Techniques in Teaching Statistics

Having spent my career as an electronics engineer, I've often had to explain ideas to other engineers, and sometime non-engineers. In virtually every instance, a diagram was very helpful in getting an abstract idea across to someone else.In every math textbook you'll find no shortage of diagrams and graphs. What would happen, I thought, if the graph could be animated, and show what happens if the parameters of the graph were changed and the graph immediately reflected the change? What if you could graph a straight line, and show what happens to the graph of a line as the slope or y-intercept is changed? It would become immediately clear what the difference between the slope and the y intercept is. Straight lines are only the beginning. Our community college is not blessedwith any of the more capable math software programs on the market, but we do have MS Excel, and after a few evenings alone, I discovered it is a rather capable program. I next developed spreadsheets that displayed a Normal Distribution. Not that much of a trick, but by having the data that the graph displays keyed on a parameter, say the Mean, the displayed graph would move left and right as the value of the Mean changed. A second parameter of a Normal Distribution is of course the Standard Deviation. By keying on this, the class can see what happens to the shape of the distribution based on the value of the Standard Deviation. Now imagine displaying the Cumulative Distribution on the same graph. As the Mean or the Standard Deviation changes, the placement and the slope of the Cumulative Distribution will change, but the ultimate value of the Cumulative Distribution always approaches one. This is an excellent way to drive home the point that the area under any Normal Distribution is always one. Relating area under the Normal Distribution to probability is another excellent use of this technique. A demonstration of the Central Limit Theorem, showing the relationship between the Population and Sampling Distribution is yet another. The illustrations that are possible arelimited only by the teacher's imagination. After developing several Excel spread sheets and using them in class via a "smartboard", I was introduced to another program. It was a screen capture program called"Camtasia". It then dawned on me that I could automate the animationsof the graphs with the macro capability of Excel and capture the movements of the graph with Camtasia. Then, using the capabilities of Camtasia, an audio track and callouts could be added to explain the concepts the graphs were revealing. By combining the capabilities of Excel and Camtasia, a teacher can make clear math concepts that may seem a bit obtuse to some students, and stir the imagination of all of them. On my website you will find a collection of videos that demonstratethis technique. There are videos that summarize the topics covered. There are also several full length videos of about ten minutes each on selected topics. These videos are only the beginning, we have plans to cover allmath topics customarily taught at theundergraduate level. So please drop by and let us know what you think.