Manipulative (mathematics education)
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 common manipulatives include number lines, Cuisenaire rods; , blocks, or stacks; base ten blocks (also known as Dienes or multibase blocks); interlocking linking cubes (such as ); construction sets (such as Polydron and Zometool); colored tiles or tangrams; pattern blocks; colored counting chips; numicon tiles; chainable links; abaci such as "rekenreks", and geoboards. Improvised teacher-made manipulatives used in teaching place value include beans and bean sticks, or single popsicle sticks and bundles of ten 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. Some of the manipulatives are now used in other subjects in addition to mathematics. For example, Cuisenaire rods are now used in language arts and grammar, and pattern blocks are used in fine arts. (Wikipedia).
