitative Difference-2 better in visibility

  21. ICCE2008　Invited Talk 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]

  22. ICCE2008　Invited Talk Management of EBS Equation Behavior Correct equation Correct behavior Suggestiveness Visibility Problem of dynamics Error-Mapping erroneous equation Reliability EBS

  23. ICCE2008　Invited Talk 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 Mapping Error-Based Simulation Erroneous equation Formulation Problem Difference in behavior The way to correct Suggestiveness Normal Simulation Correct equation

  24. ICCE2008　Invited Talk Categorization and Preference Evaluation of EBS Reliability Suggestiveness Visibility Direct Indirect Visualized Object Satisfied Conditions Modified Parameter Modified Method Real > Metaphor CEV-1 & CEV-2 > CEV-1 > CEV-2 No modification > Real > Metaphor No modification > Perturbation > Boundary value Suggestive > Not suggestive

  25. ICCE2008　Invited Talk Applications • Equations of motion in physics • Basic concept of “normal reaction” • Sketch drawing • Composition by animation • Multi-Digit subtraction

  26. ICCE2008　Invited Talk Sketch Drawing Sketch Motif

  27. ICCE2008　Invited Talk Sketch Drawing

  28. ICCE2008　Invited Talk EBS in Sketch Drawing 3D expression Sketch Proper sketch Proper 3D expression Visibility Error-Mapping Motif Erroneous sketch Erroneous 3D expression

  29. ICCE2008　Invited Talk Composition by Animation

  30. ICCE2008　Invited Talk Composition by Animation Animation Sentence Proper sentence Proper Animation Visibility Animation Error-Mapping Erroneous sentence Erroneous animation

  31. ICCE2008　Invited Talk 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)

  32. (a) (b) (c) F ICCE2008　Invited Talk Additional Learning Time with EBS • Each student was required to draw “arrow of force” on the following situations. • Incomplete arrows generated unusual behaviors.

  33. (a) (b) (c) F ICCE2008　Invited Talk Additional Learning Time with EBS • Each student was required to draw “arrow of force” on the following situations. • Incomplete arrows generated unusual behaviors.

  34. ICCE2008　Invited Talk Additional Lecture with EBS

  35. F (e) (d) (a) (b) (c) F ICCE2008　Invited Talk Pre-, Post-, and Delayed Post-test Learning-task: Problems used in learning. -> All tests More complex task -> Post and delayed post

  36. F (f) (g) (h) (i) F (j) (k) (l) ICCE2008　Invited Talk Pre-, Post-, and Delayed Post-test Transfer-task  Post and delayed post

  37. ICCE2008　Invited Talk 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.

  38. ICCE2008　Invited Talk 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

  39. ICCE2008　Invited Talk 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.

  40. ICCE2008　Invited Talk 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

  41. ICCE2008　Invited Talk 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)

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