Using spreadsheets for understanding

This is something I find myself doing increasingly often so I thought I would outline the quick idea here in a blog post and work on developing the ideas in to classroom activities. The idea is easily explained. Spreadsheets can easily be designed and programmed to perform certain functions that your calculator can. The question is, why would we bother when we have calculators that can do it for us? The answer is that the process of designing and programming to simulate calculator function requires a really thorough understanding of the mathematics behind the process and takes the mystery away from how the calculation is done. I have found that in asking students to do this task they have really developed some sound understanding and had some great discussion in the process of trying to do it.

Where can we do this?

Here are a few ideas...

• Create a compound interest calculator where you can change the interest rate, intial investment, compounding period and length of investment and watch the the final amount change accordingly.
• Create a chi² statistic calculator for diferent contingency tables. Start with a 2 x 3 for example. The user changes the numbers in this table, the totals change accordingly, a second table of expected frequencies is automatically calculated. A third table will process the difference in these and calculate the chi² statistic.
• A linear regression machine - Set up a spreadsheet to calculate the correlation coefficient and regression line for a set of 20 ordered pairs, such that you can change any of the numbers and see the change propogate.

There are more applications of this idea and they dont necessairly have to be done with spreadsheets. See this example of the trig calculator to see how dynamic geometry can be used to create a trig ratio calculator. the main point is that the programming of these calculators is a rich tasks that requires students to really explore with the mathematics and reason with each other to make them behave properly! I am planning to develop these in to classroom activities and will post links here when I have!