> Maybe I was using too-shorthand in saying `Piagetian'. What Cromer and some
> other educational analysts have done with the widely accepted work of Swiss
> psychologist Jean Piaget
It's by no means as widely accepted as it used to be
> is to look at the typical *mental tool kits* (so
> to speak) used by ordinary people, and relate these to a
> conjectured/observed series of stages of development available to the human
> mind as it encounters the world while growing up. Many people, according to
> this analysis, remain stuck in the `preoperational' and `concrete
> operational' stages, never managing the leap to `formal operational'
> abstract thinking.
Long ago I heard some rumor that people in a certain poorer working class
area of London predictably never rise above the thinking level of a
typical twelve year old (allegedly a cultural thing). I'd love to hear
more about that, even if someone knows that this definitely isn't the case.
> Children at earlier levels notoriously find it hard to
> understand conservation rules: pour a beverage from a tall thin container
> into a wide flat one and they'll wail that they've been shortchanged; they
> can't grasp that the same amount of `stuff' is still there--it's obviously
> *less*, since *lower*. And so on.
This has been debunked, to a large degree. I recall in 1969 doing a term
paper on Piaget and wondering, absently, if he was sure that the children
knew what he was talking about when he used the words "more" and "less".
Finally someone much later repeated the experiments and, well, here is how
Keith Devlin tells it: (there is a similar, but not so graphic, account in
"The Number Sense" by Stanislas Dehaene)
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
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
educational systems. Unfortunately, as often happens with ground-braking research,
investigations have show that many of Piaget's conclusions were almost certainly wrong. (I
"almost certainly" because some psychologists still maintain that Piaget was right, and
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,
observing the world around it, gradually pieces together a coherent and steadily
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
and his experiments are one reason why his work was so influential.. It took great
and equipment not available in Piaget's time for subsequent generations to devise more
experiments. When they did so, they reached very different conclusions.
For example, according to Piaget, children younger than ten months old have no proper
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
or younger will fail to reach for it. According to Piaget, "object permanency," as he
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
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
six glasses and six bottles and ask whether there were more glasses or more bottles. The
invariably answered that there were the same number. Presumably the child observed a
correspondence between the rows. The experimenter then spread out the glasses to form a
longer row and asked the child again whether there were more glasses or more bottles. Now
the child would answer that there were more glasses, apparently misled by the longer
of that row. "Obviously," Piaget concluded, "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
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
science. Unfortunately, his methods had serious flaws. He relied on the motor actions of
babies in the object permanency test and on a dialogue between the experimenter and the
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
ceased to exist. Perhaps he simply does not yet have sufficient hand-arm coordination to
for a hidden object. In fact, we now know that this explanation is correct. Recent
more sophisticated than Piaget's, indicate that even very young babies have a
sense of object permanency.
Likewise, dialogue with a small child is highly unreliable. Communication via language is
100 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
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-
five-year-olds. The children succeeded perfectly. Consequently, unless we believe that
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
explanation of Piaget's observations. Remember the way the experiment was performed. First
experimenter arranges the glasses and bottles in two equally spaced rows and asks the
which row has more objects. Then the experimenter rearranges one of the rows, making it
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
sees the experimenter rearrange the objects in one of the two rows and then ask the very
question as a moment earlier, "Which row has more objects?" She may well reason, "Hmm.
the same question she just asked me. Adults are not dumb, and this is a special kind of
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
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
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.
and Bever's younger subjects took the experimenters' questions literally, and counted
What Piaget's original experiment really showed is that four- and five year-old children
reason rationally about the motivations and expectations of another person. That's an
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
simple. Instead of glasses and bottles they presented the child with two rows of M&Ms. One
contained six M&Ms, the other had four. Sometimes the rows were the same length; sometimes
row of six M&Ms was longer; other times the row of four M&Ms was longer. Instead of being
to indicate which row had more candies, the child was simply told he could pick one row
them. The outcome was precisely what any parent would predict. The child invariably
the row of six candies, regardless of its length. He knew full well which row had more
and moreover realized that the number was not dependent on the arrangement. The result was
as conclusive with two-year-old children as with four year-olds.
Another ingenious variation of the original Piaget experiment reached the same conclusion.
time, James McGarrigle and Margaret Donaldson of the University of Edinburgh carried out
experiment in a small puppet theater. Like Piaget, they started by aligning two rows of
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
two to five invariably gave the correct answer. Since the teddy bear had rearranged one of
rows, unseen by the experimenter, the child presumably found it reasonable for the adult
the same question again. Yet when the experimenter repeated the process with the same
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.
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