Abstract
The purpose of this study is the realization of learning/teaching that links
pre-existing knowledge to new knowledge．For this purpose, to exploring the derivation of a
theorem is valid. And this is appropriate to the thinking of emphasizing a learning process in
recent years. Therefore, this study has done some teaching materials research that focus on the
derivation of a theorem. In this paper, some of the results of the research are arranged from the
viewpoint of "seeing the determining condition of triangles as a function." And, it’s proposed as
a new teaching material. In addition, this shows "usefulness of the derivation research." On the
other hand, the aim of this paper is also to show "an example of a spiral-learning which
progresses by considering one viewpoint as an axis."
