May 10, 2006

After viewing many examples of digital textbooks and learning objects, I have come to realize the importance of including teaching guides to help teachers incorporate these learning objects into their claases. Offering digital texts or exercises is only part of the process. Here is an example that shows how learning objects which help teach mathematics can be presented to provide math teachers with the exercises, building tools and open source code that will assist them in applying the learning objects in the classroom.

The Open Source Sharable Applet (OSSLET) Collection is part of the Mathematical Sciences Digital Library, hosted by the Mathematical Association of American. The collection contains only a few entries, however the open source and collaborative approach is compelling. Overall, the design is simple but functional, with the interactivity being more important to the osslet's success. Allowing students to manipulate objects in order to see mathematical relationships in real time cannot be replicated in print text. Each applet demonstrates a mathematical concept through interactive exercises. One can easily imagine, with an expanded collection, this resource could be used throughout an entire syllabus. What this project needs (and I hope it finds) is a community with enough resources to contribute and develop the site to its potential.

To be included in the site the osslets, must be interactive, come with several curriculum units, work off the shelf, and be open source and editable. The initial examples use Flash and Director, whose sources files are also available for download. Teachers without Flash or Director skills can use the pre-existing examples as well as use web forms to create new exercises. Discussion boards (which are admittedly underused) provide a space for teachers to share strategies and ask questions.

1. Multiparameter Animation:
Kerry Moore and Frank Wattenberg's "the Multiparameter Animation" osslet animates various functions to show students the effect of changing a parameter of a function. Students can both watch the function animate automatically or adjust the parameters themselves. The function is one of the most basic ideas in mathematics. Being able to understand how parameters similarly work across all functions is crucial to understanding higher level mathematics.

Moores and Wattenberg of the United States Military Academy provide the most fully developed resources to go along with the exercises. The curriculum units offer full lesson plans on how to use the examples in a classroom. For instance, in the data-fitting exercise using the World Records for the Mile Run, students first see the raw data, and then the data plotted on a graph. Students, then use the controls to fit a line to the data, thereby estimating the function which describes the data. The lesson utilizes pedagogical concepts including inquiry-based and contextual learning through real world examples. The authors also include a web form tool to create examples of new functions and graphs for students use. In the case where the teacher knows how to use Director, they can have access to the actual source files and code.

2. Linear Transformation:
Linear Algebra is used across many areas of advanced mathematics. The Linear Transformation is a basic concept used in Linear Algebra, which involves the manipulation of vectors. Jack Picciuto and Frank Wattenberg of the United States Military Academy created The Linear Transformation osslet and accompanying resources to be able to be used for a variety of applications and degrees of difficulty. Students manipulate vectors on a graph to see how their values are related to each other. Both quick examples and fully developed curriculum units are provided. As well, extensive resources and instructions on how to create new exercises and sample exercises using a web form are included. As with the Multiparamenter Animation osslet, teachers can download the Director source files.

3. Planar Graphs:
The Planar Grapher Tool, developed by Doug Ensley of Shippensburg University, helps student understand connections between planar and non-planar graphs. Basically, a planar graph is a graph whose nodes (the dots in the figure) can be arranged such that the edges (the lines in the figure) do not cross. This applet includes a sample exercise with instructions and questions to accompany the web-based activity. As well, the osslet provides both step by step instructions to allow teachers to create their own Planar Graph exercises without using Flash, as well as, the Flash source files.

Mathematics is highly visual and interactivity, yet it is rarely taught in that matter. Recently, teachers have created an enormous number of small scale tools and modules which demonstrate and test mathematical concepts. However, they often act as permanent stand alone objects which other teachers cannot edit. Further, the creators generally provide student directions on the operation of the learning object, but often fail to provide any guidance for teachers on how to integrate the material into a class lesson. The OSSLET collection avoids these pitfalls. More than offering simple-to-use tools, it provides enough support materials to assist other teachers. The site is a strong model for future open source and collaborative math textbooks, however it is only a start.

Posted by ray cha at 4:28 PM