megumi kurayama(hiroshima univ.) masayuki murakami(kyoto univ. of foreign studies)

Analysis of Lesson using Interactive Environment for Learning by Problem-Posing

in Elementary School Arithmetic

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

Tsukasa HIRASHIMA(Hiroshima Univ.)

• 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).”

Introduction

2

Pose a problem that can be solved by “5+4”.

E-Learn2012@Montreal, CANADA

Introduction• An example arithmetic class by problem posing – The teacher shows the expression, and the learner

poses a problem. They discuss the problem.

3

Pose a problem that can be solved by “8+6”.

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?

E-Learn2012@Montreal, CANADA

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

4E-Learn2012@Montreal, CANADA

Interactive Environment for Learning by Problem-Posing ～ MonsakunⅡ ～

5

A condition of the problem

Cards to pose a problem

The Button to check the problem

E-Learn2012@Montreal, CANADA

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.

6E-Learn2012@Montreal, CANADA

Introduction• A teacher planed a arithmetic class

using MonsakunII. • The class has original point of –Posing problems–Choosing cards–Checking problems

7E-Learn2012@Montreal, CANADA

Purpose of our studyWe analyzed the arithmetic class using the interactive environment for learning by problem-posing.① Different leading ways in

problem-posing– Choosing cards or not.

② Discussion a result of the problems posed by children

– Checking problems8E-Learn2012@Montreal, CANADA

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

9E-Learn2012@Montreal, CANADA

INTERACTIVE ENVIRONMENT FOR LEARNING BY PROBLEM-POSING: MONSAKUN II

10E-Learn2012@Montreal, CANADA

Monsakun II

11

A condition of the problem

Cards to pose a problem

The Button to check the problem

E-Learn2012@Montreal, CANADA

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.

12

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

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.

13

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

LESSONS USING MONSAKUN II

14E-Learn2012@Montreal, CANADA

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.

15E-Learn2012@Montreal, CANADA

Practice Lessons• Date Correction and Analysis– Record of the lessons– Observation of the lessons–Wrote the state of a white board in these

lessons.

16E-Learn2012@Montreal, CANADA

Practice Lessons

17

The children used MONSAKUN II

The general lesson

E-Learn2012@Montreal, CANADA

A Lesson plan using MonsakunII• A process of problem-posing in a general lesson (a

result of the observation)① The teacher shows a expression and a story structure

of the problem that children should pose.② Children repeat every card, which is necessary to pose

a problem.③ Children find unnecessary cards to pose a problem in

these cards.④ Children show the reason that this card is unnecessary.⑤ Children choose and set three cards from the remnants

of these cards.⑥ The teacher and children judge the posed problem.

18E-Learn2012@Montreal, CANADA

A Lesson plan using MonsakunII

① The teacher shows a expression and a story structure of the problem that children should pose.

② Children repeat every card, which is necessary to pose a problem.

19E-Learn2012@Montreal, CANADA

A Lesson plan using MonsakunII

20E-Learn2012@Montreal, CANADA

A Lesson plan using MonsakunII

③ Children find unnecessary cards to pose a problem in these cards.

④ Children show the reason that this card is unnecessary.

21E-Learn2012@Montreal, CANADA

A Lesson plan using MonsakunII

22E-Learn2012@Montreal, CANADA

A Lesson plan using MonsakunII

⑤ Children choose and set three cards from the remnants of these cards.

⑥ The teacher and children judge the posed problem.

23E-Learn2012@Montreal, CANADA

A Lesson plan using MonsakunII

24E-Learn2012@Montreal, CANADA

ANALYSIS OF LESSONS USING MONSAKUN II

Lessons and Activity of children using MONSAKUN II

25E-Learn2012@Montreal, CANADA

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 IIE-Learn2012@Montreal, CANADA 26

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.

27

32 33 34 35 36 37 38 39 40 41 42 43 440

20

40

60

80

0%

20%

40%

60%

80%

100%number percentage

5 6 7 8 9 101112 3940414243444546470

20

40

60

80

0%

20%

40%

60%

80%

100%number percentage

A general lesson

A general lesson

the number of posed problems and correct problem rate in reverse thinking problems

Third lesson Forth lesson

E-Learn2012@Montreal, CANADA

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

28E-Learn2012@Montreal, CANADA

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.

29E-Learn2012@Montreal, CANADA

• 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.

Analysis of class contents~Discussing a result of a problem posed by children~

30E-Learn2012@Montreal, CANADA

ANALYSIS OF LESSONS USING MONSAKUN II

Learning Effects

31E-Learn2012@Montreal, CANADA

Learning Effectspre-test post-test

p-valueaverage standard

deviation average standard deviation

number of posed problems 3.525 0.835 4.000 0.000 0.0027number of correct problems 1.650 1.347 3.051 1.168 1.48×10-5

number of forward thinking problems 0.975 1.038 2.256 1.044 1.37×10-5

number of reverse thinking problems 0.675 0.805 0.794 0.922 0.5401

32

After the children pose a problem with MONSAKUN II and these classes, the children can pose problems with the smooth.

E-Learn2012@Montreal, CANADA

Learning Effects

33

Children of the low score group are especially able to pose problems.

E-Learn2012@Montreal, CANADA

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.

34E-Learn2012@Montreal, CANADA