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COPYRIGHTED MATERIAL There are five content standard domains in mathematics: 1. number and operations 2. algebra 3. geometry 4. measurement 5. data analysis and probability Although the focus in early childhood education is on number and operations, geometry, and measurement (National Council of Teachers of Mathematics 2006), all five content standards are interconnected and important for STEM education. For young children, number and operations includes quantifying small amounts, comparing sets of objects as more, less, or equal, counting, ordering numbers (first, second, last, and so on), patterns. The language of math that permeates math-rich classrooms helps children analyze problem situations. An example of this might be whether three friends can go to the gross-motor room together when only two spaces are open on the waiting list. The concrete materials that are a mainstay in quality programs enable children to represent mathematical problems in ways that they can understand. Geometry in the early years involves much more than naming shapes. It also includes un- derstanding spatial relationships, positional statements, and the properties of two- and three- dimensional objects. Through concrete experi- ences with blocks and other materials, children form the foundation for later, analytic processes in geometry. Measurement for young children includes •• understanding the measurable attri- butes of objects, •• constructing the concept of an appro- priate unit of measure, combining sets (early addition) •• the application of number to measure- ment, and taking away from sets (early subtrac- tion), and •• measurement comparisons. dividing materials among friends (early division). It involves understanding underlying relation- ships, such as one-to-one correspondence (one number word for each object counted) and cardi- nality (the last number counted equals the total). Much of the mathematical learning that occurs through children’s play involves number and operations. Algebra includes understanding patterns and relationships, as well as analyzing, represent- ing, and modeling mathematical situations. In preschool and kindergarten, children construct algebraic relationships by sorting and classify- ing materials and eventually arranging them in 8 c ha p te r 1 Seriating, or ordering objects by size, is an aspect of measurement frequently explored by young children. Data analysis encompasses •• gathering information, •• organizing the information in a useful way, and •• asking and answering questions related to it. For young children, data come from their life ex- periences. They may sort their toys into groups, compare how many buttons are in two groups, or vote for their favorite fruit. Preschool and kin- dergarten teachers often help children organize this information on a bar graph. The probability COPYRIGHTED MATERIAL