Korean High School Students' Understanding of the Concept of Correlation

우리나라 고등학생들의 상관관계 이해도 조사

Correlation is a basic statistical concept which is necessary for understanding the relationship between two variables when they change values. In the middle school curriculum of Korea, only informal definition of correlation is taught with two-way data representations such as scatter plots and contingency tables. In this study, we investigated Korean high school students' understanding of correlation using a test consisting of 35 items about interpretation of scatter plot, contingency table, and text in realistic situation. 216 students from a high school in Seoul took the test for 20 minutes. From the results, we could observe the following: First, students did not have right criteria for determining the strength of correlation presented in scatter plots. Most of students could determine if there is correlation/no correlation and if the correlation is positive/negative by seeing the data presented in scatter plots. However, they did not judge by the closeness to the regression line but rather judged by the closeness between data points. Second, when statements about comparing the strength of correlation in the context of real life situation were given in text, the students had difficulty in understanding the distribution-related characteristic of the bi-variate data. Students had difficulty in figuring out the local distribution characteristic of data, which cannot be guessed merely based on the expression 'The correlation is strong' without statistical knowledge of correlation. Third, a large number of students could not judge the association between two variabels using conditional proportions when qualitative data are given in 2-by-2 tables. They made judgement by the absolute cell count and when the marginal sum of two categories are different for explanatory variable they thought the association could not be determined. From these results, we concluded that educational measures are required in order to remove such misconceptions and to improve understanding of correlation. Considering that the current mathematics curriculum does not cover the concept of correlation, we need to improve the curriculum as well.

상관관계는 두 통계적 변량 사이의 관계를 이해하는 데 필요한 핵심적인 통계의 개념이다. 우리나라의 중등교육과정에서는 제7차 교육과정까지 산점도와 분할표를 이용하여 상관관계를 비형식적으로 다루도록 하였고, 2007 교육과정 이후 상관관계에 대한 내용을 삭제하였다. 이 연구에서는 비형식적인 상관관계의 교육을 받은 고등학생들의 상관관계와 관련된 이해도 및 오개념을 조사하였다. 학생들은 상관관계가 선형적 관계성에 근접한 정도를 의미하는 것을 잘 알지 못하였고 자료의 밀집된 모양이 유발하는 시각적 오개념에 취약하였다. 또한 글로 표현된 상관관계의 강도 비교에 대한 서술문의 진위성을 잘 판단하지 못하였다. 많은 학생들이 $2{\times}2$ 분할표에 제시된 범주형 자료를 보고 상대빈도수의 개념을 이용하여 연관성을 판단하지 못하였다. 우리나라 고등학생들의 상관관계 개념의 이해도가 부족하고 오개념이 빈번한 것으로 볼 때, 통계의 기본적 소양인 두 변량 사이의 상관관계에 대한 지도가 강화되어야 할 것이다.