children’s numerical skills

People appearfor saleThanksgiving Gemmy Airblown Inflatables to born to compute. The numerical skills of children develop
so early and so inexorably that it is easy to imagine an internal clock of
mathematical maturity guiding their growth. Not long after learning to walk
and talk, they can set the table with impress accuracy---one knife, one
spoon, one fork, for each of the five chairs.

Soon they are capable of nothing that they have placed five knives, spoons
and forks on the table and, a bit later, that this amounts to fifteen pieces
of silverware. Having thus mastered addition, they move on to subtraction.
It seems almost reasonable to expect that if a child were secluded on a
desert island at birth and retrieved seven years later, he or she could
enter a second enter a second-grade mathematics class without any serious
problems of intellectual adjustment.

Of course, the truth is not so simple. This century, the work of cognitive
psychologists has illuminated the subtle forms of daily learning on which
intellectual progress depends. Children were observed as they slowly
grasped-----or, as the case might be, bumped into----- concepts that adults
take for quantity is unchanged as water pours from a short glass into a tall
thin one. Psychologists have since demonstrated that young children, asked
to count the pencils in a pile, readily report the number of blue or red
pencils, but must be coaxed into finding the total. Such studies have
suggested that the rudiments of mathematics are mastered gradually, and with
effort. They have also suggested that the very concept of abstract
numbers------the idea of a oneness, a twoness, a threeness that applies to
any class of objects and is a prerequisite for doing anything more
mathematically demanding than setting a table-----is itself far from innate