In order for children to know mathematics, they must have a solid understanding of the four operations of addition, subtraction, multiplication and division.  The NCTM Standards assert that to understand the concepts of operations, children must be able to relate the use of operations to real-world experiences (NCTM, 1989).  In other words, children must know that what they are learning in school about the four operations has direct use in the real world.  What this means for teachers is that instruction should no longer focus on concepts and relationships (NCTM, 1989).  Research has shown that traditional textbook instruction underestimates children's mathematical ability (Baroody, 1993).  Children have a wealth of prior knowledge that they have gained from real-life experiences.  When children begin school, they have no formal knowledge of symbolic notation, but they have practical knowledge (Baroody, 1993).  Take, for example, a child who is asked to solve 5 + 7.  The child may have difficulty with this symbolic equation.  However, if the child is given 5 apples and 7 bananas, the child most likely can say that there are 12 pieces of fruit.  When a child is given concrete objects to manipulate, deep understanding of the operations will develop.  Students who are only taught the operations through the use of symbols are misled to believe that operations are only black marks on papers (Richardson, 1984).  They cannot make any connection to the real world. It is very important to model with concrete materials and to use real-life examples.

As a teacher or prospective teacher, it is good to have a solid understanding of the four operations.  Since many of us experienced math using rote memorization, it is helpful to review the elements of each operation to provide an understanding that will enable us to effectively teach students to use the four operations.

Addition:  Addition is the operation that is used to join things together and is the operation that students understand first.  There are two types of addition - combining and static.  Combining addition is the joining of two separate groups to form one whole group (Hatfield, 232).  For example, a sample problem would be:  Susie went to the market and bough 12 chocolate chip cookies and 10 sugar cookies.  How many cookies did she buy?