Since the Meiji period mathematics teachers have been instructing the contents using a blackboard and a piece of chalk. And instructional methods have been identical to the traditional ones. Now Japan’s education is changing greatly. People want changes in every aspect. Soon the new revised version of the Course of Study (the 6th version) will be issued.
　
1. The History of Japan's Mathematics Education
　
        With regard to Japan's mathematics education, there are three major transitions.
　
(1) The first transition
　
        The first transition is the adoption of Western mathematics (Yosan, 洋算 in Japanese) which took place during the Meiji period from 1868 to 1911. In this period, Japan adopted mathematics and spread it nation-wide. In this period, there were many Wasanka (i.e., Wasan mathematicians) in Japan. Wasan (和算) is mathematics indigenous to Japan, which had existed before the Meiji Restoration and whose origin was the Chinese classical mathematics. And there were very many private-temple-schools (Terakoya, 寺小屋 in Japanese). Therefore imported Western mathematics spread quickly. Since 1892, mathematics has been called "Sugaku"( ) in Japan.
　
(2) The second transition
　
        The second transition is "Mathematics Education Reform Movement" which took place in the middle of the Taisho period from 1912 to 1925. But scholars such as FUJISAWA and KIKUCHI emphasized the special branches of analysis and logical treatment of geometry. It was in 1901 when this movement began in the world. But in Japan this movement took place 17 years later, in 1918.
　
(3) The third transition
　
        The third transition is "Modernization of Mathematics Education" which took place during the middle of the Showa period from 1926 to 1988. In 1957, the so-called "Sputnik shock" happened, industrial structures were developed, and the role of modern mathematics became more important. "Modernization of Mathematics Education" rapidly spread worldwide since about 1960. But in Japan’s mathematics education, it was in 1968 when the curriculum, that is, the "Course of Study for Elementary Schools," was established.
　
        H. TOYAMA designed the so-called "The Water Supply Method" (水道方式). He laid down the theory of quantity and established the Method based on this theory. This Method met remarkable success in primary schools and is now adopted more or less by all the authorized textbooks for primary schools.
　
2. Children's School Life
　
(1) Curriculum standards
　
        Curriculum standards for elementary schools are prescribed in the "Course of Study" issued by the Minister of Education, Science and Culture. The Course of Study provides the basics for curricula, that is, aims of each subject and the teaching content at each grade from the first to the sixth. The revised Course of Study (now in use) was issued in 1989 and went into effect in elementary schools in April, 1992. The revised Course of Study is the fifth revised edition after the Second World War. That is, these versions were published in 1947, 1958, 1968, 1977 and 1989.
　
        The Course of Study now in use was revised on the basis of the following four guidelines:

1. Young people should possess richness of heart and strength of mind.
2. Children's capacity to respond to changes in society, creativity, and the willingness to learn.
3. Learning essential knowledge and skills, and developing full individuality. For them, a consistent curriculum from kindergartens to upper secondary schools.
4. Respect for Japanese culture and traditions, and understanding cultures and histories of other countries. Quality living in the international community.

Subjects, Moral Education, and Special Activities                       5:47
Non-prescribed activities (class meeting, cleaning rooms, etc.)     0:19
Learning outside school (crammer, Juku 塾 in Japanese)             1:13

Easy problem: the proportion of correct answers is more than (m + s )%,
Difficult problem: the proportion of correct answers is less than (m - s )%,
where m = average of the proportions of correct answers,
           s = standard deviation.

Correct answer: 12262
Proportion of correct answers: (3rd grade) 87.6%, (4th grade) 93.4%
Incorrect: (the most) 12162
Easy problem for 3rd grade and easy for 4th grade

Correct answer: four tenths (十分 四)
Proportion of correct answer: (3rd grade) 52.7%, (4th grade) 71.5%
Incorrect (the most): four (四) (27.5%, 10.7 %)
Incorrect (2nd most): one fourth (四分 一) (16.3 %, 14.9 %)
Difficult for 3rd grade and difficult for 4th grade
* Usually 「10分 4」, 「100分 4」,「4分 1」are used.
Children are not familiar with kanji numerals.

Correct answer: Divide each number in List 1 by 5.
Proportion of correct answers: (3rd grade) 36.4%, (4th grade) 49.2%
Incorrect: Multiply 5 by each number in List 1. (25.5%, 24.9%)
Incorrect: Subtract 8 from each number in List 1. (24.1%, 14.5%)
Incorrect: Add 8 to each number in List 1. (10.7%, 8.8%)
Difficult for 3rd grade and difficult for 4th grade.
 

