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Techniques in Teaching Statistics
Having spent my career as an electronics engineer, I often had to explain ideas to other engineers, and sometimes to non-engineers. In almost every case, a diagram was very helpful in conveying an abstract idea to someone else. In every math textbook, you won’t run out of charts 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 when the slope or intercept changes? It would immediately become clear what is the difference between the slope and the y-intercept.
Straight lines are just the start. Our community college doesn’t have any of the best math software on the market, but we do have MS Excel, and after a few evenings alone I found it to be a pretty good program. I then developed spreadsheets that showed a normal distribution. This isn’t really a trick, but having the data the graph displays on one parameter, say the average, the displayed graph would move from left to right as the value of the average changes. A second parameter of a normal distribution is of course the standard deviation. By entering this, the class can see what happens to the shape of the distribution as a function of the value of the standard deviation.
Now imagine displaying the cumulative distribution on the same graph. When the mean or standard deviation changes, the placement and slope of the cumulative distribution changes, but the ultimate value of the cumulative distribution always approaches one. This is a great way to make people understand that the area under any normal distribution is always one. Connecting the area under the normal distribution to the probability is another great use of this technique. A proof of the central limit theorem, showing the relationship between the population and the sampling distribution is yet another. The possible illustrations are limited only by the imagination of the teacher.
After developing several Excel spreadsheets and using them in class via a “smartboard”, I was introduced to another program. It was a screen capture program called “Camtasia”. It then occurred to me that I could automate chart animations with Excel’s macro capability and capture chart movement with Camtasia. Then, using Camtasia’s capabilities, an audio track and captions could be added to explain the concepts revealed by the graphics.
By combining the capabilities of Excel and Camtasia, a teacher can create clear math concepts that may seem a little silly to some students and spark everyone’s imagination.
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