Values of Manipulatives

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).

The ability for a manipulative to present different situations to students is important. Through the various manipulations they encounter with one form of manipulative, students begin to recognize common mathematical elements (Fennell and Rowan, 2001). This understanding of the concepts students learn can also be enhanced if students can transfer their understanding to various manipulatives using the same idea (Fennell and Rowan, 2001). Also, students using manipulatives to represent concepts “give[s] learners useful tools for building understanding, communicating information, and demonstrating reasoning” (Fennell and Rowan, 2001, p. 289). From this evidence it can be seen that manipulatives can be an asset to any classroom.