Piaget and Alternative Explanations (crosspost)

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    > The Math Gene pp. 27-31 "The Rise and Fall of Piaget", by Keith
    > Devlin: Much of our current popular wisdom about small children's
    > mental abilities originates in the work of the cognitive psychologist
    > Jean Piaget fifty years ago. Piaget's influence can be found not only
    > in many of our current beliefs about the way children learn, but also
    > in our educational systems. Unfortunately, as often happens with
    > ground- braking research, subsequent investigations have show that
    > many of Piaget's conclusions were almost certainly wrong. (I say
    > "almost certainly" because some psychologists still maintain that
    > Piaget was right, and that the experimental results I shall describe
    > admit alternative conclusions.) In the 1940s and I950s, Piaget
    > developed a "constructivist" view of child development. According to
    > this view, a newborn baby enters the world with a cognitive clean
    > slate and, by observing the world around it, gradually pieces together
    > a coherent and steadily increasing understanding of that world. In
    > other words, the child constructs a mental model or conceptualization
    > of the world. Piaget did not arrive at his conclusions by armchair
    > speculation. He was an experimentalist, and his experiments are one
    > reason why his work was so influential.. It took great ingenuity and
    > equipment not available in Piaget's time for subsequent generations to
    > devise more reliable experiments. Whcn they did so, they reached very
    > different conclusions. For example, according to Piaget, children
    > younger than ten months old have no proper sense of physical objects
    > as things that endure in the world. Piaget based this conclusion on
    > his observation that, when an object such as a toy is hidden under a
    > cloth, a baby ten months old or younger will fail to reach for it.
    > According to Piaget, "object permanency," as he called it, is not
    > innate but is acquired sometime after ten months of age. Similarly,
    > Piaget believed that children do not have a number sense until they
    > acquire it at around four or five years of age. In one of Piaget's
    > experiments, repeated many times by different groups, a psychologist
    > would show a four-year-old child two equally spaced rows of six
    > glasses and six bottles and ask whether there were more glasses or
    > more bottles. The child invariably answered that there were the same
    > number. Presumably the child observed a one-to-one correspondence
    > between the l rows. The experimenter then spread out the glasses to
    > form a longer row l and asked the child again whether there were more
    > glasses or more bot-l ties. Now the child would answer that there were
    > more glasses, apparently l misled by the longer length of that row.
    > "Obviously," Piaget concluded, l "this shows that the child does not
    > have a properly developed number sense." In particular, Piaget
    > claimed, four- and five-year-old children have not yet grasped the
    > idea of number conservation: the notion that rearranging the objects
    > in a collection does not change their number. At the time, Piaget's
    > experiments were held up as triumphs of experimental science in
    > psychology. As a pioneer, Piaget was blazing a trail for future
    > generations. And that is good science. Unfortunately, his methods had
    > serious flaws. He relied on the motor actions of the babies in the
    > object permanency test and on a dialogue between the experimenter and
    > the subject for the various number tests performed on older children.
    > In the case of object permanency, a baby's failure to reach for an
    > object hidden under a blanket does not support the rather dramatic
    > conclusion that the baby thinks the object has ceased to exist.
    > Perhaps he simply does not yet have sufficient hand-arm coordination
    > to reach for a hidden object. In fact, we now know that this
    > explanation is correct. Recent experiments, more sophisticated than
    > Piaget's, indicate that even very young babies have a well-developed
    > sense of object permanency. Likewise, dialogue with a small child is
    > highly unreliable. Communication via language is never loo percent
    > objective and free of the influences of context, emotion, social
    > factors, and possibly several other things. Just how unreliable
    > dialogue can be was demonstrated by Jacques Mehler and Tom Bever at
    > MIT during the late 1960s. In one experiment, Mehler and Bever carried
    > out the original Piaget experiment to test for number conservation,
    > but with two- and three-year old children instead of Piaget's four-
    > and five-year-olds. The children succeeded perfectly. Consequently,
    > unless we believe that children temporarily lose their sense of number
    > conservation between the ages of four and six, we clearly need some
    > alternative explanation for Piaget's results. One is readily
    > available. Around five years of age, children begin to develop the
    > ability to reason about another person's thought process ("What Daddy
    > means by this is . . . "). This provides the most likely explanation
    > of Piaget's observations. Remember the way the experiment was
    > performed. First the experimenter arranges the glasses and bottles in
    > two equally spaced rows and asks the child which row has more objects.
