Megumi KURAYAMA(Hiroshima Univ.) Masayuki MURAKAMI(Kyoto Univ. of Foreign Studies)

1. Analysis of Lesson using Interactive Environment for Learning by Problem-Posing in Elementary School Arithmetic MegumiKURAYAMA(Hiroshima Univ.) Masayuki MURAKAMI(Kyoto Univ. of Foreign Studies) Tsukasa HIRASHIMA(Hiroshima Univ.)

2. Introduction • Problem-Posing • The learner poses a problem based on some information given to him. • The knowledge about problems stays the learner • “When (condition) are given and we want to get (goal), we can solve the problem by following (solution plan).” Pose a problem that can be solved by “5+4”. E-Learn2012@Montreal, CANADA

3. Introduction • An example arithmetic class by problem posing • The teacher shows the expression, and the learner poses a problem. They discuss the problem. Question There are eight peaces. There are six apples. How many peaches and apples in total are there? There are eight oranges. Six oranges were gotten. How many oranges are there now? Pose a problem that can be solved by “8+6”. E-Learn2012@Montreal, CANADA

4. Introduction • The point at issue of the class by problem-posing • The child poses one or two problems in class. • The child evaluates the problems with others. • Teach problem-posing using ICT(Information and Communication Technology) • The problems which a child poses in class increases. • ICT judges the problem that a child posed E-Learn2012@Montreal, CANADA

5. Interactive Environment for Learning by Problem-Posing ～MonsakunⅡ～ A condition of the problem Cards to pose a problem The Button to check the problem E-Learn2012@Montreal, CANADA

6. Introduction • Arithmetic class using “MonsakunII” • The main of the class is to pose problems using MonsakunII by the children. • The teacher taught places where the children can not pose a problem. • In case of a class that a teacher gives using ICT, a new class design is important. • It doesn’t share a traditional class design. E-Learn2012@Montreal, CANADA

7. Introduction • A teacher planed a arithmetic class using MonsakunII. • The class has original point of • Posing problems • Choosing cards • Checking problems E-Learn2012@Montreal, CANADA

8. Purpose of our study We analyzed the arithmetic class using the interactive environment for learning by problem-posing. • Different leading ways in problem-posing • Choosing cards or not. • Discussion a result of the problems posed by children • Checking problems E-Learn2012@Montreal, CANADA

9. Table of this Presentation • Interactive Environment for Learning by Problem-Posing: MONSAKUN II • The Lessons using MONSAKUN II • Analysis of Lessons using MONSAKUN II • Lessons and Activity of children using MONSAKUN II • Learning Effects E-Learn2012@Montreal, CANADA

10. Interactive Environment for Learning by Problem-Posing: MONSAKUN II E-Learn2012@Montreal, CANADA

11. Monsakun II A condition of the problem Cards to pose a problem The Button to check the problem E-Learn2012@Montreal, CANADA

12. Forward Thinking Problems and Reverse Thinking Problems • Forward Thinking Problems • The operational structure of the calculation is same with the operational structure of the story. • There are three apples. • There are four oranges. • There are some apples and oranges in total. • How many apples and oranges in total are there ? • Story operation structure: 3+4=? • Calculation operation structure: 3+4 E-Learn2012@Montreal, CANADA

13. Forward Thinking Problems and Reverse Thinking Problems • Reverse Thinking Problems • The operational structure of the calculation is not same with the operational structure of the story. • There are some apples. • There are four oranges. • There are seven apples and oranges in total. • How many apples are there at first? • Story operation structure: 3+4=? • Calculation operation structure: 3+4 E-Learn2012@Montreal, CANADA

14. Lessons using MONSAKUN II E-Learn2012@Montreal, CANADA

15. Practice Lessons • Situation • Six Lessons by problem-posing ( 45minutes per a lesson) • 39 children in a class of second grade at a elementary school • One personal computer to a child • The pre-test before the lesson practices, the post-test after. E-Learn2012@Montreal, CANADA

