e that these classes are formed only on the basis of perceptual attributes such as color and form and not on the basis of any quantitative characteristics. Moreover, although children can name and identify members of different classes cow, dog, or car, they cannot as yet operate on these categories in a systematic way. That is to say they cannot logically add categories and recognize that cats, dogs, and cows are all animals. Nor can they logically multiply classes and appreciate that a cat is both a cat and an animal at the same time.
             In short, the one-many or quantitative dimension of classes escapes young children. Only when they have attained the concrete operations of childhood (age 6 to 7 years) will they begin to be able to coordinate sameness and difference and arrive at the notion of a unit that is basic to all quantitative thinking. A unit, for example the number 3, is at once like every other number in that it is a number but also different in that it is the only number that comes after 2 and before 4. Once children have a notion of a unit, they can engage in numerical as well as logical addition and multiplication (Gesell, 1949).
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