The foundation for children’s mathematical development is established in the earliest years. Mathematics learning builds on the curiosity and enthusiasm of children and grows naturally from their experiences. Mathematics at this age, if appropriately connected to a child’s world, is more than “getting ready” for school or accelerating them into elementary arithmetic. Appropriate mathematical experiences challenge young children to explore ideas related to patterns, shapes, numbers, and space with increasing sophistication.—(NCTM, 2000, p. 73)
Mathematics is a particular way of thinking and all children everywhere do it quite naturally. From their earliest encounters, children explore the abstractions of mathematics. Parallel to the development of language skills is the development of concepts related to basic areas of mathematics. We can follow the development of mathematical concepts as we look at infants and toddlers. The basic mathematical concepts addressed here are pattern, sequence, seriation, spatial relationships, object permanence, sorting, comparing, classifying, and one-to-one correspondence.
An important mathematical concept that infants develop is pattern. Pattern is the underlying theme of all mathematics and science. It is our ability to discover and recognize patterns that helps us understand how our world works in logical and predictable ways. Experiences with observing and making sense of patterns are what helps young children become logical thinkers who can reason and think critically.
As infants are cared for in predictable ways, they experience the idea of patterns. They easily begin to recognize and anticipate the rhythm or pattern of their care. As they experience this daily routine, infants come to anticipate the sequence of events. Such experiences are important to the development of recognizing the logical patterns that will be discovered later in their mathematical and scientific experiences. As babies approach their first birthday, they anticipate sequences and patterns in games that include patty-cake, peek-a-boo, singing, dancing, touching of the nose and toes, and feeling different textures. These rich experiences help children to develop the ability to predict and anticipate events.
Sequence, like pattern, is a mathematics concept that children internalize early in life. Sequence refers to the organization and order of successive events and experiences. Recognizing sequences helps young children’s developing sense of order, logic, and reason. They begin to recognize the sequencing of their day and are able to predict what may happen next. They may also observe the sequence of seeds growing into plants, the sun rising and setting, the melting of snow, or the leaves falling from the trees. Each of these events involves sequences in nature. As children become more sophisticated observers, they can discover sequences in daily activities and involvements.
Before the age of 2 years, children tend to involve themselves in activities that require sequencing, such as taking turns, following a certain order when doing a task, or learning how to get dressed. Children may also use sequencing in play; for example, they may push all the blocks off the table and then one by one pick them up and put them back on the table, only to knock them all off again. Young children often repeat a sequence of events numerous times, because the predictability of these actions is enjoyable.
As children listen to stories either from books or other people, they begin to build concepts for sequence: what comes first in the story, next, and how the story logically unfolds. They often like to predict what may happen next. This type of activity helps to build a mind-set for rational and logical thinking, which again are important skills for budding mathematicians and scientists.
When children play in a sandbox they are constructing. When they use building blocks they set goals for what they want to build. Playing with dolls and figures requires that the children develop story lines about what the dolls are doing. Playing with racing cars promotes decisions about which car comes in first. Each of these activities designed by children requires an understanding of the concept of order and sequence. We can evaluate children’s true understanding of sequence better by watching their actions than we can by listening to their verbalization. A child might be using sequence skills in many activities, but because of their developing language skills, may not be able to describe to you the process they are doing through play.
Soon after children start to make sentences, they give great detail about processes they use to make play-doh cookies, paint a picture, or create roads in the sandbox. They tell about how they will plant seeds in the garden or in the flower box.
Children will act out sequences of events with toy figures that may represent family members—Mom-mom, Poppy, Daddy, Mommy, Aunt Rachel, and cats Shadow and Sunshine. This type of play illustrates how a child makes sense out of events. Such active play fosters personal meaning (Isenberg & Quisenberry, 2002). Children can also be encouraged to put photographs of the family vacation at the seashore in order according to what happened first, second, and so forth. Such observations are valuable in evaluating the developmental level of children.
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