Computer technology as an instructional tool for the teaching of mathematics offers unique “hands-on” environments in which abstract concepts can be explored. These environments enable active engagement by students, an experimental approach to math concepts, and an avenue to understanding abstract ideas not readily accessible through other mediums. Virtual manipulatives are the key. In animated scenarios learners see objects on the computer screen that they can move and change, and each change has a visual and immediate effect.

To experience the teaching/learning power of such an environment, you may enjoy exploring Algebra Balance Scales—Negatives from the National Library of Virtual Manipulatives (NLVM). It’s a good example of the mathematical scenarios available online.

So what about the offline classroom? My assumption here is that you have Internet access on one computer, hopefully your own laptop, or even a school computer. You need to go online to find the manipulatives, but at a few sites you can either purchase a CD containing all the applets or download them to your computer after purchasing a license.

Once you have the CD or downloaded material, you will need a way to project onscreen in your classroom. If your school has a computer projector, you’re in! Otherwise, you may use a television set or a Smart Board. A special cable (inexpensive and available for purchase) connects the computer to the TV. Once connected, your class can work together to explore mathematical concepts visually, hands-on!

The sites below contain virtual manipulatives for the middle school and beyond, not all equally appropriate for your classroom but all worth exploring. For each site I refer you to an example and also to the purchasing guidelines.

Principles and Standards for School Mathematics E-Standards CD
The CD contains the full text of the document plus interactive tools and a version of the Illuminations site with its hundreds of lessons and applets. It comes free with your purchase of the NCTM Principles and Standards (purchasing information). My favorite example, for its insights into graphing and slope: Distance, Speed, Time. 

Shodor’s Interactivate
The entire Interactivate collection, including 155 activities, is available on a CD for a moderate donation [tax deductible] to the Shodor Student Program. Examples include Surface Area and Volume and the Maze Game.

National Library of Virtual Manipulatives
NLVM offers a collection of K-12 activities for download to your computer or as a CD (purchasing information). This allows you to work interactively without Internet connection. As an example, explore Factor Trees and select “two” trees.

Middle School Geometry
This site from Japan includes challenging problems on parallel lines, circles, congruent and similar figures, and the Pythagorean theorem, a good example.  Information on downloading the material is available, but there is currently no CD for purchase.