Mathematics is a subject which requires precision and exactness. Without a concrete understanding of the mathematical concept, the child will encounter many difficulties in learning math.
We use 1 to represent the quantity of 1, and 2 to represent the quantity of 2 but in actual fact, numbers are just symbols without meaning or purpose. A child normally cannot conceive the quantity of a specific number.
Parents and teachers find it frustrating when the child is unable to tell them if 1 or 2 is a larger amount over and over again. For young children, they need to see and understand the concept in concrete form (something they can feel, manipulate with hands and experience) before they can transfer this concrete knowledge into abstract form of understanding. Therefore, the most effective way to help develop a young child’s math skill is to present mathematics to the child in its simplest form.
Forget about forcing your 2 years old to memorize the numerals 1 100 so she can beat your neighbour’s or best friend’s kid. For the young child, 2 and 100 are just figures or symbols with no real meaning, unless of course, you have first introduced to them what is 2 by allowing them to count and feel 2 items in their hands.
For example, you can put a basket of apples in front of your child and count 2 apples, then say: 2 apples, 2. This is 2. Then you continue to count 3 or 4 using apples. On another day, you can use another objects but they should be the same objects for counting different numbers so your child will not confuse the object and quantity.
Learning comes much more easily when the child works with concrete educational materials that graphically and physically show what is taking place in a given mathematical process. Without the concrete experience of manipulating and developing and understanding of the attributes of the physical world, the child has little preparation for tackling the abstract symbols for concepts they have not yet encountered.
When you are trying to introduce addition or subtraction, start by using objects so the child can have a strong visual impression of what addition/subtraction is. The key is to present the concept in a concrete form, and only introduce the symbol of + -etc later when the child has internalized these concepts.
By working with objects (concrete materials), the child is conceptualizing and understanding quantities. He is gradually able to associate the numeral to the quantity. Now mathematics makes sense to him.