Dedicated (Applets) vs General Purpose Tools

Java applets have many advantages.

Users love them.
They are quick and easy to use.
They focus users' attention on the point being made.
The technology is not intrusive.
They can be visually attractive.

But

Java applets limit users' creativity and flexibility. They can do only the things programmed into the applet.
Users are not building up skills with more general purpose tools.
Users may not see beyond the "black box" of the applet.

Consider the following examples. Notice that, although they all are interesting and serve a useful purpose, none of them develop more general purpose skills. That is why we must be careful to use an appropriate mix of general purpose and flexible tools like computer algebra systems as well as Java applets.

The applet at the left simulates the game of "craps." On the first throw of the dice there are three possibilities.

The player throws a seven and wins immediately.
The player throws a two and loses immediately.
Any other number becomes the player's "point."

On subsequent throws of the dice there are two possibilities.

The player throws her "point" and wins.
The player throws a seven and loses.
The player keeps playing until she either wins or loses.
Click on the dice to throw the dice. Click on the "about to start" line to start a new game.

The applet below can be used to study Fourier Series. It allows users to input functions graphically by clicking on the vertical gridlines to input values. Click the salmon button to add one more term of the Fourier series and click on the light blue button to clean the graph.

The applet at the left illustrates the connection between the algebraic expression
(1 - t) A + t B = A + t (B - A)
and points on the line between A and B. The red dot marks the point represented by the vector A and the blue dot marks the point represented by the vector B.

Click anyplace along the line determined by A and B to see the corresponding value of t.
Enter a value for t in the box and click the move button to see the corresponding point.

The applet below uses exactly the same algebra to mix two pictures. Click the scale on the bottom of the applet to input a value of t between zero and one. This pair of applets demonstrates the power of linear algebra.

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