People seem to be born to the calculation. The numerical skills of children develop so early and so inexorably that it is easy to imagine an internal clock of mathematical maturity guide their development. 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 year the chair. Soon they are capable of noting that they have placed five knives, spoons and forks on the table, and a little later, which amount to fifteen pieces of silver. Thus, in addition to master, they move on to subtraction. It seems to be reason to believe that if a child were secluded on a desert island at birth and retrieved seven years later, he or she can enter a mathematics class classroom Monday 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 Daily study of the intellectual progress depends. Children were observed as they slowly took - or as the case may be, bumped into- concept that adults take for granted, such as they have refused for example, to admit that the number is unchanged as water pours from a short stout glass into a tall thin. Psychology has proven that since young children, asked to count the pencils in a pile, ready to report the number of pencil blue or red, but must be coaxed into finding the total. These studies have suggested that the rudiments of mathematics are mastered gradually, and with effort. They also said that very abstract concept of numbers - the idea of a unity, a twoness, a threeness apply to any class of objects and is a prerequisite for anything to do mathematics more demanding than setting a table - is itself far from congenital.
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