Osslets: Mathematical Applets To Use and Revise

From Better Practices

[edit] Osslets: Mathematical Applets To Use and Modify

NEW -- This Osslet has now been published in JOMA

We hope that The Better Practices Workshop will provide a model for how we can use the Web and collaborative technologies like wikis to improve the pedagogical and scientific quality of mathematics learning and the extent to which the very best learning reaches all students at all levels.

Open this link in a new window (right click and select open link in new window) for one example that came out of this workshop. This link shows an open source shareable mathlet (OSSLET) that enables students to experiment with affine transformations and to use them to produce some of the visual effects they see in movies like Harry Potter and Star Wars. You can experiment with this OSSLET by clicking the Play button. You will see the Army "Black Knight" spinning around its vertical axis and you will see the affine transformation that accomplishes this in the upper left. Clicking different buttons in the upper right will show different effects in the lower left. Students learn about affine transformations by duplicating these effects by editing the entries in the matrix and vector shown in the upper left.

This version is much better than the fairly crude version that existed before the workshop and it shows the benefits of bringing together a diverse group of people and expertise in one place, giving them time to work on their own projects in a stimulating environment with lots of help available, and then supporting their continuing collaboration with a wiki. Here are a few of the results of this combination for this particular example of a Web-based resource.

• The display of the mathematical expressions look great and they resize well. This was one of the most important themes of the workshop.
• The Osslet is resizeable and, thus, can be used on a variety of platforms, taking advantage of as much screen real estate as is available without requiring the kind of screen real estate associated with high end monitors.
• Although it is not apparent from the window you just opened, this OSSLET provides a great deal of flexibility to curriculum developers who do not want to spend their time programming. This is accomplished using a very user-friendly XML file to control the OSSLET. To see an example of such an XML file right click this link, choose save, and then open the file in a text editor.
• This Osslet is designed to be shareable or reusable at several levels. The first level is accomplished using XML as described above and the second level by providing the Flash source code for those who want to use their programming skills. More importantly, this OSSLET was written quickly using a shareable parser written by Barbara Kaskosz, who presented the parser at the workshop.
• The design of the Osslet benefited from the collaboration at the workshop and after the workshop of people physically present at the workshop and of people whose contributions were Internet-mediated, through the Web and through a wiki.