Thursday, April 23, 2015

Virtual Manipulatives and Tools

Virtual Tools in the Elementary Classroom

When I think about it, words can sometimes get in the way of my math teaching. There are moments in my elementary math classes where I am striving mightily to put something into words that would be so much better understood without words. I wish, sometimes too late, that I had prepared a physical object, a picture, or a moving picture to show students what is happening when, say, one is regrouping in addition. There have been plenty of these moments in my teaching, where in the back of my mind I am wishing I had prepared a visual instead of trying so hard to put a math concept or process into words. I can picture myself, like a native speaker trying to explain driving directions to a tourist who doesn’t speak English.

Computer technology is helping me with this challenge in teaching elementary math. Over the years, I have become more and more dependent on visual representations developed by others that I can show to my students instead of telling them about it. One of my all-time favorites is this simple animation used to help children understand the relationships between circumference, diameter and pi:

Perhaps you will see what I mean when I talk about how this picture is worth a thousand math teacher words.

Of course, planning hands-on experiences with manipulative materials is a foundation of elementary math teaching around the world and is often the best way to get away from words. When I do not have a physical object for children to explore, or when circumstances in the classroom do not allow for the time necessary for managing the stuff for each student, it is this growing trove of helpful visuals that is becoming a well-worn tool of my math teaching toolbox.

For years I have relied on the simple but effective visual teaching tools provided in the National Library of Virtual Manipulatives (NLVM). The tools are also collected for easy access so I do not have to spend a lot of time searching the internet for the right demonstration. Consider the “fractions - adding” activity as an example of the power of these tools.

Matholia ( also offers an updated collection of virtual tools for active demonstration to students. I’ll give you an example of how I used the collection. I was doing some remediation work with a second grader who was using the standard algorithm for addition relatively well, but his errors showed that he only understood the procedure, but had weak understanding of the meaning behind the procedure. I pulled up Matholia’s place value tool, and we added numbers together, watching what happened on the screen, and connecting the action to what was happening in his pencil-paper work. I was proud that I could restrain myself from too many words as I had him articulate for himself the process of regrouping on the screen, and then the representation of regrouping on his paper.

I know that I am relying on these virtual tools more and more. Because they are so powerful, I want to access them easily and quickly. I want the whole toolbox in one place so that when I find myself in that moment when words are actually getting in the way, the visual representations are nearby and easy to use. I don’t think we are there quite yet, but we are close. I wonder, would every elementary math teacher’s toolbox be the same? Would one size fit all?

Matholia's growing library of over 100 virtual tools and manipulatives is included in all Matholia subscriptions. If you are already an adopting school and would like an offline version for the tools kit, contact and reference this blog.

by Dr Kevin Mahoney
Dr. Kevin Mahoney is an academic researcher and Math Curriculum Coordinator for an independent school outside of Boston, MA. With over 20 years of elementary teaching experience Dr. Mahoney also works as a consultant and trainer to schools and teachers implementing Singapore Math Curricula.

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