MATHEMATICS
, INDEX
Introduction to Mathematics.……………………………………………………….......................1
Materials…………..……………………………………………………………………................5
Group 1- Numbers to 10…..……………..…………………………………......................6
Group 2- The Decimal System……………………………………………………………23
Group 3- Counting 1 to 1000……………………………………………………………..97
Group 4- Memorising Essential Number Combinations………………………………...125
Group 5- Passage to Abstraction………………………………………………………..200
Fractions………………………………………………………………………………...225
Questions………………………………………………………………………………………..236
, INTRODUCTION TO MATHEMATICS
Mathematics is a ‘language’, which enables human beings to understand and explain the
laws of the universe. Part of the human history, because is the product of the human intellect.
“Numbers are the conventional symbols used by a group of men in order to indicate quantities,
in which the symbols have certain names. They have no value by themselves. What gives the
symbols and their names value? A flower may have a form, colour and a scent, but a number has
a value only because a group of men have agreed to fix that value to a special symbol. If I fix to
the symbol 1, the value of hundred and you fix the value of one to it, we shall not understand
each other. The numbers, like the alphabet, have been a means of exchanging ideas between
men, a means of understanding one another”
(Development in the child, V2 p.20)
Mathematics is a wonderful cultural heritage - intrinsic in all aspects of life particularly in
nature, art, architecture, music, science, and technology. Mathematics in Supranature, mathematics
is everywhere.
Why is maths introduced at such an early age? Montessori believed that each human being
has a capacity for mathematics. Mathematics is in everything that we do. Children are expose to
mathematical language, like half of banana, mommy has 2 sugars in her coffee, is 12:15, and more.
So, it is around the child from day one.
Mathematics is part of the nature of human being. An explanation of the Dr Montessori’s
use of the term ‘Mathematical Mind’ Montessori, suggested that every human being has a mind
that is mathematical by nature: “a sort of mind which is built up with exactity”. The mathematical
mind tends to solve problems, able to think in the abstract, see identities, similarities, differences
and more.
The child at this age, has a sensitive period for order. It is important to help the child in the
creating of mental order that will support his adaptation on the environment. The child observes
and has different sensorial experiences. Thanks to these experiences the child abstracts qualities
and concepts of his environment establishing his mental map. Is important to provide activities
that follow the child’s interests, taking into account the Absorbent Mind and Sensitive periods of
this period of development.
1
, Since the child comes into the Children’s House, has an indirect preparation of mathematics
through Practical Life and Sensorial materials. Practical Life materials are really important, are the
foundation for latter learning of any Montessori classroom. The child is attracted to these exercises
because of their real purpose which engages his intellect. The particular way in which the child
has to work with the material, requiring order and precision. Also, they follow a process of steps
that help the child in his logical thinking, really useful for mathematics. Furthermore, the repetition
of the activity, sets a pattern and facilitates the effort of the child. As well as helping the child to
be precise, judge, discriminate, problem solving, build confidence, and self-esteem.
The Sensorial materials are also mathematical materials. They are designed with exactness
and precision. So, when the child works with them, those abstractions that he makes will also be
exact. Also, the sensorial perception is being developed with these materials. The dimensional
materials present a really precise mathematic sequence. For example, read rods increasing 10cms;
10 cubes pick tower; decimal square and more. As we can see, the base number is 10. Also, some
materials have 2 sets in each material, like sounds boxes, these are for pairing. Pairing helps the
brain develop, focusing in the quality of the material making discriminations and comparations.
Other materials like the binomial and trinomial cubes have an indirect preparation for algebra.
Mathematics is and abstract topic. Is because of that, that young children need concrete
objects that can handle and manipulate. The child gets sensorial impressions of the mathematical
concepts. The material begins with concrete experiences and then, more abstract. Remember,
always one difficulty at a time. Mathematics materials are logical and built in a way which children
have the opportunity to get the basic ideas.
In the Children´s House, the adult gives an overview of the five major groups of exercises
related to mathematics: group 1, numbers from 0 to 10; group 2, the decimal system; group 3,
counting 1 to 1000; group 4, memorization of essential number combinations; group 5, passage to
abstraction; and fractions.
Group 1, numbers 1 to 10 and 0, stand-alone group. Is the basics of all maths. Understanding
of what “one” is, then, they can go on and count. A unit is a rate for one of something. Examples
of where the child has work with units, the pink tower, red rods and brown stairs.
