People appear to be born to compute. The digital skills of children 【M1】_________
develop so early and so inexorably that it is easy to imagine an internal
clock of mathematical maturity guiding its growth. Not long after 【M2】_________
learning to walk and talk, they can make the table with impressive 【M3】_________
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 adds to 【M4】_________
fifteen pieces of silverware. Having thus mastered addition, they move
on to subtraction. It seems almost reasonable to expect that if a child
was secluded on a desert island at birth and retrieved seven years later, 【M5】_________
he or she could enter a second-grade mathematics class without any
serious problems of intellectual adjustment.
Of course, the truth is not so simple. In this century, the work of
cognitive psychologists have illuminated the subtle forms of daily 【M6】_________
learning on which intellectual progress depends. Children observed as 【M7】_________
they slowly grasped—or, as the case might be, encountered—concepts
that adults take it for granted, and that they refused, for instance, to 【M8】_________
concede that quantity is unchanged as water pours from a short stout
glass into a tall thin one. Psychologists have since demonstrated that
young children, asking to count the pencils in a pile, readily report the 【M9】_________
number of blue or red pencils, but must be coaxed into finding a total. 【M10】________
Such studies have suggested that the basics of mathematics are mastered
gradually, and with effort.
【M2】
its—their
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