While nothing can adequately replace the REAL thing, virtual manipulatives play an essential role in a student’s journey towards developing a profound understanding of mathematics. That’s a bold claim! Let’s go a little deeper…
You’ve heard of CPA? Concrete – Pictorial – Abstract. Sometimes it is referred to as CRA. (Concrete – Representational – Abstract)
These are the three ways a math concept can be represented.
- Concrete – using actual physical objects represent the math concept
- Pictorial – using pictures/drawings to represent the math concept
- Abstract – using numbers, strategies, and/or algorithms to represent the math concept
So in which representation do virtual manipulatives belong? It is not entirely clear, but virtual manipulatives seem to occupy the space in between the representations. They serve as a transition from the concrete world to the pictorial…not quite concrete, but far more flexible than pictorial. The nature of the virtual manipulatives also allows the algorithm and the pictures to be placed side-by-side, making it easier for the students to shift towards abstract understanding.
Here is a small collection of virtual manipulatives to get you started.