Abstract:

The teaching of sampling is receiving increasing attention from researchers and educators, given that it is a fundamental statistical idea, which establishes a bridge between statistics and probability. Furthermore, ideas of sampling are needed when working with simulation, which is widely used today as a tool that help to improve understanding of probability and statistical inference. Moreover, sampling also plays a key role in the study of the frequentist approach to probability, as well as in inference.

In Spain, the curricular guidelines for secondary and high school include the concepts of population and sample, as well as the frequentist approach to probability in different grades. According to these proposals, in 1rst and 2nd grades (12-13 year-olds), students should learn ideas of sample and population and study the convergence of frequencies to probability by using simulation or experiments. In the third grade (14-15 year-olds), students learn different methods of collecting samples, they are introduced to the idea of representativeness, and should judge the sample representativeness through analysis of the selection procedure, in simple cases. Finally, in the second year of high school (17-18 year-olds) students are introduced to the idea of sampling distribution and to the difference between parameter and summary statistic. They also intuitively use the central limit theorem to determine the sampling distribution for means and proportions and to build confidence intervals for these parameters. Similar guidelines are introduced in other countries as well.

Despite these curricula, previous research, including our own survey, suggests that students do not perceive some properties of sampling. For example, although students are very accurate in estimating the mean and proportion when they generate random samples, they do not perceive adequately the sample variability. In addition, they do not notice the influence of the sample size on this variability. On the other hand, students also prefer biased methods of sampling and confuse the variable distribution with the sample distribution when they build confidence intervals. In this paper, we propose some activities that may help students to progressively acquire a sense of sampling which includes knowledge of the concepts involved, adequate reasoning about sampling and a critical attitude to analyse sampling information.

These activities have been compiled after an analysis of previous research that evaluates secondary and high school students’ understanding of sampling and sampling distribution. Along the paper, we will inform about the first results of this research and we will suggest possible ways to use the selected activities to teach and assess knowledge of sampling.

Keywords:

Statistical sense, sampling, evaluation and teaching tasks.