Emergent mathematics is a term we will use to describe how children construct mathematics from birth and continuing throughout the life of the person through a combination of cognitive development and interaction with their environment. The principle is similar to the concept of emergent literacy, which has become the standard for teaching children to read and write in early childhood classrooms. Both emergent mathematics and emergent literacy suggest that, young children, whether they are 6 weeks, 6 months, or 6 years old need to be immersed in mathematics and literacy from the day they are born, through interactions with parents or caregivers.
Educators and researchers are beginning to look at the construction of mathematical concepts the same way that we understand literacy development—as emergent. The idea that literacy learning begins the day that children are born is widely accepted. Noam Chomsky has discovered strong evidence for an innate “language acquisition device” that provides humans with a framework for learning language (Chomsky, 2006; Chomsky, Belletti, Rizzi, & Chomsky, 2002). The internal structure of this “device” allows children to interact with language at a very early age without being directly taught the rules of grammar and syntax (Otto, 2002). Reading to infants, toddlers, and preschoolers is known to be an early predictor of positive literacy because it immerse children in language and gives them an opportunity to interact with it (Feiler & Webster, 1997; Kamii, Manning, & Manning, 1991; Lally et al., 2001; Pickett, 1998).
Mathematical understanding can be viewed in a very similar way. During the first few months of life, children begin to construct the foundations for future mathematical concepts as they interact mentally, physically, and socially with their environment and with others. Even before a child can add or count, he must construct ideas about mathematics that cannot be directly taught. Just as emergent readers learn that letters in the alphabet correspond to spoken sounds the understanding that numbers have a quantity attached to them is actually a complex relationship that children must construct (Xu, Spelke, & Goddard, 2005). There is evidence for a “mathematics acquisition device” (MAD) that provides a framework for mathematical concepts similar in function to the “language acquisition device” (Sinclair, Kamii, & University of Alabama at Birmingham, 1994; Sinclair & Kamii, 1995). This MAD allows children to:
- Naturally acquire some mathematical concepts even without direct teaching;
- Follow a generally standard sequence of gradual development;
- Construct mathematical concepts from a very early age.
With careful examination of infants, toddlers, preschoolers, and children in primary grades, one can see evidence of all these criteria.
Young children may not be able to add or subtract, but the relationships they are forming and their interactions with a stimulating environment encourage them to construct a foundation and framework for what will eventually become mathematical concepts (Powell & Butterworth, 1971; Butterworth, 1999a, 1999b, 1999c). If you watch long enough you will see some amazing mathematical thought going on in even the youngest children (Butterworth, 1999). Consider the following example:
An 18-month-old child playing in a large pit filled with different colored balls drops one ball, then a second ball, and then a third ball over the side of the pit. The child then goes to the opposite side of the pit and drops two balls. He then goes back to the first side, reexamines the grouping of balls, moves to the second side and drops another ball over the side to make a grouping of three.
The coordination and comparison of “threes” on opposite sides of a structure is clear evidence of this 18-month-old child making a mathematical relationship and putting order into his world. It is not yet a numerical relationship because the child is solely using visual perception—what he sees—to make the judgment of “same” or “different.” However, the coordination of dropping three balls each time is evidence of an early understanding of “more,” “less,” and basic equality. This child may not be developmentally ready for number concepts like counting and quantification, which we will discuss in Part II, but this simple task shows that children as young as 18 months are making relationships and exercising their logical thought processes. Teachers of infants and toddlers need to be aware of these actions and abilities and provide activities to encourage construction of these mathematical concepts. Emergent mathematics continues throughout early childhood. Encouraging children to construct many different relationships between and among objects, to interact with other children and adults, and to mentally and physically act on the objects around them promote the concept of building we refer to in discussions of emergent mathematics.
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