[논문]우리나라 초등학교 수학에서 가능성 지도에 대한 고찰과 개선 방안 탐색

고은성; 탁병주

doi:10.7468/mathedu.2022.61.1.29

[국내논문] 우리나라 초등학교 수학에서 가능성 지도에 대한 고찰과 개선 방안 탐색
A study on the mathematics curriculum for elementary school in Korea to improve teaching of chance 원문보기

Journal of the Korean Society of Mathematical Education. Series A. The Mathematical Education, v.61 no.1, 2022년, pp.29 - 45

고은성 (전주교육대학교) , 탁병주 (전주교육대학교)

초록
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본 연구는 우리나라 초등학교 수학과 교육과정에서 가능성 지도가 우연(chance)과 무작위성(randomness)의 개념과 관련하여 어떻게 이루어지고 있는지 비판적으로 고찰하여 문제점을 분석하고자 한다. 이를 위해 먼저 우연과 무작위성 개념에 대해 살펴보고, 이를 바탕으로 우리나라 초등학교 수학에서 가능성 지도의 문제점을 제시하였다. 우리나라 초등학교 수학과 교육과정에서는 자료에 기반을 둔 추론의 경험이 결여되어 있었으며, 무작위성 지도가 적절히 이루어지지 않고 있었다. 또한 표본공간의 지도가 누락되면서 모순적인 소재가 활용되고 있었다. 마지막으로 가능성에 대한 지도가 특정 학년에 편중되어 지도되고 있음을 지적하였다. 확률 지도의 개선을 위해 크게 확률 실험의 지도와 표본공간의 지도를 제안하며, 또한 특정 학년에 편중된 구성을 위해 자료 영역의 내용을 조절할 것을 제안한다.

Abstract ▼ AI-Helper

This study tried to analyze the problems by critically examining how the chance is taught in relation to the concept of chance and randomness in the Korean elementary school mathematics curriculum. To this end, the concepts of chance and randomness were first examined, and problems were presented in based on this by the literature analysis on mathematics curriculum material and textbooks for elementary school in Korea. As a result, there was a lack of experience in reasoning based on data, and randomness instruction was not performed properly. In addition, as the teaching of the sample space was omitted, contradictory materials were being used. Moreover, it was pointed out that the teaching of chance is focused on a specific grade level. For the improvement of the teaching of chance, a teaching of the probability experiment and the sample space were mainly suggested, and it was also suggested that the contents of the data area be adjusted for the composition focused on a specific grade.

주제어

표/그림 (11)

그림 Figure 1. The numbers of chances when the sums of points by throwing three dice are 11 and 12.
그림 Figure 2. Montmorn's distribution table for the sum of points for two dice (Hald, 2003, p. 205).
그림 Figure 3. Graphs of Montmort’s distribution of sums of points by throwing one, two, four, and eight dice (Hald, 2003, p. 210).
표 Table 1. A framework of probability thinking (Mooney et al., 2014, p. 502).
그림 Figure 4. Framework for probability modeling cycle (Pfannkuch et al., 2016, p. 24).
그림 Figure 5. A task of chance with randomness in the Korean mathematics textbook (MOE, 2019b, p. 91).
그림 Figure 6. Tasks of quantifying chances in the Korean mathematics textbooks (MOE, 2019a, pp. 139, 143; MOE, 2019b, p. 91).
그림 Figure 7. Tasks of representing chances in the Austalian mathematics textbooks for 1st grades (Weeks, 2012, p. 113) and the Korean mathematics textbooks for 5th grades (MOE, 2019a, p. 133).
표 Table 2. Chance and probability in mathematics curriculum for 1st ~ 8th grades in Korea, US, Australia, and New Zealand.
그림 Figure 8. Distribution of the number of times a coin comes down tail when tossed 6 times (Ko & Hwang, 2020, p. 952).
그림 Figure 9. Tasks of randomness and sample spaces in the Australian mathematics textbooks (Weeks, 2011, p. 121; Carr, 2011, p. 128).

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