On Teaching Statistics - Part I

Last June, I posted an item regarding why I felt college students should take a class in statistics to fulfill any mathematically oriented course requirements that they had for their degrees. I'm not going to change my mind regarding that opinion, but I've had an opportunity to think about how we teach the subject, and why our various approaches might make the material much more difficult than is necessary.

Over the course of my career, I've had the opportunity to read and review a rather large number of textbooks devoted to statistics, and to examine several teaching approaches, many of which make use of those texts as the bases for teaching the class. I've gradually come around to the view that we make life more difficult for our students by focusing too much of our teaching on the techniques used to generate statistical results, and not nearly enough on the basic concepts, which, if properly understood, will allow a student to apply those techniques correctly.

There are a relatively few statistical concepts that, if properly grasped, can make the entire subject straightforward for most students. These include the following: what is the probability that something will or will not happen, is a statistical process discrete or continuous (that is, can we count the number of occurrences of some event, or do those occurrences happen over some continuous range of outcomes), exactly how many outcomes of a discrete process are possible (or is that number too large to count), and over what ranges are the outcomes of continuous processes possible.

These concepts, along with a few others related to the measurement of central tendency and variation, make up the bulk of the central ideas necessary for a basic understanding of statistics. How we find all of these numbers and interpret the results of our calculations can wait until later. However, current teaching practice seems to be to rush to the data, generate all manner of charts, graphs and numbers in an attempt to get students to "see" the beauty of it all. I think that this well-intentioned effort results in our losing more students than we gain.

I'd like to see an approach based on conceptual understanding, with a discussion of many situations and where they all fit into the conceptual context of statistics. When students can properly frame the situation they're dealing with, and place it in the proper context, the necessary calculations and development of appropriate charts and graphs, along with interpretation of the results of that effort, becomes much easier than would otherwise be the case. So I'd encourage teachers to spend more time describing situations and how they fit into the basic concepts, and encouraging students to evaluate many situations, before inundating them with calculation techniques.

What I'm advocating here is the same approach that chess masters and other specialists use to become experts in their fields - namely, exposure to as many situations as possible, thereby developing the ability to recognize how each one fits into the framework of the body of knowledge of that field.