Physical, or concrete, manipulatives are physical objects that are used as teaching tools to engage students in the hands-on learning of mathematics to introduce math concepts. It’s important for children to have a variety of materials to manipulate and the opportunity to sort, classify, weigh, stack, and explore to help them construct their own mathematical thinking and knowledge with Cuisenaire Rods, Base 10 Blocks, and Fraction Circles.
Virtual manipulatives are cognitive technological tools that are a dynamic visual representation of physical manipulatives which can be operated through a computer mouse (or a finger on a tablet) to slide, flip, and turn just like a three-dimensional object. Virtual manipulatives give learners the same opportunity to make meaning and see relationships as the result of their actions, just like a physical manipulative. Although virtual manipulatives have some similarities with their physical manipulative counterparts, as cognitive tools virtual manipulatives have unique characteristics that go beyond the capabilities of physical manipulatives.
