A Case Study of a Lesson on the Sample Mean for Prospective Mathematics Teachers

In statistical inference, many students have a difficult time learning the sample mean, sampling distribution, and the central limit theorem, even though these are key concepts in statistics. This study aimed to identify and correct prospective mathematics teachers' misconceptions about the sample mean and sampling distribution during the statistical inference process in an introductory statistics course at two Korean universities. It also aimed to develop an exploratory lesson by applying Keller's ARCS (attention, relevance, confidence, and satisfaction) model so that the prospective teachers could better understand the sample mean and sampling distribution and correct their misconceptions. The exploratory lesson was implemented, observed, and analyzed. The findings showed that the exploratory lesson had positive effects on prospective teachers' attention, relevance, confidence, and satisfaction. In addition, through communication and discussion with their peers, they could better understand the concepts, discover new facts, and correct their misconceptions in the exploration process of the lesson. Thus, this study provided empirical evidence to show that an exploratory statistics lesson using Keller's ARCS model can be an effective lesson model for teaching statistical inference.