The Journal of Online Mathematics and Its Applications, Volume 7 (2007)

Creating Mathlets with Open Source Tools, Markus Hohenwarter and Judith Preinder

We are currently using the following environment of open source tools and collaborative software with mathematics teachers in the NSF math and science partnership project Standards Mapped Graduate Education and Mentoring of Florida Atlantic University and The Broward County School District. Our environment consists of the following parts that are used by the teachers in this project to create and edit interactive online materials.

- GeoGebra: an open source software for dynamic geometry, algebra and calculus
- NVU: an open source software for creating and editing web pages
- GeoGebraWiki: an open pool of materials for online collaboration of teachers (based on MediaWiki)
- GeoGebra User Forum: an online forum for users of GeoGebra (based on phpBB)

GeoGebra is an easy-to-use tool for learning and teaching mathematics that lets you export interactive web pages, so called *dynamic worksheets*. These mathlets can then be changed and extended using GeoGebra, a text editor or html editor (e.g. NVU). The GeoGebraWiki is a pool of materials that allows everyone to contribute their own creations or take an existing worksheet and produce a customized version. In the user forum educators can help each other with specific questions. By using collaborative software like a wiki and a forum, we want to support cooperation among teachers by giving them the opportunity to share their ideas and materials as well as discuss problems and solutions.

Our dynamic worksheets usually consist of an interactive applet together with a short description of the mathematical situation and several questions. Students should then work on these questions by using the applet for mathematical experiments.

Discovery learning is a type of learning where learners construct their own knowledge by experimenting with a domain, and inferring rules from the results of these experiments. The basic idea of this kind of learning is that because learners can design their own experiments in the domain and infer the rules of the domain themselves, they are actually constructing their knowledge. Because of these constructive activities, it is assumed they will understand the domain at a higher level than when the necessary information is just presented by a teacher or an expository learning environment. (van Joolingen 1999, p. 386)

Although this open approach of discovery learning is desirable from an educational point of view, we have to make sure that students don't get lost due to a lack of guidance. Therefore, we are using a *guided discovery learning* approach where we provide a series of specific questions or tasks to guide the students' experiments. In this way, they can make step by step discoveries towards a predetermined goal with a minimum risk of failure.

In the following sections we will explain how to create and modify dynamic worksheets by looking at a series of examples. We will also discuss design principles for multimedia learning and present several guidelines for the creation of effective materials based on our experiences with the teachers in our NSF project.