Early Childhood - Connecticut State Department of Education

Mathematics Chapter 6
Representing
Representation is a means of communicating. Learners
should be encouraged to represent their thinking by
using clay, blocks, drawing, language, diagrams, charts
and eventually number symbols. Merely writing number
symbols should not be a primary focus. The experience
of conveying thoughts becomes a tool for making
relationships in mathematics. Children remember what
they were thinking, rethink new possibilities and make
connections to new and old ideas. Representation is
an opportunity to revise and make thoughts clearer to
ourselves and to others. To encourage development of
representation skills, teachers should use the following
strategies:
• encourage representation as a continuous
journey rather than as discrete projects that
are finished and never addressed again;
• make learning an ongoing series of
investigations that are all connected and
integrated by the learner; and
• encourage children to visually and
physically represent math ideas with blocks,
manipulatives, in drawing and in many
media forms.
CONTENT STANDARDS
This section presents broad concepts that should be
included in a preschool mathematics curriculum. Each
concept includes appropriate performance standards, a
brief description of the topic area, skills to be cultivated,
suggested teacher strategies, and ideas for maintaining
a home-school connection.
Number Sense And Operations
Performance Standards
• Demonstrate understanding of one-to-one correspondence
while counting.
• Show curiosity and independent interest in
number-related activities.
Number sense is the ability to think and work with
numbers, and to understand their uses and relationships.
This ability includes:
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• distinguishing between small and large
groups;
• understanding the relationship between and
among quantities;
• using one-to-one correspondence; and
• understanding operations such as adding
and subtracting.
Research indicates that the development of
number sense is the most important element in preschool
mathematics (NCTM, 2000). The development of number
sense and the understanding of operations provides the
foundation for much of what is taught in mathematics.
Young children come to preschool with many informal
mathematical experiences, for example those of quantity
or comparison. Their existing knowledge must be
connected with the language, symbols and operations
of mathematics (Griffin and Case, 1998; Gelman and
Gallistel, 1978).
In teaching preschool mathematics, the focus
should not only be counting, reading and writing
numbers. It is more important that children spend
time creating a mental structure for number concepts.
Encouraging thinking, making decisions and talking
about quantity is the main goal (Kamii, 2000). Consider
the experience of preparing a snack. Instead of giving
specific directions such as, Please get 15 napkins, try
asking children to gather enough napkins for everyone
(Kamii, 2000). This encourages problem solving. The
child may count the children; use trial and error with a
random number; or create a one-to-one correspondence
with the children or chairs. Whatever process is chosen,
the experience of thinking and doing results from
purposeful teaching that helps children learn to use
numbers rather than just count.
Understanding quantity is central to developing
one’s mathematical thinking abilities. Multiple
experiences in counting help children understand that
the last number in a counting sequence represents the
entire quantity. As children come to understand quantity,
they begin to understand part and whole relationships
and to see many ways to use and represent numbers.
(For example: “There are 10 children here today. Four of
them are girls.”) This gradually leads to the child’s ability
to see relationships around increasing and decreasing
quantities (Ginsburg, Greenes and Belfanz, 2003).