California Preschool Learning Foundations - ECEZero2Three ...

A developmental progression by age
range is articulated within each substrand.
That is, the substrand description
and foundations for children at
around 60 months of age are written to
indicate a higher level of development
than the foundations for children at
around 48 months of age in that same
substrand. For some foundations, the
change between 48- and 60-monthold
children is more pronounced than
for other foundations. Although there
is a developmental progression from
around 48 months of age to around
60 months of age within a substrand,
the order in which the strands are
presented is not meant to indicate any
sense of developmental progression
from strand to strand or from substrand
to substrand within a strand.
At the end of the foundations, bibliographic
notes provide a review of
the research base for the foundations.
Following the bibliographic notes, a list
of references for the entire set of mathematics
foundations is provided. Brief
explanations of each strand are as
follows:
Number Sense—important aspects
of counting, number relationships,
and operations
Preschool children develop an initial
qualitative understanding of a quantity
of small groups of objects without
actually counting the objects. This
understanding is referred to as visually
knowing or “subitizing.” It supports
the ability to compare small groups of
objects: to know if the groups are the
same, if one group is larger (smaller),
or which has more (fewer). Also developing
is the ability to approach simple
arithmetic-like operations on groups
of objects with ideas such as “adding
California Department of Education • Preschool Learning Foundations, Volume 1
145
to,” “putting together,” “taking apart,”
“taking away,” and so forth. Preschool
is the time when children learn to recite
the numbers in order, recognize numerals,
and begin to incorporate the idea
of one-to-one-correspondence and true
counting. This is also a time when preschool
children begin to learn about
cardinality, which is the concept of
knowing the last number named is the
quantity of objects counted.
Algebra and Functions
(Classification and Patterning)—
sorting and classifying objects;
recognizing, extending, and
creating patterns
Classification involves sorting, grouping,
or categorizing objects according
to established criteria. Analyzing, comparing,
and classifying objects provide
a foundation for algebraic thinking.
Although preschool children may not
know how all the objects in a mixed set
can be sorted or be able to say much
about why some objects go together,
they do begin to group like with like at
around 48 months of age and will do so
more completely at around 60 months
of age. These foundations use the idea
of sorting objects by some attribute.
The term “attribute” is used here to
indicate a property of objects, such
as color or shape, that would be apparent
to a preschooler and that the preschooler
could use as a basis for grouping
or sorting. A younger preschool
child is expected to show some sorting
of a group of objects, but not necessarily
do so completely or without errors.
A young preschooler might sort farm
animals but remove only the cows and
leave the rest ungrouped, and there
may be a pig or two or a horse mixed
in. But an older preschool child might
MATHEMATICS