Numicon

In mathematics education, a manipulative is an object which is designed so that a learner can perceive some mathematical concept by manipulating it, hence its name. The use of manipulatives provides a way for children to learn concepts through developmentally appropriate hands-on experience.

The use of manipulatives in mathematics classrooms throughout the world grew considerably in popularity throughout the second half of the 20th century. Mathematical manipulatives are frequently used in the first step of teaching mathematical concepts, that of concrete representation. The second and third steps are representational and abstract, respectively.

Mathematical manipulatives can be purchased or constructed by the teacher. Examples of commercial manipulatives include tangrams; Cuisenaire rods; numiconpatterns; color tiles; base ten blocks (also known as Dienes or multibase blocks);interlocking cubes; pattern blocks; colored chips;links; fraction strips, blocks, or stacks; Shape Math;Polydron; Zometool; rekenreks and geoboards. Examples of teacher-made manipulatives used in teaching place value are beans and bean sticks or bundles of ten popsicle sticks and single popsicle sticks.

Virtual manipulatives for mathematics are computer models of these objects. Notable collections of virtual manipulatives include The National Library of Virtual Manipulatives and the Ubersketch.

Multiple experiences with manipulatives provide children with the conceptual foundation to understand mathematics at a conceptual level and are recommended by the NCTM.

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