                                Formula containing  and the physical situation

The expression 1000 - 120 *   denotes various numbers and quantities depending on their situations.  For example:  『The destination is 1000km far from here.  One goes towards the destination for  hours on a train of speed 120 km per hour.  How much is the remaining distance?  The remaining distance』is denoted by the following expression:  1000 - 120 * . Consider the physical situation like the above, and describe the part:『 』and describe the unit suitable to the situation in (    ).        _______________________________________________            『                                                                                          』        is denoted by the following expression:  1000 - 120 *   (    )

Types of answers:
    1. train (R) bus, etc.
    2. buying something, etc.
        120 yen a notebook, buy  copies of the notebook, pay 1000 yen. The change?
    3. distribution of a thing, etc.
        A string 10 m long, make  strings 1.2 m long from it. The length of the                     remainder?
    4. velocity of movement
        1000 m to the goal, run for  minutes with 120 m per minute. The remaining               distance? 1000 m to the goal,  runners relay, 120 m per runner. The                        remaining distance?
    5. others
        Expressible by 1000 - 120 * 
    6. explanation is not complete, and it is 120 * .
        1000 m to the goal, go on for  minutes with 120 m per minute. The distance              travelled?
        1000 kg of rice, consume for  months, 120 kg per month. The weight of rice              consumed?
    7. question only
        120 yen per piece of cake, buy  pieces. Is the amount 1000 yen sufficient?
        1000 candies, each bag contains 120 candies. How many candies remain?
    8. other answers
    9. nothing about answer.
 

4. Designs by Teachers
　
        All Education Boards guide schools to seek for their uniqueness or to build their school with distinctive features. Furthermore, all Education Boards emphasize "Change your school."
　
(1) A "password" in elementary schools
　
        Thus elementary school teachers give each other a password "Let us get a free hand and create." They create newly devised ideas for instructional methods of school subjects and for school events. Therefore many educational practices are presented at educational study workshops or meetings. At the 78th nationwide meeting for Arith-Maths Education under the sponsorship of the Japan Society of Mathematical Education (JSME), 197 educational practices (10 branches) were presented in 5 - 7 August, 1996. And at the 29th meeting for mathematics education study under the JSME, 108 research papers (19 branches) were presented in 2 - 4 November, 1996. At the meeting, "Gender Branch" was newly established.
　
(2) Teachers' ideas
　
        We shall introduce some new ideas for instruction. In general almost all schools use fieldwork in which teachers try to instruct Subjects, i.e., Social Studies, Arithmetic, Art and Handicraft, etc.
 
 

　

[Design 4]                Aim: Power of collecting and processing information.                     (4th grade)

        1.   2  4  6  8 10 12 14
                                                    making up pairs
                              
        2.                  rearrangement
                        10            4

        3.   6 = 2 + 4            8 + 2 = 10            10 + 4 = 14

    Demonstrate each calculation, explain it and discuss it with classmates together.

        *  : small disks (Ohajiki, )
 
 

The Central Council for Education has finished consideration and has come to some conclusions, and will soon report the findings to the Minister of Education. Recently change appears in teachers’ minds, and self-questioning arises, that is, to ask, "For what purpose do we devise new instructional methods and materials?" Children should gain power for living in the 21st century. Teachers think "Mathematics is power, and mathematics is to be power." "Power in life" and "Mathematics in effect" are becoming their new "passwords."

References

[1] Ministry of Education: Course of Study for Elementary Schools 1989 edition, Gyosei (1989).

[2] JSME : 日數教YEARBOOK (JSME Year Book) I, Sangyo Tosho (1995).

[3] JSME: 日數教YEARBOOK (JSME Year Book) II, Sangyo Tosho (1996).

[4] National Educational Institute:小、中學生之算數、數學，理科之成績 -- 第3回國際數學、理科教育調查(Achievements for Arithmetic, Mathematics of children and pupils -- The report of the 3rd TIMMS), Toyokan Shuppan (1996).

[5] JSME : Journal of JSME Arithmetic Education, Vol.78, No.10, JSME (1996).

[6] JSME : Journal of JSME Mathematics Education, Vol.79, No. 3, JSME (1997).

[7] HISHIMURA, Yukihiko: 變化之時代之學校像 (School status in the time full of variety), kyoiku Kaihatsu Kenkyu (1995).

[8] Ministry of Education: the extract of Survey of Enforcement Stuation of Curriculum, National Educational Institute (1996).

[9] Toyama, Hiraku: Introduction to Mathematics for teachers, Kokudo Sha (1965).

回《數學教育》第五目錄