Attractive Objects May Be Distracting Manipulatives

Another implication of the present analysis is that objects that are interesting in their own right may not make the best manipulatives. Observations of manipulative use in other countries have supported the idea that a good manipulative is not necessarily an inherently interesting object. For example, in Japan, children use the same set of manipulatives throughout the early elementary school years. Stevenson and Stigler (1992, pp. 186-187) who have conducted several cross-national comparisons of mathematics achievement in Asia and the United States, have observed the following:

Japanese teachers . . . use the items in the math set repeatedly throughout the elementary school years. . . . American teachers seek variety. They may use Popsicle sticks in one lesson, and marbles, Cheerios, M&Ms, checkers, poker chips, or plastic animals in another. The American view is that objects should be varied in order to maintain children's interest. The Asian view is that using a variety of representational materials may confuse children, and thereby make it more difficult for them to use the objects for the representation and solution of mathematics problems. Multiplication is easier to understand when the same tiles are used as were used when the children learned to add.

In summary, one of the challenges of effective use of manipulatives is that children sometimes have difficulty linking manipulatives-based solutions to written solutions. In this regard, the concreteness of the manipulatives may contribute to the problem by focusing children's attention on the characteristics of the objects themselves rather than on what the objects are intended to represent. It is important to stress that this perspective does not mean that manipulatives are not useful or are harmful to children's learning. Using manipulatives can indeed help mathematical thinking in several ways (see, for example, Martin & Schwartz, in press). Thus we do not deny that manipulatives can serve an important role in preschool and early elementary school education. However, effective use of manipulatives requires that teachers consider both the advantages and disadvantages of using manipulatives. In this regard, we have identified a possible challenge of using manipulatives—children may have difficulty relating manipulatives-based solutions to written solutions.

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