Helping children learn mathematics is essentially the process of placing a numerical value on objects in the real world. Like learning to read, helping children learn mathematics, is a skill they were not born with and one that requires “internalization” of the basic concepts in mathematics. To a child the concepts are abstract. Your task as teacher is to help the child understand these concepts by using real objects so that the “connection” is made in the child’s mind between the real object and the “abstraction” of that object.
Essentially, there are just a few important concepts that a young child must learn. Mathematics starts with the concept of “how many” or counting. Then comes addition. Here again, addition is an abstract process. You must help the child understand that addition is just a “quick way” of “counting.” This is where helping children learn mathematics becomes more complicated. Many children learn quickly how to add, however, it takes time, with each child learning at a different rate, for the child to make the “connection” between counting and addition. The same is true of multiplication. While a child may learn the mechanics of multiplication, it takes time for each child to make the “connection” that multiplication is a “quick way” of addition. Next comes subtraction or “take away.” The important concept here is that subtraction is the “inverse” of addition. Now to division. This is probably the most difficult because the child must come to understand that division is just a “quick way” of subtraction.
Everything goes along fine until you get to fractions or “parts of a whole.” We often use “pie charts” to illustrate ½, ¼ and 1/8. The hardest part of helping children learn mathematics is for them to understand that they are taking a “whole” of something and breaking it apart. Next comes decimals. Here the child must build upon the concepts of “parts of a whole” and make the connection that decimals are just another way to showing the same thing. The hardest part is for the child to make the connection between ½ of something and the decimal expression of .5 Then comes the hardest and must confusing concept, that of “percent.” The child has already learned to work with decimals but now must focus on the concept that “percent” “always” means “parts of one hundred” and the decimal point is “always at “two places.”
Let’s take some examples. Always use real objects. In a very young child start by using your fingers to count 1,2,3. This is easy. However, the child now has to connect the numbers 1,2,3 with real object that are “outside” of his/her body. Now you ask the child “bring me” two of something. When he/she can do this you know that the understands the concept of counting. Do the same with addition. Empty your silverware drawer on the table. Ask the child to make a pile of say 4 knives. Now ask him/her to make another pile of 3 knives. Now ask him/her to tell you “how many” in the two piles together. Use real objects throughout your teaching, even to the point of using 100 objects of something real for per cent.