Mrs. Grafaldi

Mrs. Grafaldi,

After teaching mathematics for 20 years, I am sure you are aware of the benefits of self exploration. We have all taught lessons where students draw pictures or maneuver 3-D shapes but we have also all dealt with these pieces becoming a problem in the classroom (being lost, stolen, etc). Technology now allows us to draw pictures and maneuver shapes without tangible objects. There are plenty of math programs (Geometer's Sketchmad, Maple, Mathematica, etc) that allow students to graph equations and change the view of the equation easily. Programs also allow students to quickly draw pictures, measure angles, and test theorems or conjectures.

However, knowing that programs are available simply is not enough. From your own desire and the pressure of the school, you must integrate these technologies into the classroom. The first technology to try integrating is graphing calculators. In fact, you might already be doing this without knowing it! Let the students graph line and calculate the max and min. Let students use the table. Actually, encourage students to use the table. If the students are able to use the calculator to effectively check their work then the students will be more likely to understand what is going on. After the graphing calculator is under control, try moving onto something like Geometer's Sketchpad. I suggest setting up a lesson like this.
1. Introduce the topic such as triangle congruencies with providing basic information and perhaps one or two theorems (depending on the abundancy of theorems).
2. Demonstrate to students how to use the program by having step-by-step instructions on how to create a simplified version of what they will be doing.
3. Give the students the task of creating something (like two triangle with three congruent angles) and have them make a conjecture about their shapes.
4. Have the class join together to see if the conjectures match
5. Have a discussion about why the conjecture is true and perhaps even prove it (depending on the difficulty of the proof) on the board.

If you set a lesson plan up in this manner then students are exposed to a topic both through lecture and exploration without the trouble of pulling out a compass and ruler. Of course, there are technology problems too but most of those can be quickly avoided after trying the lesson a few times.

Most importantly, don't allow the technology to cause you too much stress. Start slow with extremely specific directions for your students. As they become more advanced with the program you will be able to stop providing as many directions. Good luck.