Development of calculation abilities in young children.

This study investigates the development of skills for solving verbally and nonverbally presented calculation problems in children between 4 and 6 years of age. Identical addition and subtraction calculations were presented in three problem-type formats: nonverbal problems, story problems, and number-fact problems. The nonverbal problems involved presenting sets of physical referents that were then transformed either by adding or removing elements. The child saw the initial set and the number of elements that were added or removed, but not the final set. The task was to construct an array that contained the number of elements in the final set. The story problems and number-fact problems were presented orally, without props. Results indicate that children as young as 4 years of age have some success on the nonverbal problems, showing that they can transform sets by adding or subtracting elements. In contrast, children do not achieve comparable levels of success on the story problems or number-fact problems until 5 1/2 to 6 1/2 years of age. Moreover, throughout the age range tested, children performed better on nonverbal problems than on either story problems or number-fact problems. These results suggest that children's earliest ability to add and subtract is based on experiences combining and separating sets of objects in the world and that this ability precedes the development of conventional verbal methods of calculating.