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AGE 3-6+ GEOMETRY, MATH, MEASUREMENT:
Introduction
Manipulative materials
Reprinted from:
Child of the World, Essential Montessori for Age three to Twelve
ISBN: 1-879264-11-0
INTRODUCTION
If
men had used only speech to communicate their thought, if their wisdom
had been expressed in words alone, no traces would remain of past generations.
It is thanks to the hand, the companion of the mind, that civilization
has arisen. The hand has been the organ of this great gift that we inherit.
—Dr. Maria Montessori
I do not know when geometry and mathematics became a
study I dreaded, but I know when I started enjoying it. My father was
an engineer and loved math. He enjoyed measuring, sawing, building, explaining
the operation of the slide rule to us, working out fraction problems.
He wanted very much to have someone in the family who shared this passion;
there was no one. We had all learned in school that math was required
for practical reasons, that the multiplication tables were essential and
painful, and that teachers hated teaching math as much as we hated learning
it.
Then, during my Montessori 3-6 training, I observed school where children
chose math over everything else and worked on it for hours and hours,
and where teachers loved teaching it! Later, in teaching Montessori 6-12
classes I saw the same thing with square root, cubing, and every kind
of math and science. I learned, not to hide my prejudices, but to find
the enjoyment in every subject. Only then could I hope to pass on a true
love of learning to my students.
EXPERIENCE FIRST
The concepts of math and geometry as symbols
on paper make sense after sensorial experience. Removed from real objects
these studies become dry and meaningless. Children naturally have an interest
in all aspects of mathematics, weight, order, systems, series, time, quantities
and symbols, and so forth. We can serve the development of the mathematical
mind by feeding this interest, giving sensorial experiences first, and
only then their representatives on paper.
Sometimes people think there is something magic about sensorial math materials.
Yes, the materials are certainly ingenious, but the real value of manipulatives
is that they support the natural love of math concepts and activities
that occurs early in life. These activities include: counting, sorting,
classifying objects, experiences with series of sizes and colors, weighing
and measuring, carrying out housework such as dish washing, with many
sequential, logical steps—these are activities that nourish the mathematical
mind.
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© Copyright Michael Olaf, 2004
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MANIPULATIVE MATERIALS
When the first Casa dei Bambini in Rome was
opened in the beginning of the 20th century the children were not taught
math until they asked if they could study it. It was when the 3-6 children
asked to use the math materials from the elementary classes and were more
successful at learning these concepts (!) that math began to be an important
part of Children’s Houses for children from the age of three to six.
Many people misunderstand, at first, what it means to learn math at this
age. They remember how they learned the multiplication tables for example—tedious
and boring, hours of painful repetition that was certainly not the first
choice of activities.
In the 3-6 class, children love to learn the quantities and symbols for
numbers in the thousands. They often learn addition, subtraction, multiplication
and division with the decimal system and with fractions, simultaneously.
None of this work is required of the children, but it is offered, presented
with manipulative materials to one child at a time—by the adult and
sometimes another child. There are no teachers lecturing to a group of
children who are required to sit still and listen. The children choose
this work, and repeat each step with joy and enthusiasm until they are
ready to move to the next step.
Certainly not every child masters or even works with every piece of math
material in the 3-6 class. The main point is that an enjoyable and interesting
introduction to all of the areas of geometry and math are present in the
environment. The child is introduced to each activity as she is ready,
and given the choice of whether or not to continue to work with it. In
the meantime, she is surrounded by other children joyfully exploring math.
Math and geometry are presented and treated in the same way as art, building
with blocks, music, gardening, and all other subjects. What a different
and wonderful introduction to a subject detested and feared by many of
us adults.
A child who is allowed to explore with real mathematical objects at an
early, motor-sensorial age stands a good chance of becoming a real math
lover later in life. If his passions lie elsewhere, at least he will be
exempt from the math phobia which so many of us experience because of
our own less-than-joyful introductions to this area of learning.
Math and geometry materials do not have to be expensive; they can be made
of cardboard cubes, strings of beads, blocks, beans, anything that helps
the child grasp the concept through her senses. In fact, the more one
uses everyday objects for comparing, measuring, counting, and carrying
out any other mathematical processes, the more math becomes a part of
the real, practical, everyday life of the child.
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TEXT - To return to
the Child of the World main page of the philosophy and practice text,
go to: michaelolaf.net/
/1CWhome.html
PRODUCTS For "Age
3-6+, Geometry and Math" products, go to: michaelolaf.com/1CW36math.html
The products selected by the Michael Olaf Montessori
staff are very different from those commonly available for children. They
are made of natural materials whenever possible; they are beautiful; they
meet an important developmental need; and they have proven themselves
over the years, or have been well-tested to meet the highest standards.
Products which support this section of Child of the World, Essential Montessori
for Age Three to Twelve, include: geometry blocks, geometric solids, eight
different sets of Froebel Gifts, 1-10 number puzzle, international counting
books, math books, multiplication tape, kitchen scale, teaching clock,
timer, magnetic calendarr.
If you would like to order a copy of Child of the
World to read at your leisure, and to share with non-internet friends
and associates, please see http://www.michaelolaf.net/ordering.html
Return to the Michael Olaf home pages:
http://www.michaelolaf.net (free
information on Montessori philosophy and practice)
http://www.michaelolaf.com (products)
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