California Preschool Learning Foundations - ECEZero2Three ...

MATHEMATICS
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create new knowledge of objects and
their relationships; in Developmental
Guidelines for Geometry, he recommends
a classification activity in
which four-year-olds match shapes to
identify congruent and noncongruent
two-dimensional shapes. Certainly,
identifying triangles from within a set
of figures that include examples and
nonexamples of triangles is essentially
a classification exercise. But classification
should not be reserved solely for
work with shapes; rather, it should be
included in young children’s mathematical
activities as it also facilitates
work with patterns and data analysis.
The developmental continuum for data
analysis starts with classification and
counting and evolves into data representation
(e.g., graphing).
Seo and Ginsburg (2004) were interested
in how frequently four- and
five-year-olds engaged in mathematical
activities during play. Interestingly
enough, after studying 90 of these
children the researchers report that
classification activities were the least
frequently occurring of the mathematical
activities observed. Only 2 percent
of the mathematical activities observed
could be categorized as classification
activities.
Patterns help children learn to find
order, cohesion, and predictability in
seemingly disorganized situations.
The recognition and analysis of patterns
clearly provide a foundation for
the development of algebraic thinking
(Clements 2004a). Identifying and
extending patterns are important preschool
activities. For example, Ginsburg,
Inoue, and Seo (1999) report that
the detection, prediction, and creation
of patterns with shapes are the most
frequent mathematical activities in
preschool. However,
compared with counting, little is known
about young children’s knowledge of
patterns.
Patterns involve replication, completion,
prediction, extension, and description
or generalization (Greenes 1999).
In preschool years, young children
gradually develop the concept of patterns
that includes recognizing a pattern,
describing a pattern, creating a
pattern, and extending a pattern. To
understand a pattern, children should
be able to identify similarities and differences
among elements of a pattern,
note the number of elements in the
repeatable group, identify when the
first group of elements begins to replicate
itself, and make predictions about
the order of elements based on given
information.
Klein and Starkey (2004) report that
young children experience difficulty
at the beginning of the year with a
fundamental property of repeating patterns:
identifying the core unit of the
pattern. However, experiences can have
a positive impact on young children’s
knowledge of duplication and extension
of patterns (Klein and Starkey 2004;
Starkey, Klein, and Wakeley 2004).
In a study about the kinds of mathematical
activities in which young
children engage during play, Seo and
Ginsburg (2004) found that four- and
five-year-old children most often engage
in “pattern and shape” activities, which
the authors describe as “. . . identifying
or creating patterns or shapes or
exploring geometric properties and
relationships. For example, Jennie
makes a bead necklace, putting plastic
beads into a string one by one. She
uses only yellow and red beads for her
necklace and makes a yellow-red color
pattern” (Seo and Ginsburg 2004, 94).
Preschool Learning Foundations, Volume 1 • California Department of Education