Geometry at the high school level is difficult for many students. It requires a different kind of thinking than previous mathematics courses. The thinking skills required are on a higher level because for the first time in most of the problems there is no one formula or procedure required for solving. Geometry combines math and writing skills when proving theorems. This is new for most students. When I took geometry, I remember the most difficult part of adjusting to this course was the spatial thinking required. I always hated it when the teacher would say, "A line goes on forever, without end." I could not imagine something that never ended. I wanted to see a picture of such an object. As a matter of fact, I wanted to see pictures of just about everything. When the teacher would present a new theorem in class and ask us to imagine what would happen if one side was made longer, or an angle was changed, my brain would nearly explode! Also, my drawing skills are non-existent which made matters worse when I needed to draw a picture before solving a proof.

Fortunately, Key Curriculum Press has developed the perfect piece of software for students who have the same difficulties that I had. The Geometer's Sketchpad allows students to construct any shape and manipulate it any way they please. This opens up a whole new world for teaching geometry. First of all, allowing the students to use the computer motivates them in ways teachers could only dream. Often, in the school year, there is not enough time to cover constructions. Using Geometer's Sketchpad allows teachers to integrate constructions as part of the process of discovering new theorems rather than as a stand-alone topic. The software also allows the class to be more student centered rather than teacher centered since the students are responsible for performing the constructions, making observations, and finally putting their observations in the form of a theorem. Normally, teachers simply give the students the theorems and assign problems. The theorems do not really hold any meaning for the students because they haven't visualized why the theorem works. Also, the textbook wording of the theorems is difficult for students to understand. The students will still do the assignments from the book, but now they will have a deeper connection to the theorems. Another plus is the understanding of the vocabulary that is developed from performing the constructions. Many teachers may say, "Why do we need a computer to perform constructions, when we can do them using a protractor and compass?" My answer to this is that when using the protractor and compass, human error is involved, measurements are thrown off and the intended discovery is missed. Also, with Sketchpad, the students can make a side longer, or change an angle without having to reconstruct the entire object.

I have developed a sample unit on circle using Geometer's Sketchpad as I envision its use in the classroom. The unit begins as if no one has used this software before and correlates directly with chapter nine in Prentice Hall's Geometry book, which is similar to most other high school geometry books. Day one of the unit introduces the software functions and tools as a way of reinforcing the vocabulary covered in the first section of chapter nine in the book. There are no theorems to discover, it is basically just a familiarization process. Beginning on day two, the students will use constructions to discover theorems. You will notice that detailed directions are included when performing a construction for the first time, but the students are expected to remember how to perform these constructions the next time they are needed. The students should work in groups of two or three, sharing the computer, ideas, and printouts. The students are required to turn in printouts of their sketches daily. The teacher may simply want to have the students show that they have completed the assignment instead of actually collecting the printout so the students can use the printout when completing the book assignment. At the end of the unit, each group is to turn in a portfolio of the collection of their printouts. I would consider using the portfolio as a portion of the test grade for the unit. I have included a unit test with this unit, however, teachers could still use their own tests as before because I do not believe that the software changes the way the students should be tested on the material. It does not change what they have learned, but how they learned the material. If desired, teachers could require students to construct problems 1-8 on the test using the software rather than having them name the objects. The times noted on each lesson plan are approximate, although teachers may allow one or two days extra in case of time overflow. Two school weeks would be plenty of time to complete the unit including the test. The book assignments are to provide an opportunity for the students to apply the theorems they discover on the computer. They are an essential part of the lesson. The teacher must be familiar with the software in order to perform demonstrations of special features at the beginning of class as well as guiding groups who encounter program difficulties. I believe any teacher who uses this unit will be impressed with the level of thinking of their students.