Indicator: Math (MATH)

Children demonstrate competence in real-life mathematical concepts

Young children’s mathematical knowledge includes a wide range of skills and concepts about number, space/geometry, and logical relationships, as well as beginning ideas about measurement, patterns, and time. This developing knowledge is based primarily on children’s manipulating of and thinking about concrete objects. Concrete ideas about such concepts as number and shape develop through the everyday experiences children have with objects. Young children also acquire conventional math-related knowledge through their everyday interactions with adults and peers. This knowledge includes mathematical language, such as number words and comparison terms (“more,” “less,” and “same,” for example) that are then incorporated into their developing understanding of concepts.

Mathematical knowledge begins to develop in infancy and undergoes extensive development throughout infancy and early childhood. Infants are sensitive to quantitative (size and amounts) and spatial (location of objects in space) information in their environments. They attend to and manipulate objects. As they explore and act on their environment, they develop a conceptual understanding of physical objects and the relationships among them.

Toddlers’ growing understanding of number and of quantitative and spatial relationships is demonstrated by the way they manipulate objects in their everyday activities. For example, in their play they notice that adding objects to a group makes it bigger and taking objects away makes it smaller. They put objects together (on top of each other, for example, or one item inside another) in ways that show a growing attention to physical properties and relationships. In addition, they are beginning to acquire and use math-related language, such as number words and words that refer to measurable physical properties, such as size (“big” and “little,” for example).

These emerging concepts continue to develop during the preschool period. The numerical abilities of young preschoolers become more exact, at least when they are dealing with very small numbers. For example, they learn to identify, match, count, and even solve simple addition and subtraction problems with groups of up to three objects. They also begin to match and name simple, familiar geometric shapes. Still, much of the mathematical thinking of young preschoolers tends to be more qualitative than exactly quantitative, since it relies heavily on the overall appearance of things.

The mathematical thinking of older preschoolers becomes more quantitative and exact. Older preschoolers can learn to apply purposeful strategies to finding out about numbers and shapes and to solving problems. For example, they may use a calculation strategy, such as counting objects or fingers, to solve simple arithmetic problems. Or, they may use a simple measurement strategy, such as directly comparing height, in order to position several objects in a series, from shortest to tallest. Children’s knowledge of the concrete world continues to develop well beyond preschool and forms an important foundation for the symbolic knowledge of math that they will learn in school.