[논문]이산확률분포에 대한 예비수학교사의 이해 분석

이봉주; 윤용식; 임해미

doi:10.7468/mathedu.2020.59.1.47

이산확률분포에 대한 예비수학교사의 이해 분석
A study on the understanding of mathematics preservice teachers for discrete probability distribution 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.59 no.1, 2020년, pp.47 - 62

이봉주 (경북대학교) , 윤용식 (제주대학교) , 임해미 (공주대학교)

초록
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본 연구에서는 이산확률분포 파악에 필요한 지식을 표본공간의 각 원소에 정의된 확률, 이산확률변수의 정의, 이산확률변수에 정의되는 확률, 그리고 이들 사이의 관계에 대한 지식으로 정의하고, 예비수학교사가 해당 지식을 어느 정도 이해하고 있는지에 대하여 살펴보았다. 이를 위해 검사 도구를 개발하고 사범대학생 47명을 대상으로 조사하였다.

Understanding the concept of probability distribution becomes more important. We considered probabilities defined in the sample space, the definition of discrete random variables, the probability of defined discrete probability distribution, and the relationship between them as knowledge of discrete probability distribution, and investigated the understanding degree of the mathematics preservice teachers. The results are as follows. Firstly, about 70% of preservice teachers who participated in this study expressed discrete probability distribution graphs in ordered pairs or continuous distribution. Secondly, with regard to the two factors for obtaining discrete probability distributions: probability for each element in the sample space and the concept of random variables that convert each element in the sample space into a real value, only 13% of the preservice teachers understood and addressed both factors. Thirdly, 39% of the preservice teachers correctly responded to whether different probability distributions can be defined for one sample space. Fourthly, when the probability of each fundamental event was determined to obtain the probability distribution of the discrete random variables defined in the undefined sample space, approximately 70% habitually calculated by the uniform probability. Finally, about 20% of preservice teachers understood the meaning and relationship of binomial distribution, discrete random variables, and sample space. In relation, clear definitions and full explanations of concept need to be provided from textbooks and a program to improve the understanding of preservice teachers need to be developed.

주제어

표/그림 (24)

그림 [Fig. 1] Relationship between sample space, probability variables, and probability distributions
표 [Table 1] Contents related to 'distribution' in the curriculum
표 [Table 2] Definition of probability distribution in textbooks
표 [Table 3] Diagram of random variable and probability distribution in textbooks
그림 [Fig. 2] Research procedure
표 [Table 4] Table and graph of probability distribution in textbooks
그림 [Fig. 3] Development procedure for test tool
표 [Table 5] Research target
표 [Table 6] The final test tool
그림 [Fig. 4] Location error case of discrete point zero (0)
표 [Table 7] Understanding discrete probability distributions graph
그림 [Fig. 5] Correct responses of item 3
표 [Table 8] Recognizing the two factors of discrete probability distributions
그림 [Fig. 6] Incorrect responses of item 3
그림 [Fig. 7] Different probability distributions for the same experiment
표 [Table 9] Understanding the different probability distributions for one sample space
그림 [Fig. 8] Responses of different probability distribution response using examples of two trials with the same element in the sample space
그림 [Fig. 9] Descriptive error case for probability distribution in one sample space
그림 [Fig. 10] Misunderstanding of probability variable and probability distribution
그림 [Fig. 11] Student responses that is judged to take into account probability in item 5
표 [Table 10] Understanding the probability distributions of discrete probability variables for sample spaces with undefined probability
표 [Table 11] Understanding of binomial distribution
그림 [Fig. 13] Student responses in which binomial distributions are partially recognized, but the probabilities are not answered
그림 [Fig.12] Example of obtaining probability at each discrete point of a discrete probability variable following a binomial distribution

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