Using Graphing Calculators or Geometer's Sketchpad

Graphing Calculators

Algebra is a very difficult, abstract concept for many students to grasp – especially now that students are being taught it as young as 7th grade. One of the most difficult ideas is finding where multiple functions intersect. Using the TI-83 or TI-86 calculators, students can put the function into the graph, find intersection points many different ways: using the table to see where the y values match or on the actual graph where the calculator has you identify the intersecting point and will tell you where. Instead of just seeing a bunch of confusing math, students can now visualizes the why and the meaning behind what they are doing. However, the calculators are not perfect, and students need some understanding as well as the ability to do the math before they are shown the shortcut. Texas Instruments has resources for teachers online as well as seminars.

If I wanted to a students to show me they could solve a system of equations (find where they all intersect), I could have them do it in three ways:
1. show all the math by hand
2. prove their answer using a their calculator to make the graph and find the intersection point (They would then draw the graph and write the point.)
3. use their graphing calculator’s table to find the point of intersection (They would then have to copy part of the table down on paper and circle the intersecting point.)
This assessment would then show me that the student understood the math, the meaning behind the math, as well as 3 different ways to solve the same problem. I would call that a thorough understanding.

http://education.ti.com/educationportal/sites/US/homePage/index.html

Geometer's Sketchpad

I have found that students either like geometry or they like Algebra. Geometry is based on the idea of proving properties of lines and shapes. Many of us have had to do this through constructing using protractor’s and compasses. While this is fun (or frustrating depending how you look at it), students can use the exact same mathematical skills they would have needed to construct by hand to construct the shapes in geometer’s sketchpad. Not only can they build shapes, they can easily manipulate them, see what happens when you move points, midpoints, and hundreds of other options. Things that would take hours to build by hand can easily be experimented with in Sketchpad. Students are able to build more knowledge through this computer tool.

http://www.ocdsb.edu.on.ca/Teacher_Res/secondary/tecint/gsp.htm
Here is a list of activities as well as other websites of resources for teachers.