Using Virtual Manipulatives in Math Class

Mathematics is more than a combination of numbers and symbols that result in the calculation of an abstract solution. It is about solving problems, creating artistic expressions, and designing construction. That is why classrooms that provide opportunities for students to apply mathematical concepts to authentic situations are more conducive to fostering engagement and retention of learned concepts.

For decades, research studies have supported the use of concrete manipulatives during mathematics instruction. Tools such as connecting cubes, colored tiles, and place value blocks can be moved and manipulated by students to support their development of mathematical thinking. Findings from as early as the 1980s have suggested that students who used manipulatives during math instruction outperformed students who did not, and recently some states have passed laws mandating the use of these tools in kindergarten through fifth-grade classrooms. Considering their importance, you might consider using manipulatives that are accessible, flexible, and inexpensive—that is, manipulatives that are virtual. 

‘CONCRETE’ DOES NOT NECESSARILY MEAN PHYSICAL

It may surprise you that concrete manipulatives can be either physical or virtual. Mathematics manipulatives are properly described as “concrete” when they support students’ understanding of actual things in the real world. So, experiences in mathematics should be “concrete” as opposed to hypothetical or theoretical.

Virtual manipulatives might provide some advantages over physical manipulatives because they eliminate some of the constraints associated with physical objects. They are inexpensive and readily available. They are flexible. They can be moved in the same ways as physical manipulatives even on a vertical board, and they can be annotated like pictures. We can change their size, shape, and color. They are highly accessible and convenient because they can be introduced and put away within seconds. Pictorial representations that can be moved and manipulated to illustrate mathematical concepts can be just as effective as physical manipulatives like wooden Cuisenaire rods or plastic fraction models.

HOW CAN PHYSICAL AND VIRTUAL MANIPULATIVEs BE USED TOGETHER?

There are many ways to combine the uses of different types of concrete manipulatives. Consider these suggestions as you imagine the possibilities in your own classroom.

Introducing an activity. Before you pass out physical manipulatives to elementary students, use corresponding virtual manipulatives on a digital board in front of the class to model what you want students to do. This might eliminate some of the distractions that result from students playing with objects before you get a chance to explain the assignment. (Shout out to fourth- and fifth-grade geometry teachers passing out geoboards and rubber bands.)

Exploring before explaining. Allow middle and high school students to handle physical manipulatives first so that they can discover concepts on their own before the teacher’s instruction begins. Afterward, they can make connections as they annotate corresponding virtual manipulatives by labeling parts or writing equations. Organizing those colorful fraction bar models can be a great way to gain focus before instruction.

Solving problems in groups. Challenge high school students to solve problems in groups with physical manipulatives. They can share their learning with the whole class later using the virtual manipulatives on the board or in a recorded video. These presentations could make great posts on social media.

Catching students’ attention. Display virtual manipulatives as quick images that students see only for a few seconds. Challenge the students to reproduce what they saw on the board at their table with corresponding physical manipulatives. This is a phenomenal way to introduce a lesson on volume using connecting cubes, area with tiles, or composing numbers with rekenreks or circular counters.

The first time I tried to facilitate quick images for some first graders with a physical rekenrek, it was a disaster. Juggling the rekenrek as the beads slid back and forth while I tried to scribe the equations on the whiteboard was awkward and chaotic. These days, I prefer using Number Rack to present my teacher model in front of the class. I can set the beads where I want them to stay, and digital pens and other markup tools are available in 10 different colors. There is even a built-in, virtual cover that I can use to conceal the number rack until I am ready for the students to see it.

WHERE CAN I FIND VIRTUAL MANIPULATIVES?

A vast array of virtual manipulatives can be found online. Sites like Didax, Toy Theater, and The Math Learning Center are repositories of versatile tools that often have built-in text features for annotation. Do your students need something more interactive with built-in challenges? Try the mathematical demonstrations by Visnos, PHET, or the mathematical playground on Polypad by Amplify.

Students are growing up in a world that is just as virtual as it is physical. Beginning with their state standards, teachers can find ways of leveraging the advantages of both physical and virtual manipulatives to provide greater opportunities for constructing knowledge of mathematical concepts that will benefit their abilities to solve problems in the future.