The experiences of young students just entering school can vary greatly, depending on their maturity and the opportunities they've had. This is especially true of their communication skills. The following examples of communication are presented in developmental order. These skills, however, are not developed in isolation -- that is, as one type of communication is experienced and used, the use of other forms of communication will be developing as well.

For very young children, non-verbal communication, such as gestures and the use of materials to demonstrate their thinking is the earliest form of communication. For example, as children attempt to recognize and describe a shape, they might begin by "drawing" the shape in the air. Walking around the shape drawn on the floor or the ground is another way for children to use movement to develop, demonstrate, or communicate their early understanding of a mathematical idea. As a group, children can also represent geometric figures by holding yarn, string, or rope, for instance, each child could stand at a vertex (corner) of the figure. (This is a particularly good way to show that a triangle is any shape with three corners and three sides.) Physical movement helps young children internalize these mathematical ideas before they may be ready for the more formal types of communication.

Think back to the "Finding the Area of Dot-Paper Shapes" activity. This activity could be used with younger children who might try to draw the shapes in the air to act them out, as shown below:

Another non-verbal form of communication for children is to demonstrate their thinking using manipulative materials -- ideally, items from their own experiences. Sorting buttons, making a "graph" by sorting real objects into piles, grouping pennies, and building with geo-blocks are all examples of communicating mathematical thinking by using manipulative materials.

  Some additional communication strategies