표본 결과의 범위에 대한 중학생의 추론

Abstract

Reasoning about ranges of sample results in empirical sampling distributions at the middle school level can provide learning experiences regarding statistical concepts such as sampling variability and uncertainty. Simultaneously, it can also help lay the foundation for statistical learning in higher grades. Extending prior studies on middle school students’ reasoning about ranges of sample results, this study categorized the levels of reasoning about ranges of sample results by 9th-grade students during repeated random sampling activities in a technology environment, and analyzed changes in the levels of reasoning according to the activities. The analysis revealed that the types of reasoning by students were categorized as intuitive reasoning, additive reasoning, process-level proportional reasoning, and object-level proportional reasoning. The majority of students improved their levels of reasoning in the order of intuitive, additive, process-level proportional, and object-level proportional reasoning through activities in the teaching experiment. However, a minority of students did not reach the object-level proportional reasoning level. Based on the analysis results, we discussed the characteristics of each reasoning type with their roles in statistics learning, the characteristics of student thinking that led to changes in reasoning levels, and the learning trajectories about ranges of sample results.