I believe that we really want students to gain an understanding of ideas such as the following:
Statisticians are already discussing these general notions as central goals for student learning. A list of prioritized topics is given by Hogg (1990) based on a discussion at a workshop of statisticians regarding what the goals for an introductory statistics course should be. Moore (1991) has also specified core elements of statistical thinking in terms of what students should be learning in statistics classes.
In addition to concepts, skills, and types of thinking, most statisticians would probably agree that we also have attitude goals for how we would like student to view statistics as a result of our courses. Such attitude goals include:
Once we have articulated our goals for students in statistics classes, we need to address the issue of how we enable students to learn these ideas and to change their already established beliefs about statistics. Many college statistics classes consist of listening to lectures and doing assignments in textbooks or in computer labs. Do these activities help achieve the goals for our students? Are students being adequately prepared to use statistical thinking and reasoning, to collect and analyze data, to write up and communicate the results of solving real statistical problems?
Much research has been done that indicates that students aren't learning what we want them to. Reviews by Garfield and Ahlgren (1988), by Scholz (1991), and by Shaughnessy (1992), summarize research related to learning and understanding probability and statistics. The studies reviewed tend to fall in two categories: psychological research and statistics education research. In addition, some studies in mathematics education offer additional insights into the teaching and learning of quantitative information. Relevant findings from these three areas of research are summarized briefly below.