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Materials for Teaching Mathematics |
Manipulative materials are an important part of introducing students to a new or more complex mathematical concept or procedure. They have a significant effect upon what children learn and the ideas they construct. To help select the appropriate manipulative the following categories of manipulative materials can be identified.
| Concrete "Concrete" materials are the most basic form of manipulative. The size of the referent is maintained throughout the manipulative. For example, a piece or pieces representing 10 will be exactly ten times larger than the one. Examples of concrete materials are Cuisenaire rods, Base Ten or Dienes blocks and most plastic or wooden cubes. |
Symbolic Symbolic materials are those comprising numerals and other symbols such as pictures, shapes and patterns. Examples of symbolic materials are Rook cards, playing cards, some dominoes, and numeral cards.
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| Representational Representational materials are those where a piece of the material represents a certain number but is not proportional to the referent (one) in size. Chip trading is a good example of this type. Plastic blocks can be used as a representational materials when the red one, for example, equals ten blue ones. |
Tools Tools are the manipulatives that we use to help us solve problems in mathematics. They come in many forms and sizes and levels of complexity. Examples of tools commonly found in the middle school curriculum are graphing calculators, protractors, compasses, and rulers. |