California Preschool Learning Foundations - ECEZero2Three ...

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Research suggests that children
start developing number sense in early
infancy (Feigenson, Dehaene, and
Spelke 2004). Much of what preschool
children know about number is closely
related to and depends on their understanding
and mastery of counting
(Adding It Up 2001). Counting builds a
foundation for children’s future understanding
of mathematics, and this
basic skill becomes the reference point
as children learn to manipulate larger
quantities in the future.
Children’s understanding of numbers
is initially qualitative, as they gain
an understanding of “number-ness”
(e.g., three-ness, four-ness) with small
quantities, using subitizing: visually
knowing “how many” are in a set without
actually counting them (Clements
2004a; Fuson 1988, 1992a). Counting
is a natural activity for young children
as their everyday contexts often involve
numbers and quantities, although it
requires them to have a sophisticated
set of skills based on many experiences
to be able to count accurately.
Literature suggests that the three
major basic building blocks for counting
are learning of (1) the sequence of
number words, (2) one-to-one correspondence,
and (3) cardinality (knowing
that the last number assigned to
the last object counted gives the total
number in the set) (Adding It Up 2001;
Becker 1989; Clements 2004a; Fuson
1988, 1992a, 1992b; Hiebert and
others 1997; Sophian 1988). Children
are likely to experience the aspects
MATHEMATICS Number Sense
Bibliographic Notes
of counting at different times and in
different contexts. As they gain more
experience, they start to connect and
coordinate these individual concepts
and develop skill in counting with fluency.
The specific ways in which these
different aspects of counting develop
depend largely on individual children
and their experiences. Research, however,
is in agreement that very young
children (ages up to three) may be able
to handle small quantities first (groups
of two to three), and as they grow
older, they are more likely to be able to
manage larger sets (by age five, groups
of 10). Cardinality is typically developed
between the ages of three and
four years (Fuson 1988). The preschool
years are a critical time for children
to master the art of counting small
numbers of objects.
Young children’s understanding
of quantities and numbers is largely
related to counting, as noted in the
previous section. Another important
factor in children’s development of
number sense is early experience with
number operations (Adding It Up 2001;
Clements 2004a; Hiebert and others
1997; Principles and Standards for
School Mathematics 2000). Research
shows that counting and number
operations are related and that children
as young as three years are able
to understand simple visual number
patterns that involve number operations
such as, “two fingers and two fingers
make four” (Fuson 1988, 1992a).
When children enter elementary
schools, much of their engagement
Preschool Learning Foundations, Volume 1 • California Department of Education