Discovering and Internalizing Numbers

We use the ideas in the Mathmatics Their Way Program to get an  understanding for the concept of number.  Each child explores the numbers in order from two to ten in a variety of ways using many different materials such as wooden cubes, pattern block, toothpicks, tiles, geoboards, Unifix cubes, beans, jewels, and junk boxes.  Here  are examples of using three of these materials to internalize the number 5.
 

There is a lot more happening  than counting objects in these activites.  Children are discovering and internalizing the unique patterns and combinations each number forms naturally.  The understanding children gain from exploring the numbers below six have a profound impact on their later explorations, for understanding all the numbers greater than five is based on concpts discovered for five and below.  If a child sees a group of seven object pushed together she or he would not immediately think seven.  The child separates them in hisorher mind, seeing perhaps three and four, and the thinking seven.
 

The concept of number is extended further as the children explore and record these combinations in the mathmatical operation of addition as shown here.
 

These experiences are the building blocks for the later stages of the child's number concept development in mathematics;  if this foundation is firmly laid, dealing with abstract numbers will be easy.

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