Sampling—A Good Start
This quote from an Australian curriculum document of the early 1990s sets the scene for a consideration of the development of student understanding of sampling. Long before students are involved in inference, however, they are building ideas associated with the concept of sample. In the English language the word sample has a colloquial usage with the potential both to assist and to hinder the development of the statistical meaning. The word also has a direct relationship to the part-whole concept that is a feature of many topics in the mathematics curriculum. What sample does not have is an algorithmic foundation that can be memorized and tested in a straightforward manner. The descriptive nature of the concept provides an excuse for some mathematics teachers to skim over it and move on to the more technical and product-oriented aspects of statistics such as drawing graphs and calculating means. Without an appreciation, however, of the part sampling plays in a statistical investigation, the rest of the process can turn out to be totally useless. Students need an appreciation of this contribution, both to
carry out their own statistical investigations and to question claims of others if they are not based on adequate methods.