If one set has members left over after this pairing, then that set has a greater numerosity (more items in it) than the other does. One common conception of whole number says that two sets have the same numerosity (same number of members) if and only if each member of one set can be paired with exactly one member of the other (with no members left over from either set). To get a sense of both the difficulty of the concept and how much of it is taken for granted, try to define what a whole number is.
The most fundamental concept in elementary school mathematics is that of number, specifically whole number. In this chapter we describe the current state of knowledge concerning the proficiency that children bring to school, some of the factors that account for limitations in their mathematical competence, and current understanding about what can be done to ensure that all children enter school prepared for the mathematical demands of formal education. During the last 25 years, developmental psychologists and mathematics educators have made substantial progress in understanding the ways in which these strands interact. Preschoolers’ mathematical thinking rests on a combination of conceptual understanding, procedural fluency, strategic competence, adaptive reasoning, and productive disposition. Applying the framework to research on preschoolers’ mathematical thinking also provides a good example of the way in which the strands of proficiency are interwoven and interdependent. That framework is useful in thinking about the skills and knowledge that children bring to school, as well as the limitations of preschoolers’ mathematical competence. The state of children’s mathematical development as they begin school both determines what they must learn to achieve mathematical proficiency and points toward how that proficiency can be acquired.Ĭhapter 4 laid out a framework for describing mathematical proficiency in terms of a set of interwoven strands. Starting from infancy and continuing throughout the preschool period, they develop a base of skills, concepts, and misconceptions about numbers and mathematics. THE MATHEMATICAL KNOWLEDGE CHILDREN BRING TO SCHOOLĬhildren begin learning mathematics well before they enter elementary school.
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