本報告は、教員研修センターが主催し、文部科学省・青少年教育振興機構が共催する環境教育指導者養成研修のねらいとそれを具体化するプログラムの企画立案の視点、および実施・評価についてまとめたものである。最初に、研修のねらいを明確にし、それに基づくプログラムデザインを作成する。その後、会場となる施設の下見や打合せなどを行い、講師間の連携を蜜にし、研修を実施した。その後、アンケートによる評価を実施し、次年度への改善の指針とした。3つの機関の連携による研修であるために、それぞれをつなぐコーディネーターの役割が重要であり、そのことにも言及する。

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We have argued about the formalization of the locus of Apollonius using analytic geometry in the articles). It can be expressed in two ways as follows: one is done by means of finding out "a center and a radius" of the circle determined by the locus of Apollonius; the other by finding out "both ends of the diameter" of its circle. We presented three typical methods on determining "both ends of the diameter" of the circle in the elementary geometrical style. Besides, we thought over the significance of teaching the formalization of the locus of Apollonius in senior high school. It is usual, when dealing with this locus in senior high school, to decide "the center and the radius" of the circle using analytic geometry. But it is always the case to find out "both ends of the diameter" of the circle using elementary geometry. We scarcely find how to decide "the center and the radius" of the circle using elementary geometry. Can it be possible to treat the method in senior high school teaching? This question motivated us to write this article. This article aims at making clear the followings: (1) to construct any point satisfying the condition of the locus of Apollonius in the elementary geometrical style, (2) to construct "the center and the radius" of the circle of Apollonius in the same way, (3) to present some properties of the circle of Apollonius. We described five individual methods on the construction of "the center and the radius" of the circle using elementary geometry, in the second part of this article. This is an important part of this article. Especially, the fourth method of this construction is equal to a means of finding out "both ends of the diameter" of the circle in the elementary geometrical style. The circle of Apollonius is one of the most excellent materials of teaching geometry in senior high school.

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"The Locus of Apollonius" is old and well known, and it has been playing an important part in the study of locus. Accordingly, it has been dealt with in teaching materials in high school mathematics. The solution of this locus in general is methodically settled by means of either elementary or analytic geometry. In the case of the latter, it is usual to search for the center and the radius when finding the equation of the locus. In some high school mathematics textbooks there is a "Note" as follows: Note. Let A and B be two fixed points in the plane and let m and n be given positive constants. Then the locus of a point P, such that AP:BP=m:n is either (i) (if m≠n) a circle with a diameter where both ends divide internally or externally line segment AB into the ratio of m to n, (this circle is called the "Circle of Apollonius"), or (ii) (if m=n) the perpendicular bisector of line segment AB. However, elementary geometry is not being taught in many high schools in Japan, so it is almost impossible to find the equation by using the Note mentioned above. In this article, we have examined the answer using analytic geometry (rectangular coordinates, position vectors, complex numbers, and polar coordinates), so that we have not become deeply involved in solving the problem with elementary geometry. We especially analyzed "the center and the radius" and "both ends of the diameter" in comparison to each other. As a result of our examination, we concluded that "both ends of the diameter" is better than "the center and the radius" for finding the equation. From the viewpoint of math-education, we feel that the locus of Apollonius remains a very useful tool.

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The definition and terminology of Budo is a frequently discussed topic in the area of the science of Budo. In recent years, at the 2005, 2006 and 2007 congress of the Japanese Academy of Budo, a forum was opened with the title ‘Searching for a modern definition of Budo' and discussion continued along with topics like ‘what is the difference between Budo and competitive sports?', ‘what are foreigners looking for in Budo?'. On the other hand, as Sakai has pointed it out, basic research in the field of Budo must deal with the problem of ‘making it clear what terminology and how it was used in a given era'. He added, ‘as for the future, I hope for an unraveled general picture of what terminology, from what period, which way was in use', claiming the need for a clear understanding of terminology which could help in defining Budo and its cultural implications.

The necessity to clarify Budo terminology is connected to the problem of translation of Budo-related terms in the progress of internationalization. To translate Budo terminology properly, a thorough understanding of all the contents of its meaning is mandatory. We are convinced that an analysis of the terminology having been in use through the history of Budo would create the foundation for this work. Research on the examples of terminology in the history of Budo would greatly help people with different cultural backgrounds to comprehend these expressions, contributing to not to lose the real goals of Budo culture in this rapidly changing world.

Objectives of the research is as below,

1. ‌Concentrating on Kojiki, the oldest historical record in Japanese history, we analyze all occurrences of expressions connected to Budo, exploring the distribution of these expressions in the text.

2. ‌Especially in the case of sword-related terminology, clarification of context and tendencies of usage.

Our research produced the following results:

1. ‌We organized the Budo-related expressions in Kojiki, Japan's oldest book, into three categories: warriors, weapons (and their use) and general terms on warfare. We found that while there were no instances in the general terms category, 85 % of the terms fell into the category 'weapons'.

2. ‌We clarified how terms falling into the categories 'warriors' and 'weapons' are distributed in the three volumes of Kojiki. As an interesting result the fact can be cited that the term 'totsukatsurugi' appears only in the first volume about the age of gods, while the term 'tachi' can be found only in the second and third volumes.

3. ‌From its context it is clear that the term 'totsukatsurugi' was used to describe swords worn by the gods.

4. The term 'tachi' was used in connection with swords that came to earth from heaven.

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