This first process involves the preschool child's ability to solve a variety of math problems given to him. Not only is this viewed from the perspective of the variety of problems, such as word or number problems, but also how the preschool child explains his mathematical process when completing the tasks. For a preschooler, this process will be very basic, but it is important to help him see the importance of the problem-solving process even at this young age.
Teach your preschoolers that math is more than memorization; it is proving an answer to a mathematical problem. For young children, simple math problems that use Cognitively Guided Instruction forces them to focus on the process rather than simply the right answer. A CGI problem is any math problem that is presented to children in a way that allows them to solve it using any method that suits their needs. The manipulatives used with CGI allow you to see the child's thought process, even if the young child is not able to articulate it to you.
The importance of communicating mathematical ideas is the focus of this third NCTM standard. A preschooler should not only solve the problem, but also gain the ability to talk about the answer and understand its meaning. Encourage this in your preschool classroom by allowing group work when teaching math. Children will then be forced to work with their peers and practice math communication skills.
NCTM emphasizes the importance of establishing a connection between math concepts and the real world. Develop your preschool math lessons around daily activities and relate them to other areas of academic instruction. For example, you may ask students to count the number of pencils in your classroom and make sure there are enough for each member of the class. This type of math lesson will help your preschoolers relate the importance of math to everyday life.
Many mathematical concepts are represented in visual formats in our everyday world. It is therefore important to teach this concept to your preschoolers. Introduce this NCTM standard through the use of simple graphing lessons. For example, create a simple bar graph representing your class' favorite foods. A student then begins to understand how math concepts can be represented in a variety of visual ways.