Virtual Manipulatives Revisited

Occasionally, I am asked if I know of any virtual math manipulatives. “I do. Why?” I reply.

I have a tough time with this type of app. Wanna know what make excellent pattern blocks? These:

pattern blocks

I am not an “ever optomistic techno-cheerleader.” Asking questions such as “What are the benefits of replacing a tactile experience with a simulation of a tactile experience?” make it difficult not to be seen as a cynic


“A SMART Board has transformed the teaching and learning of mathematics in your classroom?”

or a grump.


“That’s silly.”

Geoboard has softened my position on virtual manipulatives. Last week, as part of an investigation (Pick’s theorem), we asked teachers to figure out the area of the shape below (from Marian Small).

geoboard 1

Teachers calculated the area in a variety of ways. Filling shapes with colour in Geoboard helps illustrate each strategy. Most groups divided this shape into a rectangles and two triangles, used the formulas for the area of a rectangle and a triangle, and calculated the sum.

geoboard 2

Some groups emphasized the relationship between rectangles and triangles.

geoboard 3

Other groups subtracted the area of three triangles from the area of a square.

geoboard 4

Many groups counted squares and visualized pieces being rearranged to create new squares.

geoboard 5

The use of geoboards (real ones) led to answers of “approximately eleven.” With the elastic bands having to wrap around the pegs, the relationships between partial squares were more difficult to see. Similarly, in the investigation of Pick’s theorem, it was sometimes difficult to tell whether a lattice point was a border point. It’s not an issue within the iPad app; the virtual elastic bands connect rather than wrap around the virtual pegs. Plus, working with virtual bands was easier than working with real bands. This encourages even more “what if?” thinking. I don’t think this is true of all virtual manipulatives.

More importantly, learners can share their solutions through an AppleTV. This can also be accomplished with real manipulatives and the iPad’s built-in camera. True, students can push, pull, or drag their real geoboards to the front of the class to show and share their solutions, but technology just makes this seamless.

While I may have warmed up to virtual manipulatives, don’t expect me to warm up to virtual flashcards any time soon. Some teaching practices are harmful to students. Retina display doesn’t change that.


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