    > Then the experimenter rearranges one of the rows, making it longer,
    > and again asks the child, "Which row has more objects?" Now, by four
    > or five years of age, a young child knows that adults are powerful and
    > are knowledgeable. Moreover, she has probably observed the respect her
    > parent showed the experimenter when they arrived at the laboratory.
    > How is this child likely to react when she sees the experimenter
    > rearrange the objects in one of the two rows and then ask the very
    > same question as a moment earlier, "Which row has more objects?" She
    > may well reason, "Hmm. That's the same qucstion she just asked me.
    > Adults are not dumb, and this is a special kind of adult who knows a
    > lot. We can both see that the number of objects hasn't changed. So I
    > must have misunderstood the question the last time. I thought she was
    > asking me about the number of objects in the row, but obviously she
    > was really asking me about the length, since that's what she just
    > changed." And so the child gives the answer she thinks is expected of
    > her. Of course, we can't know for sure. Attempts to find out by
    > interrogating the child are unlikely to yield conclusive evidence, for
    > the same reason that the original Piaget experiment is suspect! This
    > is where the Mehler and Bever experiment came into its own. The kind
    > of "what-does-she-really-want?" reasoning just described is beyond
    > two- or three-year olds. Mehler and Bever's younger subjects took the
    > experimenters' questions literally, and counted correctly. What
    > Piaget's original experiment really showed is that four- and five
    > year-old children can reason rationally about the motivations and
    > expectations of another person. That's an important and useful
    > discovery. But it's not the one Piaget thought he had made! To confirm
    > that children from age two upward have a good sense of number, Mehler
    > and Bever redesigned the Piaget test to avoid the reliance on
    > language. Their idea was breathtakingly simple. Instead of glasses and
    > bottles they presented the child with two rows of M&Ms. One row
    > contained six M&Ms, the other had four. Sometimes the rows were the
    > same length; sometimes the row of six M&Ms was longer; other times the
    > row of four M&Ms was longer. Instead of being asked to indicate which
    > row had more candies, the child was simply told he could pick one row
    > and eat them. The outcome was precisely what any parent would predict.
    > The child invariably plumped for the row of six candies, regardless of
    > its length. He knew full well which row had more members, and moreover
    > realized that the number was not dependent on the arrangement. The
    > result was just as conclusive with two-year-old children as with four
    > year-olds. Another ingenious variation of the original Piaget
    > experiment reached the same conclusion. This time, James McGarrigle
    > and Margaret Donaldson of the University of Edinburgh carried out
    > their experiment in a small puppet theater. Like Piaget, they started
    > by aligning two rows of the same number of objects and asking the
    > child which row had more objects. After the child responded correctly,
    > the experimenter pretended to look away while a teddy bear puppet
    > lengthened one of the rows. Turning back, the experimenter exclaimed,
    > "Oh dear, that silly teddy has mixed up the rows. can you tell me
    > which row has more objects again?" Children from two to five
    > invariably gave the correct answer. Since the teddy bear had
    > rearranged one of the rows, unseen by the experimenter, the child
    > presumably found it reasonable for the adult to ask the same question
    > again. Yet when the experimenter repeated the process with the same
    > children but rearranged the objects him- or herself, the four- and
    > five-year-old children responded exactly as they had for Piaget,
    > basing their answer on length. -Keith Devlin, The Math Gene (2000)

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