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 19th 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.
As previously stated, “manipulatives help children visualize abstract mathematical ideas (Heuser, 2000, p. 288). Students are able to use hands-on activities to create a knowledge base for mathematical thinking, allowing a greater understanding of the nature of mathematics, and some of its basic concepts, at an earlier age (McCarty, 1998). This is based on the findings of people such as Piaget, who helped prove that young children at the Primary and Elementary grades think at the concrete level. Therefore, the use of concrete objects in teaching abstract ideas would bring these abstract ideas down to the students’ concrete level, making problems tangible and tractable for these young learners (Uttal, Scudder & DeLoache, 1997).
The value of mathematical manipulatives can also be seen in the work of Driscoll, Sowell, and Suydam, who all discovered that students who use manipulatives outperform students who do not use them (Clements and McMillen, 1996). And this is not just true of students at the concrete level of thinking; students in all grade and ability levels, as well as students working in many topics, benefit from the use of manipulatives (Clements and McMillen, 1996). In the Driscoll, Sowell and Suydam study, retention and problem solving test scores were also improved if the students were exposed to manipulatives, and “attitudes toward mathematics [were] improved when students are instructed with concrete materials by teachers knowledgeable about their use” (Clements and McMillen, 1996, p. 270).
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