单项选择题
| People appear to be 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 impressive
accuracy--one plate, one knife, one spoon, one fork, for each of the five
chairs. Soon they are capable of noting 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-grade mathematics class without any serius 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 granted, as they refused, for instance, to concede that quantity is unchanged as water pours from short stout 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 threenes 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. |