確率 學習指導 改善에 關한 硏究 : 高等學校 數學科 內容을 中心으로 = (A) Study on Improvement of Teaching Method of Probability in High School

다국어 초록 (Multilingual Abstract)

We have studied the teaching process fitful for the probability theory and its basic applications which should be emphasized in the set-theoretical approach against the present text in high school.
Methods.
The mathematical thinking ability of the students will be developed when we instruct the student with the following methods in the teaching period :
(1) Without regard to their ability the students are divided into the experimental class and the above two classes are looked upon as the almost same I.Q. and scholarship by the testing hypothesis.
(2) If an instructor should teach experimental class probablility theory and its applications putting emphasis on the set-theoretical and axiomatic approach, mathematical achievement of the experimental class would be more advanced than the controlled class which be taught probability without the above approach.
Result.
Testing in the two classes through the observation, the experimental class has shown, the improvement in the following points when compared with the controlled class.
(1) Before the experiment, there was no significant difference of learning achievement between the experimental class and the controlled class but after it the learning achivement of the experimental class increased satisfactory than the controlled.
(2) As there were lots of chances of expressing their views, the students showed much interest and their will to participate in the learning activities was very high, and they had great confidence in the subject.
(3) The students were thought to put-more emphasis on the learning process than on the results in school work.

목차 (Table of Contents)

• 목차 = 1
• Ⅰ. 緖論 = 3
• 1. 硏究의 目的 및 必要性 = 3
• 2. 假說 = 4
• Ⅱ. 硏究方法 및 節次 = 5
• 1. 標集 = 5
• 2. 硏究道具 = 6
• (1) 敎材 = 6
• (2) 知能檢査 = 6
• (3) 學力檢査 = 6
• 3. 硏究期間 및 硏究節次 = 6
• (1) 硏究期間 = 6
• (2) 硏究 節次 = 7
• Ⅲ. 硏究의 內容 = 8
• 1. 集合과 그 演算 = 8
• (1) 集合의 槪念 = 8
• (2) 集合의 演算 = 11
• 2. 確率空間의 公理 = 17
• (1) 標本空間의 定義 = 17
• (2) 事象 = 18
• (3) 代數(Algebra)의 定義 = 19
• (4) 排反事象의 定義 = 20
• 3. 公理論的 確率 = 20
• 4. 條件附 確率 = 24
• 5. 獨立性 = 30
• 6. 組合的 確率에의 適用 = 33
• (1) 餘事象의 定理 = 33
• (2) 確率의 덧셈정리 = 34
• (3) 確率의 곱셈정리 (Ⅰ) = 35
• (4) 確率의 곱셈정리 (Ⅱ) = 35
• (5) 獨立試行의 定理 = 36
• Ⅳ. 結論 및 提言 = 38
• 參考文獻 = 40
• Abstract = 41