Measure 26 — MATH 1

Number Sense: Understands Quantity and Counting

Child uses number names to represent quantities and count increasingly larger sets of objects

Learning about numbers and how to use them in a meaningful way to quantify things is an important achievement of early childhood. For the young child, this involves learning the words for numbers (including the counting series), understanding that a number word refers to a particular quantity, and learning how to count objects to find out how many are in a group.

Infants begin to build a foundation for understanding concepts about objects and quantity as they attend to and manipulate objects in their everyday environment. Research has shown that infants can discriminate between very small numbers of objects (1 vs. 2 or 2 vs. 3) and can discriminate differences between larger groups (6 vs. 16). In their play, they organize objects into groups and manipulate amounts. For example, a child might place one plastic ring on top of another, then remove it and replace it with a different ring; or he might put toys in a container one by one, dump them out, and then do it again. In their social interactions, infants hear and begin to register the meaning of number words as they are used to refer to groups of things.

Even very young children appear to know that number words have special quantitative properties. Toddlers begin to use the number words they are learning to label quantities. The word “two” is usually used first, then “one” and “three,” although they are not always used accurately. Toddlers may even show some beginning notions of counting by randomly pointing at objects and saying the number words they know.

Young preschoolers can typically use the number words “one,” “two,” and “three” to identify very small quantities without counting them. The onset of rote counting varies greatly among children, depending on their experience. Most young preschoolers learn to recite the number series to ten and are beginning to try to count objects. When taught to coordinate their number words with their counting actions (one word, one object), young preschoolers are capable of learning to count objects accurately. Additionally, with instruction, they have the capacity to understand that the last number word in the count gives the total number in the counted group. Young preschoolers are first successful counting very small groups of objects (two or three). Since preschoolers are also able to quantify these very small groups without counting, early experiences with very small numbers can aid children’s understanding of counting. With experience, young preschoolers learn to count five or more objects accurately.

With support and experience, children’s skills and conceptual understanding of number and counting continue to develop. Older preschoolers learn to count larger groups, up to ten objects or more, and their counting becomes more purposeful and numerically meaningful. They are increasingly able to count accurately and reliably to find out how many; to count out objects to produce a given number; and to solve simple, everyday problems with numbers, for example, by counting the napkins at a snack table to make sure there are enough to go around. Toward the end of preschool or during kindergarten, young children begin to learn that written numerals represent the number of objects in a group.