This article offers a new perspective on the use of concrete objects to teach mathematics. It is commonly assumed that concrete manipulatives are effective because they allow children to perform mathematics without understanding arbitrary, written mathematical symbols. We argue that the sharp distinction between concrete and abstract forms of mathematical expression may not be justified. We believe instead that manipulatives are also symbols; teachers intend for them to stand for or represent a concept or written symbol. Consequently, research on how young children comprehend symbolic relations is relevant to studying their comprehension of manipulatives. We review evidence that many of the problems that children encounter when using manipulatives are very similar to problems that they have using other symbol systems such as scale models. Successful use of manipulatives depends on treating them as symbols rather than as substitutes for symbols.
ASJC Scopus subject areas
- Developmental and Educational Psychology