Number Sense and Numeration
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
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
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.
with permission from Curriculum and Evaluation Standards for
School Mathematics. Order from NCTM, 1900 Association Drive,
Reston, VA 22091. Telephone: 1-800-235-7566.