高等学校数学における数学的活動を生かした 授業づくりに関する実践研究（Ⅰ） ─ オープンエンドアプローチによる「二元一次不定方程式」の学習指導を通して ─

抄録

　　The purpose of this paper is to show whether mathematical activity is really activated by open approach, and to clarify the educational value of the open approach.

　　The value that the author describes refers to the transition of students into higher levels based on “the levels of mathematical ability” defined by Nagasaki (2007).

　　The author developed the open problem in the unit of a “linear indefinite equation with two unknowns” in action research training.　Moreover, the lesson which solves it by group study was tried. The author analyzed the proposals from every group, the videos, the protocol, and the students’ reports. The following things became clear from the result.

(1) Although it was analysis of the specific group, providing an environment where students can speak in comfort makes it easier to improve “the ability to discuss topics in mathematical terms” more effectively for the students who are hesitant to make a presentation or raise questions.

(2) Although there is the necessity for examination of an assessment standard, the open problem method effectively raises “the ability of students to use mathematics by following the rules.”

(3) Many proposals beyond the teacher’s anticipation were made through productive group study.　By devising how to take up various views, “the ability to find mathematical law, a rule, etc.” is raised.

(4) Through the open approach, a teacher can evaluate the students’ activities as well as the lessons carried out previously.

　　However, the educational value of open approach will not be achieved without enough structured lessons using a teacher’s tools, ideas and mathematical activity efficiently.