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

2. ICCE2008 Invited Talk 2 Concept and Method  Concept: Error -Visualization s 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

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

4. ICCE2008 Invited Talk 4 Contents s Learning from Errors s Theoretical Framework of EBS Using mechanical problems and errors in equations. s Applications of EBS Pencil Drawing English composition s Practical Use of EBS in Junior High School Primitive mechanical concept

5. ICCE2008 Invited Talk 5 Learning from Errors s 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 s 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. s 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 6 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. ICCE2008 Invited Talk 7 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

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

9. ICCE2008 Invited Talk 9 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

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

11. ICCE2008 Invited Talk 11 An Example of EBS Ø 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. ICCE2008 Invited Talk 12 An Example of EBS Ø 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. ICCE2008 Invited Talk 13 An Example of EBS Ø 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. ICCE2008 Invited Talk 14 An Example of EBS Ø 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 By changing Ø, unnatural behavior is generated

15. ICCE2008 Invited Talk 15 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-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 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 16 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)

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

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

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

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

21. ICCE2008 Invited Talk 21 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 22 Management of EBS Problem of dynamics Equation erroneous equation Behavior Correct behavior EBS Error-Mapping Correct equation Visibility Reliability Suggestiveness

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

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

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

26. ICCE2008 Invited Talk 26 Sketch Drawing Motif Sketch

27. ICCE2008 Invited Talk 27 Sketch Drawing

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

29. ICCE2008 Invited Talk 29 Composition by Animation

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

31. ICCE2008 Invited Talk 31 Practical Use of EBS -- EBS in classroom -- s 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. s Subjects: Junior high school students s 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. ICCE2008 Invited Talk 32 Additional Learning Time with EBS (a) (b) F (c) s Each student was required to draw “arrow of force” on the following situations. s Incomplete arrows generated unusual behaviors.

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

34. ICCE2008 Invited Talk 34 Additional Lecture with EBS

35. ICCE2008 Invited Talk 35 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

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

37. ICCE2008 Invited Talk 37 Pre-, Post-, and Delayed Post-test s Pre-test: (a), (b), (c): just before the lecture s Post-test: (a)-(l) : just after the lecture s Delayed post-test: (a)-(l): three months later s Scoring method: one correct arrow is plus one point. One wrong arrow is minus one point.

38. ICCE2008 Invited Talk 38 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 39 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 40 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 41 Special thanks for the EBS project members s Tomoya Horiguchi (Kobe University) s Noriyuki Matsuda (Wakayama University) s Hidenobu Kunichika (Kyushu Institute of Technology) s Isao Imai (Shinjyuku Junior High School) s Takahito Toumoto (Waseda University) s Akihiro Kashihara ( University of Electronic-Communication )