数学教師を志望する大学生の標本分布に基づく統計的推論に関する調査研究：変動性に着目して

抄録

The purpose of this study is to clarify the state of statistical reasoning based on sampling distributions for Japanese college students aspiring to be mathematics teachers with a focus on variability, and to identify problems in recognizing variability through sampling distributions. To achieve this objective, this study developed and conducted a survey, and analyzed the results. The results revealed that the college students were not able to make appropriate statistical reasoning based on the sampling distribution, and that there were three problems in recognizing variability: (1) There was a problem in reasoning the range of the sampling distribution, and a tendency to reason a wider range compared to the range guaranteed by the confidence interval; (2) A certain number of students had problems in understanding and reasoning the effect of sample size by relating the population distribution to the sampling distribution; (3) More than half of the students confused the properties of the sample distribution with those of the sampling distribution, and did not understand the effect of sample size on the standard deviation of the sampling distribution compared to the its mean.