California Preschool Learning Foundations - ECEZero2Three ...

MATHEMATICS
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Children with special needs can
demonstrate mathematical knowledge
in various ways and do not necessarily
need to engage in motor behavior.
For example, a child might indicate
to an adult or another child where to
place each object in a sorting task. Or
a child might ask a teacher to place
objects in a particular order to make a
repeating pattern. Children with visual
impairments might be offered materials
for counting, sorting, problem solving,
and so forth that are easily distinguishable
by touch. Any means of
expression and engagement available
to the child should be encouraged.
Organization of the
Mathematics Foundations
The California preschool learning
foundations in mathematics cover five
main developmental strands: Number
Sense, Algebra and Functions (Classification
and Patterning), Measurement,
Geometry, and Mathematical Reasoning.
These strands were identified
after a careful review of research, the
Principles and Standards for School
Mathematics (NCTM 2000), and the
California mathematics content standards
for kindergarten through grade
twelve (K–12).
The preschool mathematics foundations
expand on the standards identified
by the NCTM (2000) for the preschool
age to include more detailed,
age-specific expectations in the key
mathematics content areas. In addition,
the preschool foundations for
mathematics are closely aligned with
the California K–12 mathematics
content standards, yet there are some
particular differences in the organization
of the mathematics strands. In the
preschool learning foundations, Mea-
surement and Geometry are two separate
strands rather than one combined
strand of Measurement and Geometry.
Also, the preschool learning foundations,
unlike the K–12 mathematics
content standards, do not include a
separate strand for statistics, data
analysis, and probability. The foundations
for Patterning are included in the
strand for Algebra and Functions, along
with the foundations for Classification.
The numbering system for the
mathematics foundations follows the
same numbering system used in the
California K–12 mathematics content
standards. The major divisions within
a strand are referred to as substrands
and are numbered 1.0, 2.0, and so
forth. Each substrand is divided into
a column for children “around 48
months of age” and a column for children
“around 60 months of age” on
each page. The description for younger
preschool children is different from
the one for older preschool children.
The separate foundations are written
under their substrand column by age
range and are numbered sequentially.
Where a substrand is numbered 1.0,
the foundations under the substrand
would be 1.1, 1.2, and so forth, where
a substrand is numbered 2.0, the foundations
under the substrand would be
2.1, 2.2, and so forth for both columns.
Immediately below each foundation,
a few examples are given. The examples
are meant to clarify the foundation
by illustrating how the competency
described in the foundation might be
observed in the preschool environment.
They are not meant to be used as a
checklist of the knowledge and skills
that a child must demonstrate before
the teacher can decide that a competency
is present.
Preschool Learning Foundations, Volume 1 • California Department of Education