People appear 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
国外常见的碳酸饮料
Looking the other way?
A long shot?
Power play?
Out and out?
Big hat, no cattle
Count your blessings?
Take a bow?
做个有趣的人
Stirring the pot
Hold your horses
Capturing the imagination
女性一辈子的事业
Learning it the hard way
周黎明:管他谁是真正的娘炮!
Fighting chance
Far cry?
Down for the count?
Coming to a head?
Let’s go shopping!
True to form
Hard yards?
燃尽
Stealing a march?
Wenger’s red herrings?
Proof is in the pudding
Pie in the sky?
Keep them on side
Sunshine laws?
Sheep's skin
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