Today, my Pure Math 30 students, took out our department laptops and logged into Wolfram Alpha.
We were investigating the general form of an equation of a conic. Ax^2+Cy^2+Dx+Ey+F=0.
I had the students graph many different equations and observe what graph Wolfram Alpha created.
The students then had to compare the equations with their graphs and answer the following questions.
1. Describe what values you must use for A and C in order to generate a circle?
2. Describe what values you must use for A and C in order to generate an ellipse?
3. Describe what values you must use for A and C in order to generate a parabola?
4. Describe what values you must use for A and C in order to generate a hyperbola?
Wolfram Alpha made this investigation quite easy for the students. All they had to do was type the equations into Wolfram Alpha and it gave them nice, easy to read graphs.
I could have just lectured for this lesson. However, I believe that the discovery approach I used was much more powerful.
Some math teachers would say that they could have their students use their graphing calculator to do the same thing. You are right. I have had the students use a graphing calculator for this lesson before. However, I had to install a special program on the calculator for the students to complete the activity. Wolfram Alpha is accessible to all students with a computer and an Internet connection. It is a far more valuable tool than a graphing calculator. Wolfram Alpha can do so much more than a graphing calculator.
Wolfram Alpha was an awesome "TOOL" in my math classroom today.
If you have not looked at Wolfram Alpha I think every mathematics teacher should.