高等學校 敎育課程에 導入된 確率· 統計의 理論的 背景에 關한 硏究

Abstract

In short, this treatise herein stated intends to provide the students, particularly for high school, with the sufficient theoretical grounds in making themselves more practically adaptable to mastering the formulas of mathematics concerning probability and statistics, which will be employed in the high school curricula as the required subjects in 1979. In-depth analysis for general uses which was made a research by the author hereto is as follows : 1. Probability As for probability, it is fundamentally necessary for the high school teachers to intruct students to enable to under-stand that what-and-how formulas to probability, mostly used in the curricula, should be given, chosen, to solve the problems. An approach to probability suggested by me, therefore, i.e. application of what-and-how formulla to it, means that the approach interpreting over it is based on auxiomatic theories, whereby the author's study shown here is intensively concentrated on the ways of mathematical probability, statistical probability. Those raised to the problematic solutions that most students should be taken as easily as applied to any situations are considered to be core solution in an approach to settling down probability problems. 2. Statistics It is found that all the materials used in the middle school textbooks have centered on the guiding programs of having the students understand frequency table, histogram, average. However, the study attempted by me is belived to focus itself on the introduction of what method is best one to serve the students understand so easily that they could figure out arithmetic mean, geometric mean, harmonic mean, median, mode. In addition to the above, my study on this domain have given a particular stress to making student understood more clearly of the questions of deriving out range, quartile deviation, mean deviation, standard deviation, into the more practicable solutions in terms of statistics. In terms of descriptive statistics, on the otherhand, specific illustrations over the case of discrete random variable and continious random variable are analytically presented in an attempt to have students be able to capture the core of problems more understandably, easily, by author's suggestions as a conceptual approach to the statistics. However, the author deals in inductive statistics in a way that, to make the students get used to conceptual theory of inductive statistics, the detail illustrations over the case are tried explained on what methodological way of approach can be materialized. To the last, his conceptual approach to inductive statistics, in fact, taken a concrete factors as cases to be studied, tends to have widely dealt in more suitable way by exemplifying.;1979년부터 실시 예정인 인문계 고등학교 수학과 교육과정중 확률과 통계에서 다루도록 되어있는 사항에 대하여 그 이론적 배경을 규명하였다. 그 내용을 대략 요약해 보면 다음과 같다. 1. 확률 확률은 학생들에게 지도하거나 또는 현실문제에 적용하려고 하는 경우 어떻게 해석할 것인가 하는 문제를 생각할 수 있다. 이에따라 확률의 해석을 본 연구에서는 공리적인면으로의 정의, 수학적 확률, 통계적 확률, 주관적 확률의 방법으로 생각해 보았다. 2. 통계 중학교에서는 돗수분포, 히스토그램, 대표값등을 써서 그 자료의 분포 상태를 파악하는 지도를 하였으나 본 연구에서는 대푯값에 대해서는 산술평균, 기하평균, 조화평균, 중앙값, 최빈수를 소개하였고 산포도에 있어서는 범위, 사분편차, 평균편차, 표준편차를 취급하고 그 뜻을 밝혀 이해를 깊게 하였으며 기술통계에 있어서는 이산인 경우, 연속인 경우 확률변수의 뜻과 이항분포와 정규분포에 관한 정리를 구체적으로 설명함으로써 이 부분에 대해 이해를 깊게 하였으며 추측통계에 대해서는 기본적인 개념을 이해시키기 위해 구체적인 사실을 보기를 들어 설명하였고 모집단에서 표본을 취하여 그 성질에서 모집단의 특성을 추정하는 문제를 다루어 보았다.