His teacher and principal are interested in trying to determine what level math he is capable of doing and plan to construct a program especially for him. My husband and I do not "work with him" and have not explained the traditional way to add. He has his own way of calculating in his head.
My questions are: First, what is the best way to evaluate his ablility? Second, should he learn the traditional way to calculate, or continue using his own way?
It's great that the teacher and principal also recognize your son's talent and are willing to develop a special program for him. A fuller understanding of young children's math abilities is gained through giving them individual intelligence and achievement tests. These tests can determine the appropriate instructional level for your son in math.
Instruction for young children who are gifted in math typically allows them to move at their own pace, and to work on challenging problems. The math instruction should emphasize concepts rather than procedures, allowing kids to construct their own ideas about how math works. Clustering gifted students together for math instruction also helps.
Good mathematical instruction, according to the National Council of Teachers of Mathematics, teaches children to become problem-solvers, to reason mathematically, to value math, and to become confident in one's own ability. It's also important that children be assessed frequently to monitor their mastery of concepts.
An accelerated math curriculum coupled with exposure to others who are gifted in and interested in math is the best way to maintain your son's motivation in math.