(From "Principles of Mathematics Education" by GINBAYASHI Koh, former President of AMI, 1984)
The Association of Mathematical Instruction (AMI) was founded in 1951. At that day, Japan was still occupied by U.S. Armed Forces and the core curriculum system which prevailed in some states of the U.S.A. was also dominant in Japan. As a result, this core curriculum caused a general lowering in scholastic ability and in particular the mathematical achievements of children were drastically affected. Initiating its activities with a small number of supporters against this curriculum, AMI has aimed to establish correct ideas and methods for mathematics education.
Since then, the Japanese Government has abandoned the core curriculum and instead gradually strengthened its control over the contents of education. Today it has come to be almost the sole determiner of educational content through the course of study published by the Ministry of Education.
People who were dissatisfied with this situation and wished to practice more liberal instruction have according to each discipline voluntarily gathered themselves together and organized bodies called civilian education research groups. Today more than 40 such bodies have been organized, and AMI is one of them.
A civilian education research group is neither a kind of guild, an academic society nor a union, but consists entirely of those who approve of its guiding principles and is financed solely through its membership fees. It is a free organization that has no power and expects no support derived from other authorities.
At present, AMI consists of about 2,000 members who are mostly teachers, instructors of pre-schools, elementary schools, middle schools, and high schools, as well as professors and researchers of universities. University students and parents are also included. AMI issues a monthly organ the "Mathematics Classroom", which has already surpassed issue No. 500 and whose number of copies per issue has approached nearly 10,000. In addition, various books and based on its members' research and practices have been published.
In spite of interference and suppression by the Ministry of Education, AMI has succeeded through its activities during the past 40 years in creating and developing several principles and methods of mathematics education. These have been tested in classrooms and, as a result, gradually have become highly evaluated and are now having considerable influence on mathematics education in Japan. Especially, the "Theory of Quantity" and the so called "Water Supply Method" have clearly obtained excellent results. More recently, AMI has proposed the "Creation of Enjoyable Lessons" which ensures the success of teachers when they work for these principles.
The "Theory of Quantity" not only clarifies the meaning of numbers and the four arithmetic operations, but also makes it possible to apply mathematics to the real world, and to connect elementary mathematics with the Calculus.
The "Water Supply Method" is concerned rather with the procedures of such calculations, analyses them completely and has pursued this project. For explanation of procedures, it employs tiles as teaching tools and schema, which can connect the above mentioned quantities with procedures for calculations.
"Enjoyable Lessons" attach much importance to the subjective part of the understanding of mathematics, and it creates many teaching tools, various games and performs experiments and measurements.
In short, according to the terminology of Charles William Morris, an American linguist, these three principles are thought to correspond to the semantic, syntactic, and pragmatic aspects of mathematics education respectively.