California Preschool Learning Foundations - ECEZero2Three ...

other shapes. At first, they recognize
geometric shapes by their overall holistic
physical appearance. As they gain
more experience comparing, sorting,
and analyzing shapes, children learn
to attend to individual attributes and
characteristics of different shapes.
Younger preschool children use shapes
in isolation, while older preschool children
use shapes to create images of
things they know and may combine
shapes into new shapes (Clements
2004a, 2004b). In the early preschool
years, children also develop spatial
reasoning. They can visualize shapes
in different positions and learn to
describe the direction, distance, and
location of objects in space. Teachers
can facilitate children’s development
of geometry and spatial thinking by
offering many opportunities to explore
attributes of different shapes and to
use vocabulary words about the position
of objects in space.
Mathematical Reasoning—using
mathematical thinking to solve
problems in play and everyday
activities
Children in preschool encounter situations
in play and everyday activities
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that require them to adapt and change
their course of action. Although they
may not realize it, some situations
call for mathematical reasoning—to
determine a quantity (e.g., how many
spoons?) or to reason geometrically
(e.g., what shape will fit?). Other
situations require general reasoning.
For preschoolers, when the context
is familiar and comfortable enough,
a simple strategy may be applied to
solve an immediate problem—even
something as simple as counting the
number of objects held in the hand or
carrying a block over to see if there
are others like it. A young preschool
child may begin this process by trying
a strategy that is not always effective.
An older preschool child may try several
strategies, finally finding one that
works. The important point is that
both younger and older preschool
children learn through reasoning
mathematically. As the above examples
suggest, encouraging young children
to engage in mathematical reasoning
is not only beneficial in itself, it also
opens the door to children’s exploration
of the other mathematics foundations,
such as geometric shapes,
counting, and classification.
MATHEMATICS