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Montessori
Curriculum |
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Mathematics
-
Our
students
are
typically
introduced
to
numbers
at age
3:
learning
the
numbers
and
number
symbols
one to
ten: the
red and
blue
rods,
sand-paper
numerals,
association
of
number
rods and
numerals,
spindle
boxes,
cards
and
counters,
counting,
sight
recognition,
concept
of odd
and
even.
-
Introduction
to the
decimal
system
typically
begins
at age 3
or 4.
Units,
tens,
hundreds,
thousands
are
represented
by
specially
prepared
concrete
learning
materials
that
show the
decimal
hierarchy
in three
dimensional
form:
units =
single
beads,
tens = a
bar of
10
units,
hundreds
= 10 ten
bars
fastened
together
into a
square,
thousands
= a cube
ten
units
long ten
units
wide and
ten
units
high.
The
children
learn to
first
recognize
the
quantities,
then to
form
numbers
with the
bead or
cube
materials
through
9,999
and to
read
them
back, to
read and
write
numerals
up to
9,999,
and to
exchange
equivalent
quantities
of units
for
tens,
tens for
hundreds,
etc.
Linear
Counting:
learning
the
number
facts to
ten
(what
numbers
make
ten,
basic
addition
up to
ten);
learning
the
teens
(11 =
one ten
+ one
unit),
counting
by tens
(34 =
three
tens +
four
units)
to one
hundred.
-
Development
of the
concept
of the
four
basic
mathematical
operations:
addition,
subtraction,
division,
and
multiplication
through
work
with the
Montessori
Golden
Bead
Material.
The
child
builds
numbers
with the
bead
material
and
performs
mathematical
operations
concretely.
(This
process
normally
begins
by age 4
and
extends
over the
next two
or three
years.)
Work
with
this
material
over a
long
period
is
critical
to the
full
understanding
of
abstract
mathematics
for all
but a
few
exceptional
children.
This
process
tends to
develop
in the
child a
much
deeper
understanding
of
mathematics.
-
Development
of the
concept
of
"dynamic"
addition
and
subtraction
through
the
manipulation
of the
concrete
math
materials.
(Addition
and
subtraction
where
exchanging
and
regrouping
of
numbers
is
necessary.)
-
Memorization
of the
basic
math
facts:
adding
and
subtracting
numbers
under 10
without
the aid
of the
concrete
materials.
(Typically
begins
at age 5
and is
normally
completed
by age
7.)
-
Development
of
further
abstract
understanding
of
addition,
subtraction,
division,
and
multiplication
with
large
numbers
through
the
Stamp
Game (a
manipulative
system
that
represents
the
decimal
system
as
color-keyed
"stamps")
and the
Small
and
Large
Bead
Frames
(color-coded
abacuses).
Skip
counting
with the
chains
of the
squares
of the
numbers
from
zero to
ten:
i.e.,
counting
to 25 by
5's, to
36 by
6's,
etc.
(Age
5-6)
Developing
first
understanding
of the
concept
of the
"square"
of a
number.
-
Skip
counting
with the
chains
of the
cubes of
the
numbers
zero to
ten:
i.e.,
counting
to 1,000
by ones
or tens.
Developing
the
first
understanding
of the
concept
of a
"cube"
of a
number.
-
Beginning
the
"passage
to
abstraction,"
the
child
begins
to solve
problems
with
paper
and
pencil
while
working
with the
concrete
materials.
Eventually,
the
materials
are no
longer
needed.
-
Development
of the
concept
of long
multiplication
and
division
through
concrete
work
with the
bead and
cube
materials.
(The
child is
typically
6 or
younger,
and
cannot
yet do
such
problems
on paper
without
the
concrete
materials.
The
objective
is to
develop
the
concept
first.)
-
Development
of more
abstract
understanding
of
"short"
division
through
more
advanced
manipulative
materials
(Division
Board);
movement
to paper
and
pencil
problems,
and
memorization
of basic
division
facts.
(Normally
by age
7-8)
-
Development
of still
more
abstract
understanding
of
"long"
multiplication
through
highly
advanced
and
manipulative
materials
(the
Multiplication
Checkerboard).
(Usually
age 7-8)
-
Development
of still
more
abstract
understanding
of "long
division"
through
highly
advanced
manipulative
materials
(Test
Tube
Division
apparatus).
(Typically
by age
7-8)
-
Solving
problems
involving
parentheses,
such as
(3 X 4)
- (2 +
9) = ?
