ABSTRACT
Mathematics education research clearly shows the value of using manipulatives to introduce topics. This is the concrete stage, providing a firm foundation for growth through the semi-concrete and semi-abstract stages, with the ultimate goal of reaching the abstract level. When teaching mathematics, we use counting and grouping skills to identify numbers. Cardinal number of a set shifts the focus to the number of elements in a set. The smallest set where all the number properties are present is the rational numbers. Addition on the number line is similar to the pictures generated when using Cuisenaire Rods. The Cuisenaire Rods can be used to do any whole number subtraction problem. As students successfully sort, classify, and perform operations on objects at the semi-concrete level, they begin to move to the semi-abstract level by using figures or marks to represents the cardinality of a set.
