Number Sense and Numeration In grades K-4, the mathematics curriculum should include whole number concepts and skills so that students can understand our numeration system by relating counting, grouping, and place-value concepts. Children must understand numbers if they are to make sense of the ways numbers are used in their everyday world. They need to use numbers to quantify, to identify location, to identify a specific object in a collection, to name, and to measure. Further-more, an understanding of place value is crucial for later work with number and computation. Prior to formal instruction on place value, the meanings children have for larger numbers are typically based on counting by ones and the "one more than" relationship between consecutive numbers. Since place-value meanings grow out of grouping experiences, counting knowledge should be integrated with meanings based on grouping. Children are then able to use and make sense of procedures for comparing, ordering, rounding, and operating with larger numbers. Mathematics as Communication In grades K-4, the study of mathematics should include numerous opportunities for communication so that students can reflect on and clarify their thinking about mathematical ideas and situations. Mathematics can be thought of as a language that must be meaningful if students are to communicate mathematically and apply mathematics productively. Communication plays an important role in helping children construct links between their informal, intuitive notions and the abstract language and symbolism of mathematics; it also plays a key role in helping children make important connections among physical, pictorial, graphic, symbolic, verbal, and mental representations of mathematical ideas. When children see that one representation, such as an equation, can describe many situations, they begin to understand the power of mathematics; when they realize that some ways of representing a problem are more helpful than others, they begin to understand the flexibility and usefulness of mathematics. Young children learn language through verbal communication; it is important, therefore, to provide opportunities for them to "talk mathematics." Interacting with classmates helps children construct knowledge, learn other ways to think about ideas, and clarify their own thinking. Writing about mathematics, such as describing how a problem was solved, also helps students clarify their thinking and develop deeper understanding. Reading children's literature about mathematics, and eventually text material, is also an important aspect of communication that needs more emphasis in the K-4 curriculum. Reprinted with permission from Curriculum and Evaluation Standards for School Mathematics. Order from NCTM, 1900 Association Drive, Reston, VA 22091. Telephone: 1-800-235-7566.

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