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
At a young age, children
function in a concrete stage in which 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, (the stage in which traditional math takes place) 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
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Abstract Becomes Concrete
Manipulatives are basically models
that children use to learn how math works.
They 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 16 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, count
and use their imagination. For example, in the
Primary Kindergarten book, children use the teddy bear counters to tell number stories on a
picture of a playground scene, complete with a slide and sandbox.
Manipulatives Benefit
Students in Higher Grades [back to
top]
 Older
students 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 because 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.
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