Teachers' Guidebook for Primary Mathematics

School in Japan

Organization of teaching staff of school

Headmaster
Deputy head teacher
Managing teacher(1-3 by the scale of school)
Teacher(number of all classrooms)
(Clerical worker(1))
Activity as school

School year

Basically 3 term system

The 1st term: April - July
Summer holidays(25days)
The 2nd term: August - December
Winter holidays(25days)
The 3rd term: January - March
Spring holidays(about10days)
Aim of education in school (usually 2 or 3 years)

For example,

Pursuit of classroom activity forstering childrens' independence
Study of classroom activity forstering the ability of problem solving
Public lesson for elementary school teachers

After the study 2 or 3 years, sometime School has an open lesson for elementary school teachers.

Typical math. lesson in Japan

Basis: 4 steps of problem solving (G. Polya)

1. Understanding of problem.

Teacher gives students a problem(usual method)
Making problem by students

Giving students an incentive to lesson
Promoting the ability of problem solving

Orientation by teacher together students

Making the process of lessons of unit

Students know the contents(what, how) of the unit
Promoting the motivation of students to lesson

2. Planing of the solution.

Knowing by intuition
Estimating of solution

(ex. 79+38 : about 120)

Guessing of method of solution

How to solve the problem

3. Practicing the solution
(Under 2. students try to solve the problem)

Trial and error
Revising the Estimating of solution
Logical thinking

Mathematical thinking connects instuitive thinking with logic thinking.

4. Looking back on problem solving

Fullfilling of indivisual thinking
Cooperativeness among classmate
Pursuit of mathematical value
Awareness of problem to next lesson

Difference between the texbooks in Egypt and Japan.

For example (1st grade, subtraction)
Japan

Meaning

Remainder

There were five bananas and Mohamed ate three bananas, then how many bananas were remained ?

difference

There are five blue cars and three red ones. Then what is the difference between blue cars and red ones ?

( Why same subtraction 5-3 ? )

Calculation and practices
Making stories applied subtraction

Egypt

Meaning(Remainder)
Completion (giving the pictures)

8 - 3, 7 - ..., ... - 2, ... - ... etc.

Calculation and practices
Subtraction by Column form (In Japan, 2nd grade)

Content of lesson

(3rd grade: Introduction of fraction)

I. Recalling what was learned in previous lessons

Letting pupils recall studying about one third of 1 meter.

(Starting line of this class)

II. Introducing of this lesson

T : Today, let us study of finding the quauter from the daily life. (So, teacher gives students some remarks)

1. To write only one picture per one sheet

2. If you find another application, then to bring another sheet from front desk.

3. Today, to draw a picture by freehand.

III. Study of a quarter

P's : (Students consider by themselves)

T : Please, present the case you made. Then let us discuss it.
P's : (Students give the following.)

Origami (Square sheet), Tohu(Japanese food: rectangular parallelepiped.)

Apple

P's : When we devide into 4 parts, then the one part is a quarter.
P's : (question)Have all of 4 parts same sizes ?
P's : Yes, all have same sizes.
P's : (question)How many apples are there ?
P's : One apple.

Cake (column)

Clock(fifteen minutes)

Circle(mistaken idea)

Two different tapes(rectangular)

Other important questions by students

Does joining four quarter make 1?

Is four fourth equal to 1 ?

Is joining five quarter called five fourth ?

Another important opinions by students.

Is 200m of 800m a quarter ?

Is 2 chocolates in 8 chocolates a quarter ?

(ratio, This lesson is at 5 grade)

P's	:	(Students consider by themselves)
T	:	Please, present the case you made. Then let us discuss it.
P's	:	(Students give the following.) Origami (Square sheet), Tohu(Japanese food: rectangular parallelepiped.) Apple
P's	:	When we devide into 4 parts, then the one part is a quarter.
P's	:	(question)Have all of 4 parts same sizes ?
P's	:	Yes, all have same sizes.
P's	:	(question)How many apples are there ?
P's	:	One apple. Cake (column) Clock(fifteen minutes) Circle(mistaken idea) Two different tapes(rectangular) Other important questions by students Does joining four quarter make 1? Is four fourth equal to 1 ? Is joining five quarter called five fourth ? Another important opinions by students. Is 200m of 800m a quarter ? Is 2 chocolates in 8 chocolates a quarter ? (ratio, This lesson is at 5 grade)