-
Missing
sign
problems:
In a
given
situation,
should
you add,
divide,
multiply
or
subtract
?
-
Introduction
to
problems
involving
tens of
thousands,
hundreds
of
thousands,
and
millions.
(Normally
by age
7.)
-
Study of
fractions:
Normally
begins
when
children
using
the
short
division
materials
who find
that
they
have a
"remainder"
of one
and ask
whether
or not
the
single
unit can
be
divided
further.
The
study of
fractions
begins
with
very
concrete
materials
(the
fraction
circles),
and
involves
learning
names,
symbols,
equivalencies
common
denominators,
and
simple
addition,
subtraction,
division,
and
multiplication
of
fractions
up to
"tenths".
(Normally
by age
7-8)
-
Study of
decimal
fractions:
all four
mathematical
operations.
(Normally
begins
by age
8-9, and
continues
for
about
two
years
until
the
child
totally
grasps
the
ideas
and
processes.)
-
Practical
application
problems,
which
are used
to some
extent
from the
beginning,
become
far more
important
around
age 7-8
and
afterward.
Solving
word
problems,
and
determining
arithmetic
procedures
in real
situations
becomes
a major
focus.
-
Money:
units,
history,
equivalent
sums,
foreign
currencies
(units
and
exchange).
(Begins
as part
of
social
studies
and
applied
math by
age 6.)
-
Interest:
concrete
to
abstract;
real
life
problems
involving
credit
cards
and
loans;
principal,
rate,
time.
-
Computing
the
squares
and
cubes of
numbers:
cubes
and
squares
of
binomials
and
trinomials.
(Normally
by age
10)
-
Calculating
square
and cube
roots:
from
concrete
to
abstract.
(Normally
by age
10 or
11)
-
The
history
of
mathematics
and its
application
in
science,
engineering,
technology
&
economics.
Reinforcing
application
of all
mathematical
skills
to
practical
problems
around
the
school
and in
everyday
life.
-
Basic
data
gathering,
graph
reading
and
preparation,
and
statistical
analysis.
-
Sensorial
exploration
of plane
and
solid
figures
at the
Primary
level
(Ages 3
to 6):
the
children
learn to
recognize
the
names
and
basic
shapes
of plane
and
solid
geometry
through
manipulation
of
special
wooden
geometric
insets.
They
then
learn to
order
them by
size or
degree.
-
Stage I:
Basic
geometric
shapes.
(Age
3-4)
-
Stage
II: More
advanced
plane
geometric
shapes-triangles,
polygons,
various
rectangles
and
irregular
forms.
(Age
3-5)
-
Stage
III:
Introduction
to solid
geometric
forms
and
their
relationship
to plane
geometric
shapes.
(Age
2-5)
-
Study of
the
basic
properties
and
definitions
of the
geometric
shapes.
This is
essentially
as much
a
reading
exercise
as
mathematics
since
the
definitions
are part
of the
early
language
materials.
More
advanced
study of
the
nomenclature,
characteristics,
measurement
and
drawing
of the
geometric
shapes
and
concepts
such as
points,
line,
angle,
surface,
solid,
properties
of
triangles,
circles,
etc.
(Continues
through
age 12
in
repeated
cycles.)
-
Congruence,
similarity,
equality,
and
equivalence.
-
The
history
of
applications
of
geometry.
-
The
theorem
of
Pythagoras.
-
The
calculation
of area
and
volume.
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Our
Goals |
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The
Montessori
curriculum
varies
at
the
four
levels
of
our
school,
but
our
goals
are
consistent
throughout
the
programs:
- To enter into a partnership with parents in the education of their children.
- To encourage the self-motivation and self-discipline that will lead to a life-long pursuit of knowledge.
- To lead children to mastery of precisely identified intellectual, social, and physical skills.
- To help children develop a positive self-image as the key to the development of their full potential.
- To foster open minds, compassion, and respect for others.
- To balance self-reliance, independence, and responsible freedom with the skills of working cooperatively.
- To instill in each child a sense of duty and personal responsibility for the world in which we live.
- To spark in our children imagination, wonder, humor, and joy...
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Woodland Hill Montessori School
100 Montessori Place, North Greenbush, New York 12144
Tel: 518.283.5400 | Fax: 518.283.4861 | School Care &
After hours: 518.496.4136
Email:
info@woodlandhill.org
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