Foundational mathematics content for the learning in the early childhood

Abstract

This chapter describes the foundational and achievable mathematics content for young children. The focus of this chapter is on the mathematical ideas themselves rather than on the teaching or learning of these ideas. These mathematical ideas are often taken for granted by adults, but they are surprisingly deep and complex. There are two fundamental areas of mathematics for young children: (1) number and (2) geometry and measurement as identified in NCTM's Curriculum Focal Points and outlined by this committee. There are also important mathematical reasoning processes that children must engage in. This chapter also describes some of the most important connections of the mathematics for young children to later mathematics.

In the area of number, a fundamental idea is the connection between the counting numbers as a list and for describing how many objects are in a set. We can represent arbitrarily large counting numbers in an efficient, systematic way by means of the remarkable decimal system (base 10). We can use numbers to compare quantities without matching the quantities directly. The operations of addition and subtraction allow us to describe how amounts are related before and after combining or taking away, how parts and totals are related, and to say precisely how two amounts compare.

In the area of geometry and measurement, a fundamental idea is that geometric shapes have different parts and aspects that can be described, and they can be composed and decomposed. To measure the size of something, one first selects a specific measurable attribute of the thing, and then views the thing as composed of some number of units. The shapes of geometry can be viewed as idealized and simplified approximations of objects in the world. Space has structure that derives from movement through space and from relative location within space. An important way to think about the structure of 2-D and 3-D space comes from viewing rectangles as composed of rows and columns of squares and viewing box shapes as composed of layers of rows and columns of cubes.