Abstract
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.
Highlights
Recent interest in teaching methods for the development of statistical literacy has grown amid attempts to understand data science and the development of artificial intelligence [1,2,3,4]
This study proposes an exploratory lesson model that applies Keller’s ARCS model of motivational design theory [16] as a solution to remedy the shortcomings of the preceding studies that used computer simulations in an introductory statistics course for prospective mathematics teachers
They are asked, “Among the commonly known means and variances in the field of statistics, can you name all the types of means?” This question stimulates curiosity and surprise among prospective teachers (PTs) and leads them to ask themselves, “What are the various types of means?” the instructor can help the PTs recall arithmetic mean, geometric mean, harmonic mean, weighted mean, trimmed mean, population mean, and moving average, while arousing their curiosity about sample mean, which is a new concept to them
Summary
Recent interest in teaching methods for the development of statistical literacy has grown amid attempts to understand data science and the development of artificial intelligence [1,2,3,4]. Students taking introductory statistics courses face difficulties [7] when the class content progresses from the sample mean and sampling distribution to the CLT in the statistical inference section [8,9,10,11,12]. This begs the following question: What is an effective way to teach the sample mean to students?. Students learn new definitions and deductive thinking based on a premise.
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