16. Practice Lessons • Date Correction and Analysis • Record of the lessons • Observation of the lessons • Wrote the state of a white board in these lessons. E-Learn2012@Montreal, CANADA

17. Practice Lessons The children used MONSAKUN II The general lesson E-Learn2012@Montreal, CANADA

18. A Lesson plan using MonsakunII • A process of problem-posing in a general lesson(a result of the observation) • The teacher shows a expression and a story structure of the problem that children should pose. • Children repeat every card, which is necessary to pose a problem. • Children find unnecessary cards to pose a problem in these cards. • Children show the reason that this card is unnecessary. • Children choose and set three cards from the remnants of these cards. • The teacher and children judge the posed problem. E-Learn2012@Montreal, CANADA

19. A Lesson plan using MonsakunII • The teacher shows a expression and a story structure of the problem that children should pose. • Children repeat every card, which is necessary to pose a problem. E-Learn2012@Montreal, CANADA

20. A Lesson plan using MonsakunII E-Learn2012@Montreal, CANADA

21. A Lesson plan using MonsakunII • Children find unnecessary cards to pose a problem in these cards. • Children show the reason that this card is unnecessary. E-Learn2012@Montreal, CANADA

22. A Lesson plan using MonsakunII E-Learn2012@Montreal, CANADA

23. A Lesson plan using MonsakunII • Children choose and set three cards from the remnants of these cards. • The teacher and children judge the posed problem. E-Learn2012@Montreal, CANADA

24. A Lesson plan using MonsakunII E-Learn2012@Montreal, CANADA

25. Lessons and Activity of children using MONSAKUN II Analysis of Lessons using MONSAKUN II E-Learn2012@Montreal, CANADA

26. Lessons and Activity of children using MONSAKUN II • Different leading ways in problem-posing • In third lesson the teacher did not teach step 4 of the process of problem-posing in a general lesson. The teacher did not choose unnecessary cards by problem-posing in MONSAKUN II E-Learn2012@Montreal, CANADA

27. Lessons and Activity of children using MONSAKUN II • After a general lesson, • In third lesson there is not a change of correct problem rate. • In forth lesson there is a change of correct problem rate. • In forth lesson correct problem rate of second half went up. A general lesson A general lesson Forth lesson Third lesson the number of posed problems and correct problem rate in reverse thinking problems E-Learn2012@Montreal, CANADA

28. Lessons and Activity of children using MONSAKUN II • Differences between third lesson and forth lesson • A difference in a process of problem-posing • Discussing a result of a problem posed by children E-Learn2012@Montreal, CANADA

29. Analysis of class contents ~A difference in a process of problem-posing~ • In third class, the children didn’t select the necessary cards to pose a problem. → Posing a problem was difficult. • In forth class, they select the necessary cards to pose a problem. → Posing a problem was easy. E-Learn2012@Montreal, CANADA

30. Analysis of class contents~Discussing a result of a problem posed by children~ • In third class, the child couldn’t pose a correct problem. • There are many number of posed problems, but the correct problem rate is low. • In forth class, the child could pose a correct problem. • There are few number of posed problems, but the correct problem rate is high. E-Learn2012@Montreal, CANADA

31. Learning Effects Analysis of Lessons using MONSAKUN II E-Learn2012@Montreal, CANADA

32. Learning Effects After the children pose a problem with MONSAKUN II and these classes, the children can pose problems with the smooth. E-Learn2012@Montreal, CANADA

33. Learning Effects Children of the low score group are especially able to pose problems. E-Learn2012@Montreal, CANADA

34. Conclusions and Future works • Conclusions • Interactive Environment for Learning by Problem-posing: MONSAKUNII • The lessons using MONSAKUNII • Analysis of lessons using MOSNAKUNII • Future works • Analysis of the behavior that children pose problems in MonsakunII. • Making a plan of class using MonsakunII. E-Learn2012@Montreal, CANADA