People appear to be born to calculate.
People
appear
to
be
born
to
calculate
.
The numerical skills of children develop so early that it is easy to imagine an internal clock of mathematical maturity guiding their growth.
The
numerical
skills
of
children
develop
so
early
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 impressive accuracy--one plate, one knife, one spoon, one fork for each of the five chairs.
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
of
the
five
chairs
.
Soon they are capable of noting that they have placed five knives, spoons and forks on the table, and a bit later, that this amounts to fifteen pieces of silverware.
Soon
they
are
capable
of
noting
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, some people expect that if a child were on a desert island at birth and brought back seven years later, he or she could enter a second-grade mathematics class without any serious problems of intellectual adjustment.
Having
thus
mastered
addition
,
some
people
expect
that
if
a
child
were
on
a
desert
island
at
birth
and
brought
back
seven
years
later
,
he
or
she
could
enter
a
second-grade
mathematics
class
without
any
serious
problems
of
intellectual
adjustment
.
Of course, the truth is not so simple.
Of
course
,
the
truth
is
not
so
simple
.
This century, the work of psychologists has cast light on the unnoticeable forms of daily learning on which intellectual progress depends.
This
century
,
the
work
of
psychologists
has
cast
light
on
the
unnoticeable
forms
of
daily
learning
on
which
intellectual
progress
depends
.
Children were observed as they slowly grasped--or, as the case might be, came across--concepts that adults take for granted, as they refused, for instance, to admit that quantity is unchanged as water pours from a short thick glass into a tall thin one.
Children
were
observed
as
they
slowly
grasped
--
or
,
as
the
case
might
be
,
came
across
--
concepts
that
adults
take
for
granted
,
as
they
refused
,
for
instance
,
to
admit
that
quantity
is
unchanged
as
water
pours
from
a
short
thick
glass
into
a
tall
thin
one
.
Psychologists have since proved that young children, asked to count the pencils in a pile, readily report the number of blue or red pencils, but must be persuaded into finding the total.
Psychologists
have
since
proved
that
young
children
,
asked
to
count
the
pencils
in
a
pile
,
readily
report
the
number
of
blue
or
red
pencils
,
but
must
be
persuaded
into
finding
the
total
.
Such studies have suggested that the most basic parts of mathematics are mastered gradually, and with effort.
Such
studies
have
suggested
that
the
most
basic
parts
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 object and is a prerequisite for doing anything more mathematically demanding than setting a table--is itself far from natural born.
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
object
and
is
a
prerequisite
for
doing
anything
more
mathematically
demanding
than
setting
a
table
--
is
itself
far
from
natural
born
.
People appear to be born to calculate. The numerical skills of children develop so early 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 impressive accuracy--one plate, one knife, one spoon, one fork for each of the five chairs. Soon they are capable of noting 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, some people expect that if a child were on a desert island at birth and brought back seven years later, he or she could 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 psychologists has cast light on the unnoticeable forms of daily learning on which intellectual progress depends. Children were observed as they slowly grasped--or, as the case might be, came across--concepts that adults take for granted, as they refused, for instance, to admit that quantity is unchanged as water pours from a short thick glass into a tall thin one. Psychologists have since proved that young children, asked to count the pencils in a pile, readily report the number of blue or red pencils, but must be persuaded into finding the total. Such studies have suggested that the most basic parts 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 object and is a prerequisite for doing anything more mathematically demanding than setting a table--is itself far from natural born.