2
, INDEX
Introduction to Mathematics.……………………………………………………….......................1
Materials…………..……………………………………………………………………................5
Group 1- Numbers to 10…..……………..…………………………………......................6
Group 2- The Decimal System……………………………………………………………23
Group 3- Counting 1 to 1000……………………………………………………………..97
Group 4- Memorising Essential Number Combinations………………………………...125
Group 5- Passage to Abstraction………………………………………………………..200
Fractions………………………………………………………………………………...225
Questions………………………………………………………………………………………..236
, INTRODUCTION TO MATHEMATICS
Mathematics is a ‘language’, which enables human beings to understand and explain the
laws of the universe. Part of the human history, because is the product of the human intellect.
“Numbers are the conventional symbols used by a group of men in order to indicate quantities,
in which the symbols have certain names. They have no value by themselves. What gives the
symbols and their names value? A flower may have a form, colour and a scent, but a number has
a value only because a group of men have agreed to fix that value to a special symbol. If I fix to
the symbol 1, the value of hundred and you fix the value of one to it, we shall not understand
each other. The numbers, like the alphabet, have been a means of exchanging ideas between
men, a means of understanding one another”
(Development in the child, V2 p.20)
Mathematics is a wonderful cultural heritage - intrinsic in all aspects of life particularly in
nature, art, architecture, music, science, and technology. Mathematics in Supranature, mathematics
is everywhere.
Why is maths introduced at such an early age? Montessori believed that each human being
has a capacity for mathematics. Mathematics is in everything that we do. Children are expose to
mathematical language, like half of banana, mommy has 2 sugars in her coffee, is 12:15, and more.
So, it is around the child from day one.
Mathematics is part of the nature of human being. An explanation of the Dr Montessori’s
use of the term ‘Mathematical Mind’ Montessori, suggested that every human being has a mind
that is mathematical by nature: “a sort of mind which is built up with exactity”. The mathematical
mind tends to solve problems, able to think in the abstract, see identities, similarities, differences
and more.
The child at this age, has a sensitive period for order. It is important to help the child in the
creating of mental order that will support his adaptation on the environment. The child observes
and has different sensorial experiences. Thanks to these experiences the child abstracts qualities
and concepts of his environment establishing his mental map. Is important to provide activities
that follow the child’s interests, taking into account the Absorbent Mind and Sensitive periods of
this period of development.
1
, Since the child comes into the Children’s House, has an indirect preparation of mathematics
through Practical Life and Sensorial materials. Practical Life materials are really important, are the
foundation for latter learning of any Montessori classroom. The child is attracted to these exercises
because of their real purpose which engages his intellect. The particular way in which the child
has to work with the material, requiring order and precision. Also, they follow a process of steps
that help the child in his logical thinking, really useful for mathematics. Furthermore, the repetition
of the activity, sets a pattern and facilitates the effort of the child. As well as helping the child to
be precise, judge, discriminate, problem solving, build confidence, and self-esteem.
The Sensorial materials are also mathematical materials. They are designed with exactness
and precision. So, when the child works with them, those abstractions that he makes will also be
exact. Also, the sensorial perception is being developed with these materials. The dimensional
materials present a really precise mathematic sequence. For example, read rods increasing 10cms;
10 cubes pick tower; decimal square and more. As we can see, the base number is 10. Also, some
materials have 2 sets in each material, like sounds boxes, these are for pairing. Pairing helps the
brain develop, focusing in the quality of the material making discriminations and comparations.
Other materials like the binomial and trinomial cubes have an indirect preparation for algebra.
Mathematics is and abstract topic. Is because of that, that young children need concrete
objects that can handle and manipulate. The child gets sensorial impressions of the mathematical
concepts. The material begins with concrete experiences and then, more abstract. Remember,
always one difficulty at a time. Mathematics materials are logical and built in a way which children
have the opportunity to get the basic ideas.
In the Children´s House, the adult gives an overview of the five major groups of exercises
related to mathematics: group 1, numbers from 0 to 10; group 2, the decimal system; group 3,
counting 1 to 1000; group 4, memorization of essential number combinations; group 5, passage to
abstraction; and fractions.
Group 1, numbers 1 to 10 and 0, stand-alone group. Is the basics of all maths. Understanding
of what “one” is, then, they can go on and count. A unit is a rate for one of something. Examples
of where the child has work with units, the pink tower, red rods and brown stairs.
2
