A child's work is to learn about the world around him or her. Math helps this world make sense. For example, understanding the concept of bigger and smaller helps children make choices, such as which piece of cake they want. Learning to measure, even with just his eyes, develops the ability to determine whether a table is a good hiding place in a game of hide-and-seek. Understanding the concepts of "more" and "less" might foster a sense of fairness, especially when a friend gets more pieces of candy.
Early math concepts help children to become more effective problem solvers. For example, a child might first use a shape-sorting toy by trying the different holes. She will eventually realize that each shape only fits into one type of hole and start trying to match the shape of the piece with the shape of the hole. Kids can also learn that there might be many different ways to solve a problem. One child may understand that when you add one to a group, the result is always the next highest number; another child might have to count all the items again to get the new total.
In math, each new concept tends to build on the concepts previously learned. When students gain confidence in their abilities from a young age, they may be more adept at advanced concepts later on. Additionally, students will find math in a variety of subject areas throughout their schooling, from datelines in history books to the advanced mathematics needed for AP chemistry. Starting early builds the foundation.
In the early childhood classroom, mathematical concepts are frequently taught through the use of manipulative toys. Children find this to be more fun than rote learning, and it can instill a lifetime love of math. Furthermore, in using these hands-on materials, a child can gain a deeper understanding of concepts like addition or multiplication, rather than memorizing and regurgitating the math facts.