What does the pencil counting experiment suggest?

People appear to bore to compute. The counting skills of children develop so that it is easy to imagine (8) an internal clock of computing guiding their growth. (9) Not long after learning to walk and talk, they can set the table with impressive accuracy—one knife, one spoon , one fork, for each of the five chairs. Soon they are capable of anything that they have placed five knives, spoons and forks on the table and, a bit later amounts to fifteen pieces of silverware.
    Of course, the truth is not so simple. This century, the work of psychologists has explained the subtle forms of daily learning on which intellectual progress depends. Children were observed as they slowly grasped concepts that adults take for granted—quantity is unchanged as water pours from a short glass into a tall thin one. Psychologists have since demonstrated that (7) young children, asked to count the pencils in a pile, readily report the number of blue or red pencils, but must be led to find the total.
    Such studies have suggested that the introduction of mathematics is mastered gradually, and with effort. They have also suggested that the (10)very concept of abstract numbers that applies to any class of objects and is a factor for doing anything more mathematical and demanding than setting a table—is far from born to be.