The Three Stages of Learning [back to top]
Research has found that children move through three developmental learning stages;
     1- Concrete or manipulative
     2- Representational or transitional
     3- Abstract

When they start at kindergarten, children are in the concrete stage where they must touch things and move them around to develop basic math concepts. Piaget has found that the majority of children do not become abstract until between the ages of 12 and 14. To assist the movement through the transitional stage to the abstract, students must be provided with developmentally appropriate materials and activities. This is why MANIPULATIVES are so important.

Studies Confirm that manipulatives are the missing link to help students move from the concrete stage to the abstract stage.
     These studies also find that students who learn math with these type of models:
           -Understand math better
           -Develop better problem solving skills
           -Do better on standardized achievement tests.

Role of Manipulatives  [back to top]
Abstract Becomes Concrete
Manipulatives are basically models that children use to learn how math works.
In other words, they help represent abstract ideas. For example, you might use interlocking cubes to teach children addition.  They might use 9 green cubes and 7 red cubes to show that 9+7=16.  
At the same time, they can also see that 9 is composed of two different numbers.  Later, they will break apart cubes to discover that 16 can be made with many numbers.

Manipulatives Make Math Fun!
Manipulatives not only help children understand math, they also make math more fun. In the primary grades children use teddy bear counters and toy vehicle counters to sort, pattern and count. For example, in the Primary Kindergarten book, children use the teddy bear counters to tell number stories on a playground with a slide and sandbox.

Manipulatives Benefit Children in Higher Grades  [back to top]

Children in higher grades get the same benefit from using manipulatives such as fraction bars, fraction circles, colored number rods and the base ten blocks. 

Base ten blocks are the most versatile manipulative as they represent the abstract concept of place value in the Hindu Arabic Number System. After children discover the important pattern of tens, that is, that 10 ones are the same as 1 ten and 10 tens are the same as 1 hundred, they use this pattern to add, subtract, multiply and divide with whole numbers, decimals and percent.