The purpose of this module is to show you how the dynamic features of geometry software such as the Geometer's Sketchpad can be used to illustrate theorems, to foster experimentation, to support problem solving, and to encourage conjecture.
Dynamic geometry software such as the Geometer's Sketchpad or Cabri II are very powerful packages that allow you to make accurate geometric constructions and then to manipulate either the initial objects or the constructed ones to examine which relationships in the configuration are coincidental and which are inherent in the constructions.
To be able to exploit these features in the classroom you do not need to be an expert with the software, but you do need some experience with the basic capabilities and you need to see some of the "tricks of the trade" that facilitate the creation of good demonstrations and projects. And, of course, no matter how good the software is, what you don't know you can't illustrate!
This module provides you with a good deal of experience examining and experimenting with dynamic sketches. You will also have the opportunity to imitate some of these and to create examples of your own. This is all done in the context of discussing interesting topics in geometry that are accessible to high school students. Some of them are results that are already standard in the curriculum and others are not.
A brief description of the actual work needed to complete the module follows.
- Prerequisite: The module assumes that you are familiar with the Geometer's Sketchpad. You might well have gained this experience from workshops or courses, or just by experimenting yourself. The Using the Geometer's Sketchpad module provides an adequate introduction and there are other on-line tutorials available. Links to some of these electronic resources are provided in the course outline.
- Step 1: Begin by getting a feeling for some of the special "dynamic" features of Sketchpad sketches. You will work through several demonstrations and be asked to create your own versions of them.
- Step 2: You will gain experience in creating dynamic sketches by working through examples that illustrate some elementary but beautiful theorems in geometry --- in particular, Ceva's Theorem and Monge's Theorem. In the process, you will not only learn some new mathematics, but you will also see some of the techniques for creating attractive and useful dynamic sketches.
- Step 3: You will see that a triangle has many, many "centers" besides the ones we already know and love --- circumcenter, incenter, orthocenter --- and you will be given the opportunity to find some new ones of your own!.
- Step 4: Select and begin a classroom project that you would like to do for one of the classes that you teach. We will provide you with a file that contains many such projects. You can use these sample projects as a source of ideas for your own project. You can also use these sample projects as a source of inspiration programs that you can copy and modify to suit your own purposes.
All of the ingredients necessary to complete these steps are contained in the files that you will download for this module. Moreover, you can get help when you need it by e-mail to the mentor named in your welcome letter. The next section will explain how to get started.