I believe that we really want students to gain an understanding of ideas such as the following:

- The idea of variability of data and summary statistics.
- Normal distributions are useful models though they are seldom perfect fits.
- The usefulness of sample characteristics (and inference made using these measures) depends critically on how sampling is conducted.
- A correlation between two variables does not imply cause and effect.
- Statistics can prove very little conclusively although they may suggest things, and therefore statistical conclusions should not be blindly accepted.

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:

- It is important to learn some fundamentals of statistics in order
to better understand and evaluate information in the world.
- Anyone can learn important ideas of statistics by working
hard at it, using good study habits, and working together with others.
- Learning statistics means learning to communicate using the
statistical language, solving statistical problems, drawing
conclusions, and supporting conclusions by explaining the reasoning
behind them.
- There are often different ways to solve a statistical problem.
- People may come to different conclusions based on the same data if they have different assumptions and use different methods of analysis.

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.

Wed Jun 29 13:57:26 EDT 1994