What are Math Manipulatives?

A mathematical manipulative is “an object which is designed so that the student can learn some mathematical concept by manipulating it” (Wikipedia, 2006). Students can use objects as counters, play with geometrical shapes to form other shapes, can build models to understand three dimensional figures, etc. In the manipulation of these materials, students are able to learn abstract concepts in concrete, hands on ways. These materials make even the most difficult mathematical concepts easier to understand for the student (Uttal, Scudder & DeLoache, 1997).

Manipulatives have been around for many years. One of the early versions of a manipulative, the abacus, can be dated back to 300 B.C. (About, 2005). This abacus, known as the Salamis Tablet, was used by Babylonians and was discovered in 1846 (About, 2005). Manipulatives have developed greatly from this early counting device.

A new push for the use of manipulatives occurred in the 19^th century when Pestalozzi lobbied for their use, eventually making manipulatives part of the mathematics curriculum in the 1930’s (Sowell, 1989). In the 1960’s, another resurgence of the use of manipulatives occurred, with a focus on the use of concrete objects and pictorial representations to help children better understand abstract mathematical ideas (Sowell, 1989). Now, manipulatives are available in almost every classroom around the world.

Many varieties of manipulatives are available. These objects can be commercially purchased, downloaded online, or with some creativity, can be made by both the teacher and students. Some examples of manipulatives include tangrams, interlocking blocks, Dienes blocks, counters, geoboards, fraction kits, base ten blocks, pattern blocks, geo strips, and fraction strips. Some of these manipulatives are shown below. For these and many other manipulatives, please visit the National Library for Virtual Manipulatives, located in the links section, as well as other useful websites. Also, manipulatives which can be photocopied are available at the back of our text book.