Mathematical+Visualization+Toolkit


 * Mathematical Visualization Toolkit**
 * [] **

The MVT is a mathematics program designed by individuals at the University of Colorado at Boulder. It allows users to plot any two- or three-dimensional function. It also has 18 applications that allow users to interactively explore important mathematics topics, such as the unit circle, tangent lines, and Taylor series. Students could use these applications to quiz themselves at home in order to reinforce topics introduced in class. Users can also overlay multiple plots at one time. It is very useful due to its simplicity, ease, and speed.

This program would be useful in high school or college level math and physics classes, especially for students of calculus. A sample assignment would be for students to create multiple plots of variations on the same function, print them, and compare them in a project booklet to better understand how functions can be transformed. For example, f(x) = cos(x), cos(2x), cos(.5x), cos(x)cos(x), 2cos(x), etc. might be compared to one another. Its main value over the graphing calculator, which is already fairly common in high school math classes, is that it allows users to visualize the 3-D functions. The program is copyrighted, but it is free to either download or simply run straight from the Internet. This makes it accessible anywhere, even if downloads on a school computer are blocked.


 * Like GeoGebra, the MVT does not necessarily support metacognition without a teacher pushing it in such a direction. However, if students know that they are having difficulty with abstract concepts in calculus, for example, they might seek out this program in order to visualize those concepts and consciously promote their own understanding. Visualization often speeds up the process of learning, and students could use this program to purposefully reinforce their understanding, which would contribute to their metacognition. **

Below is a three-dimensional plot I created of the function f(x,y) = cos(.5y)*x.