BY AARON FOWLES

Math can be a very esoteric subject. It’s difficult for students to conceptualize numbers that are disassociated from their daily existence. Word problems have mixed success with making these concepts tangible to students. It’s necessary, then, to find a way to make these ideas “real” for students by providing them with something they can see and, if possible, touch. Virtual manipulatives are just that. They are computer programs that give students virtual objects to move around, measure, and arrange in mathematically meaningful ways. Rather than just providing students with an initial graphic that they must then mentally change, virtual manipulatives provide the means to make those thought processes tangible and apparent.

The National Library of Virtual Manipulatives, hosted by Utah State University, is a collection of Java tools that explore mathematical concepts. The activities are divided by grade level and subject matter. The 6-8 Algebra section, for example, shows activities that teach algebra through the use of balance scales. The example in the picture above shows how to develop equations based on geometrical configurations.

The activities are based on Java, and sometimes making Java work on your computer is an exercise in patience. It is well worth it, though, since these activities can help students visualize math and teachers visualize students’ understanding.

These tools are well-suited for use with an interactive whiteboard or on student computers. Each activity is aligned to nationally recognized math standards and includes instructions.

The National Library of Virtual Manipulatives

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Try some interactive learning at Learner.org