California Preschool Learning Foundations - ECEZero2Three ...

MATHEMATICS
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make a group of all cows and a group
of all pigs and a group of all horses.
This competency is the precursor to
many important mathematics abilities
that will come later (e.g., the logic of
what belongs in a set and what does
not, grouping terms in an algebraic
expression, data analysis, and graphing).
Sorting and grouping in preschool
will help prepare children for those
later steps. Researchers Seo and Ginsburg
(2004) point out that preschool
children do not often spontaneously
choose to do sorting activities on their
own. Therefore, sorting is an area in
which teacher facilitation and modeling
across a range of situations and
contexts is particularly important. The
teacher should note that how a child
sorts depends on the situation and the
child’s perception of the activity.
Thinking about patterns is another
important precursor for learning mathematics
in general and for learning
algebra in particular (Clements 2004a).
During the preschool years, children
develop their abilities to recognize,
identify, and duplicate patterns and
to extend and create simple repeating
patterns. Although less research has
been conducted for preschoolers in
patterning than in other areas, such
as numbers and counting, recent studies
(Klein and Starkey 2004; Starkey,
Klein, and Wakelely 2004) provide
information about the development of
patterning skills. Children first learn
to identify the core unit in a repeating
pattern. Once they are able to
identify the initial unit of a pattern,
they can extend a pattern by predicting
what comes next. Teacher facilitation
and modeling are particularly
important in introducing the notion of
patterns, extending it to more aspects
of the child’s environment and daily
activities, and encouraging the child’s
attempts to create patterns.
Measurement—comparing and
ordering objects by length,
weight, or capacity; precursors
of measurement
Measuring is assigning a number
of units to some property, such as
length, area, or weight, of an object.
Although much more learning will
take place later as children become
increasingly competent with core measurement
concepts, preschool is when
children gain many of the precursors
to this kind of understanding about
comparing, ordering, and measuring
things. For example, young preschool
children are becoming aware that
objects can be compared by weight,
height, or length and use such words
as “heavier,” “taller,” or “longer” to
make comparisons. They begin to
compare objects directly to find out
which is heavier, taller, and so forth.
They can compare length by placing
objects side by side and order three or
more objects by size. By the time children
are around 60 months old, they
develop the understanding that measuring
length involves repeating equalsize
units and counting the number
of units. They may start measuring
length by laying multiple copies of
same-size units end to end (Clements
2004a).
Geometry—properties of objects
(shape, size, position) and the
relation of objects in space
Geometry is a tool for understanding
relations among shapes and spatial
properties mathematically. Preschool
children learn to recognize and name
two-dimensional shapes, such as a
circle, square, rectangle, triangle, and
Preschool Learning Foundations, Volume 1 • California Department of Education