California Preschool Learning Foundations - ECEZero2Three ...

2004a). The developmental trajectory
for the composition of geometric
figures evolves as children begin to
use shapes individually to represent
objects, progress to covering an outline
with shapes, and eventually be able
to combine shapes without an outline
and make shape units (i.e., smaller
shapes that make up a larger shape
that is itself a part of a larger picture)
(Clements 2004a; Clements and
Sarama 2000).
Developing a sense of space is as
important as developing spatial sense.
Spatial sense allows people to get
around in the world and know the relative
positions of artifacts in the physical
environment (Smith 2001). Spatial
reasoning involves location, direction,
distance, and identification of objects
(Clements 1999). Very young children
do develop an initial spatial sense to
get around in the world. For example,
young preschoolers learn to navigate
their way around their school and
classroom, and this ability suggests
that they have created a mental map of
those places. In the beginning stages
of spatial reasoning, children use their
own position as a point of reference for
locating positions and orientations of
objects in space, such as in/out and
above/below. Then, children develop
the ability to relate positions of two
objects external to themselves or in
themselves such as in front/in back,
forward/backward, near/far, close
to/far from (Greenes 1999). There is
evidence that even preschool children
develop mapping skills. They can build
maps using familiar objects and as
they get older, build imagery maps in
familiar classroom settings (Blaut and
Stea 1974; Gouteux and Spelke 2004;
Rieser, Garing, and Young 1994).
California Department of Education • Preschool Learning Foundations, Volume 1
165
Children’s growth in understanding
and knowledge about shape and space
is thought to develop through education
and experience rather than merely
through maturational factors. Therefore,
it is important not only to create
a foundation for addressing this mathematics
area, but also to encourage
preschool programs to provide children
with plenty of rich and varied opportunities
to engage with various aspects of
geometry. Engagement should be done
in such a way that it grounds young
children’s experiences with shapes
in action. As a result, the preschool
foundations tend to de-emphasize the
“naming” of shapes in this foundation;
rather, they focus on children’s ability
to identify shapes, whether verbally or
nonverbally.
Mathematical Reasoning
Mathematical proficiency entails
strategic competence, adaptive reasoning,
conceptual understanding,
productive disposition, and procedural
fluency (Adding It Up 2001). Each of
these competencies sets the foundation
for what is often called problem
solving or mathematical reasoning.
Most preschool children by at least
three years of age show that they can
solve problems involving simple addition
and subtraction, often by modeling
with real objects or thinking about
sets of objects. In a study by Huttenlocher,
Jordan, and Levine (1994), preschoolers
were presented with a set of
objects of a given size that were then
hidden in a box, followed by another
set of objects that were also placed in
the box. The children were asked to
produce a set of objects corresponding
to the total number of objects
contained in the box. The majority
MATHEMATICS