The United States Military Academy (USMA) is currently conducting an experiment with laptop computers. Thirty-two cadets were issued laptop computers for use in MA205, Multivariable Calculus and SS201, Economics. They were also asked to use their laptop in the barracks instead of their desktop computer. While the Academy focused on deciding if the laptop is a viable alternative to desktops, the Department of Mathematical Sciences focused on how to use this additional technology in the classroom. Particularly, how could we use Mathcad to increase cadet discovery and understanding? We also wanted to find ways this experiment could help those without laptops.
Every classroom at West Point is equipped with a computer and projection device. Often during class instructors use Mathcad to help teach cadets how to use the program and to aid in visualizing a problem. Although better than nothing, this technique left several cadets very unfamiliar and unconfident in their ability to use technology to help solve problems. The reason for this was the time delay between seeing things in class and trying to execute the commands back in the barracks. When cadets got back to their rooms they had often forgotten the required syntax.
With laptops in the classroom there is no time delay. Cadets watch me perform operations on Mathcad and can follow along, ensuring they get the same results. If they don’t, they can immediately ask me to take a look at their worksheet. The difference is evident in student attitudes, "Before I saw the use of Mathcad as a chore and was even afraid to use it... Now I am not only more confident with Mathcad, but I enjoy using Mathcad and see the advantages."
Although my initial focus was to make cadets confident in their ability to use Mathcad, I quickly realized this was an intermediate step. What I really wanted was for cadets to better understand Multivariable Calculus by using Mathcad to perform tedious time consuming calculations or to aid in visualizing a problem. To do this I would create a worksheet and email it to cadets the day before class. As part of their assignment I asked them to "play with" the worksheet before class. During class they could ask questions and I would bring out the concepts I wanted to emphasize. This technique can also be used with students who solely have desktops.
Parametric Equations: When we study parametric equations we spend a few minutes learning the concepts, then spend several hours doing "stubby pencil" work. By using worksheets Mathcad did the "stubby pencil" work in seconds. Cadets then use the extra time to explore what affects changes in the parametric equations have on the plot. Here are a few simple examples changing the coefficients, start, and stop points. Cadets can do dozens of changes in minutes.