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With the fast-pace advancement of technology, computers in particular, we teachers need to cope up and exploit these technologies and integrate them in teaching.  In mathematics, commercial software have been developed commercially for the last three decades,  but recently, more and more free software were developed, and the source codes were even made public.  This open-source method helped software to be developed by programmers from different places around the world.

One of the best free and open-source software developed recently was GeoGebra, a dynamic geometry software developed by Markus Hohenwarter in 2001. Before, GeoGebra was just similar to other geometry software, but now it has turned into a full dynamic mathematics software capable of integrating algebra, geometry, calculus, and statistics.
I had been using well-known commercial geometry software many years before I discovered GeoGebra in 2005.  Since then, I have integrated GeoGebra in teaching, and our institute have integrated it as well in our teacher training programs.

To give you an idea of what GeoGebra can do, I have created some applets below for you to explore. The first applet shows that the angle sum of a traingle is 180 degrees, the second shows the effects of the parameters a and b in the linear function y = ax + b, and the third shows the concept of Riemann sums.

Note: If the applets do not display in your computer, you have to download and install the Java Runtime Environment to run it.

Triangle Angle Sum
Drag A,B,C to choose shape, and then drag the  circle on slider t to extreme right to rotate the triangle.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Linear Function
Drag the circles on sliders a and b and investigate the effect of their values to appearance of the graph

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

Riemann Sums
Drag the circle in slider n to investigate the sum of the area of the rectangles.

Sorry, the GeoGebra Applet could not be started. Please make sure that Java 1.4.2 (or later) is installed and active in your browser (Click here to install Java now)

You can find more applets at the GeoGebra wiki.
GeoGebra is available for download and runs in Windows, Mac, and Linux. Your computer must have Java Runtime Environment to run GeoGebra.
GeoGebra Step-by-Step Tutorials

If you want to learn more about GeoGebra, I have created more than 50 GeoGebra Step-by-Step tutorials in my blog Math and Multimedia. You can also email me at mathandmultimedia@gmail.com if you have questions about the said software.
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Guillermo Bautista is a mathematics teacher from the Philippines. He, together with Erlina Ronda, established the first GeoGebra institute in the Philippines, the GeoGebra Insitute of Metro Manila.  His academic blogs are  Math and Multimedia and GeoGebra Applet Central.

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Gaurav Tekriwal is the founder President of the Vedic Maths Forum India. Through television programs, workshops, DVDs, and Books he has taken the Vedic Maths System to over 4 million students in India, South Africa, United States, Australia, UAE, Ghana, and Colombia.