California Preschool Learning Foundations - ECEZero2Three ...

MATHEMATICS
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of three-year-olds were able to solve
these types of problems when they
involved adding or subtracting a single
item, but their performance decreased
rapidly as the size of the second set
increased.
Preschoolers demonstrate the conceptual
understanding and procedural
fluency necessary for them to solve
simple word problems (Fuson 1992b).
Simple word problems are thought
to be easier for preschool children to
solve than number problems that are
not cast in a context (Carpenter and
others 1993). All ages of problemsolvers
are influenced by the context
of the problem and tend to perform
better with more contextual information
(Wason and Johnson-Laird 1972;
Shannon 1999). However, preschool
children tend to be more heavily influenced
by the context of the problem
than do older children and adults,
thus limiting their ability to solve number
problems that are not presented in
context.
Alexander, White, and Daugherty
(1997) propose three conditions for
reasoning in young children: the children
must have a sufficient knowledge
base, the task must be understandable
and motivating, and the context of the
task must be familiar and comfortable
to the problem-solver. These conditions
probably apply to all ages of problem-
solvers (Wason and Johnson-Laird
1972; Shannon 1999).
Researchers indicate that four- and
five-year-olds engage in advanced
mathematical explorations spontaneously
in their play (Ginsburg, Inoue,
and Seo 1999; Seo and Ginsburg
2004). In their everyday activities,
young children spontaneously engage
in a variety of mathematical explorations
and applications such as pattern
analysis, change and transformation,
comparison of magnitude, and
estimations. Any logical thinking that
children exhibit to solve real-life problems
could potentially be considered
beginning mathematical reasoning.
For example, children distributing
the same (or almost same) amount of
snack to classmates or using strategies
to solve immediate situations in
play are situations in which children
begin to demonstrate their ability to
solve mathematical problems. Thus,
it is crucial for teachers to be attuned
to the fact that mathematical reasoning
happens all the time in children’s
lives, and teachers would do well to
use those occasions to nurture children’s
mathematical thinking skills.
The examples illustrate the authentic
problems that occur in preschoolers’
everyday activities and all the different
skills involved in mathematical reasoning
and problem solving.
Preschool Learning Foundations, Volume 1 • California Department of Education