edLab Review: National Library of Virtual Manipulatives
editor: Max Sklar
The NLVM is a large set of simple online apps designed to supplement material in math classrooms from K through 12. These Java applets were built over a long period of time at Utah State University (funded by the NSF), with development starting in 1999 and updates all the way through 2008. They divide the applications into 5 categories of learning: Numbers/Operations, Algebra, Geometry, Measurement, and Data Analysis/Probability.
For more on our ratings, download our rubric
Variety of topics; highly educational; easy to get started
Minor flaws in user interface
[The Bottom Line]
Great for supplementing math lessons; read directions
There is such a wide variety of lessons that all math teachers will find something relevant to their class instruction. There are equally good materials for elementary and high school students, and some of the applications are helpful for adults. If the materials are used correctly and in conjunction with appropriate lessons beforehand and/or afterwards, these programs help build a conceptual understanding of the basic concepts.
Sometimes, the way to manipulate the user interface is not immediately apparent. Due to the use of old technology, a few quirks exist in the interface. Fortunately, reading the directions always clears this up. We also found an occasional bug.
[The Bottom Line]
Use the virtual manipulative library to supplement math lessons, not to replace them. Teachers should try out these applications themselves beforehand and to read the directions if they are not clear.
A lot of thought a research has been put into this resource, and it shows. It contains such a wide variety of math instruction in K-12 that most teachers will find something relevant to their class instruction. Here are some of the highlights:
- Early Concepts: Shapes and Colors, Counting
- Geometry: Rubber Bands Lattice that calculates area and perimeter, 3D Rotating polyhedra
- Core Skills: Fractions, Algebra, Graphing equations
Advanced Skills: Chaos, Fractals, Conway's Game of Life, Public Choice Theory, Probability
- Problem Solving: Tangrams (this one is frustrating!), Fill and Pour Problems, The Tower of Hanoi, Counterfeit Coins
The apps are easy to understand and easy to find. There are two ways to search for applications. First, there's a page with list of about 100 apps. Search this using your browser's find (usually cntl-f) capability to search for keywords. Another is a grid with the five categories as rows and different grade levels as columns. Sometimes the interface is a little bit obscure or old-fashioned, but a few minutes playing around and reading the directions makes it all clear. This tool has a new take on exercises that been done using physical objects. Sometimes a physical game has its advantages (I think I'd rather play with a physical Tower of Hanoi than a virtual one) but the virtual activities have their advantages too. With this tool, access to a hundred learning games becomes instantly available.
These applications are not just built to keep students busy at the end of the school year — most of them actually help students learn math skills and build an intuitive understanding of the concepts behind them. Take as an example the Pythagorean Theorem applet. It's easy to draw a right triangle on the board and write out a2
, but it's not so easy to show how we know this fact to be true. One geometric proof involves taking a box and 4 triangles and fitting them into one space that's has area c2
, and another space that clearly has area a2
. Playing with this simulation gives the student a conceptual understanding of how the Pythagorean Theorem works rather than just presenting them with a list of equations.
For younger students, there are number line visualizations for understanding of arithmetic, visualizations for working with fractions, and games with virtual pentomino blocks.
There are also great learning applications for advanced topics and problem-solving puzzles that are fun even for adults. The counterfeit coin game is a particularly fun but simple puzzle. Some of the more advanced topics include introductions to chaos theory and computer science. They have a simulation of Conway's Game of Life which sparks interest in both those subjects.
Sometimes the way to manipulate the user interface is not immediately apparent. For example, rotate the shapes often involve finding the corner of the shape (without the mouse point changing), and dragging. These idiosyncrasies are usually explained well in the documentation. There are also a few bugs. In the diff-engine, sometimes a number needs to be re-entered before submitting (especially when the user answers several at once and comes back to the old one). The tool is free, with the paid version a downloadable PC application that does customization and data logging. The time it takes to learn the material is small, and the activities can make some math lessons more fun while focusing on important concepts.