표집변이성에 대한 추론 능력 함양을 위한 학습 경로 설계 연구

Abstract

Our understanding of statistical inference is based on our understanding of the concept of sampling variability. In this study, we aimed to explore learning trajectory that would help students meaningfully construct concepts related to sampling variability under this assumption. For this purpose, in this study, based on hypothetical learning trajectory theory, we designed a learning trajectory that is expected to develop students’ reasoning about sampling variability. We qualitatively analyzed the results of a teaching experiment conducted for a group of preparatory teachers according to the guidance of the learning trajectory designed in this study. As a result, The participants were able to generate the hypothesis that sample medians obtained through a random sampling process were normally distributed around the population median. The participants were then able to generate the hypothesis that the larger the sample size, the smaller the range of distribution of the sample median. Furthermore, it is possible to generate the hypothesis that the center of the distribution of the sample median is determined by the population median, and the range of the distribution of the sample median is determined by the sample size and the interquartile range of the population. In addition, based on the results of retrospective analysis of the difference between the hypothetical learning trajectory and the actual learning trajectory, we proposed a modification of the initially designed hypothetical learning trajectory.