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## Techniques in Teaching Statistics

Having made my career as an electronic engineer, I have often had to explain ideas to other engineers and sometimes to non-engineers. In almost every case, a diagram was very helpful in getting an abstract idea across to someone else. Diagrams and graphs are not lacking in all mathematics textbooks. What, 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 y-intercept is changed? It would be immediately clear what the difference is between the slope and the y-intercept.

Straight lines are just the beginning. Our community college doesn’t have any of the most capable math software programs on the market, but we do have MS Excel, and after a few nights I found it to be a pretty capable program. I then developed spreadsheets that showed a normal distribution. It’s not a trick, but by having the data displayed by the graph fed into a parameter, say mean, the displayed graph will move left and right as the value of the mean changes. A second parameter of a normal distribution is, of course, the standard deviation. By typing this, the class can see what happens to the shape of the distribution based on the value of the standard deviation.

Now imagine showing the cumulative distribution on the same graph. As the mean or standard deviation changes, the location and slope of the cumulative distribution will change, but the final 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 the area under the normal distribution to probability is another excellent use of this technique. A proof of the central limit theorem, which shows the relationship between the population and the sampling distribution is another. The possible illustrations are only limited by the teacher’s imagination.

After developing several Excel spreadsheets and using them in class through a “smart board”, I was introduced to another program. It was a screen capture program called “Camtasia”. Then I realized that I could automate chart animations with Excel’s macro capability and capture chart movements with Camtasia. Then, using Camtasia’s capabilities, an audio track and callouts could be added to explain the concepts the graphics revealed.

By combining the capabilities of Excel and Camtasia, a teacher can make clear mathematical concepts that may seem a bit obtuse to some students and spark the imaginations of all.

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