EPL, the abbreviated form of ‘Exercises of Practical Life’ are simple everyday activities performed by adults to maintain and control the environment in which they live and work. These activities are utilitarian and have a purpose and are a means to the end results are important than the process. The practical life curriculum area is paradoxical and it is the area that experienced Montessori teachers count on most often to draw children into purposeful activities, especially for the very young or easily distracted children. That is the main reason to call EPL activities as settling down activities.

Basically, it is any physical activity that helps a child grow in motor skills, cognitive development, self confidence and development of his or her own personality, and most of all independence. Any controlled movement of hands, arms, legs, feet, eyes, etc. helps your child achieve independence and mastery of his or her environment. Sitting up, crawling, walking, grasping a toy are practical life skills for infants. Practical life activities give the child an understanding of his environment and how it works. The child enjoys all types of work. He also enjoys keeping the environment beautiful for all to use. This work builds the child's self-esteem, making him feel of value.

In his early years, he goes through a period when he wants passionately to learn to do all the work he sees the adult doing. At first, he likes to learn the work of the home. This age will pass, but if it is used, the child will know how to do everything well in the home environment. He will grow intellectually. It is done purposely to take advantages of the child’s desire to imitate the adult and learn to function in his own environment. Most important each exercise is a potential occasion to normalize a child and is preliminary to more advanced learning.

There are certain principles we need to follow while presenting an EPL activity to a child. The most important among all of them are the

i) ‘Analysis of movements’

ii) ‘Synthetic Movements’

By analysis of movements we mean that each activity consists of a series of individual movements which are simple in nature, a successive logical, simpler, single movement follows each movement. Analysis of movement is necessary when giving a presentation to help the child understand the movement and the sequence of the movements. Synthetic movement means performing a simple task divided into several movements to achieve an intellectual goal.

EPL has four following categories:-

1. Social Graces: In this category children are taught some common social etiquette which we need in everyday life like how to cough, how to sneeze, how to shake hands or do namaste etc.

2. Preliminary activities: In this category children are introduced to familiar activities which we do in our houses everyday like how to pour solids, pour liquids, stacking books or offering a glass or a pair of scissors and many more.

3. Taking care of the environment: Activities in this category help the child to take care of his environment like sweeping, dusting, polishing different objects etc.

4. Taking care of self: In this category, activities like shoe polishing, closing and opening different types of buttons, washing off hands are introduced to take care of themselves independently.

In each category, the materials are kept in the environment in an order. All the materials are child size and kept on low shelves so that the children can easily handle their own material and after finishing the work they can put them back into the correct places.

The exercises in Practical Life are the very heart of Montessori education as it is presenting the real life activities with real apparatus and making a bridge between the home and the school environment. As young children wash tables, pour liquids, polish silver, sweep and dust, they are developing the inner aptitudes of calmness, order, concentration, coordination, and fine motor skills. At the same time, through the process of learning to meet their own needs, learning to take care of their immediate physical environment and of themselves and through the experience of helping others, children in Montessori programs begin to develop independence, self-confidence, and self-respect. By learning to complete the work cycle and replace the materials on the shelf the children establish good work habits. They also engage in grace-and-courtesy activities that foster positive social interaction. Many people when they first visit a Montessori house may immediately notice all these but what is not immediately noticed is the role EPL activities are playing in developing functional autonomy, including the ability to choose, take responsibility for one’s self, for others and also for the environment.

For young children, there is something special about tasks which an adult considers ordinary--washing dishes, paring vegetables, polishing shoes, etc. These tasks, which to adults may seem mundane, are intriguing to children because they allow them to act as adults do. Imitation is one of the strongest urges during the child's early years. One of the child's first and fundamental tasks is to adapt and orient himself/herself to her immediate environment and EPL activities are one of the best ways to do so.

There are a number of reasons to introduce EPL as one of the first activities while a child just enters a Montessori environment. One of them is surely to normalize and make a child stable in a total new environment. The practical life activities will be those the children see done in their own homes. They will be carried out in as realistic a manner as possible in the Montessori environment. Nature urges the child to acquire these skills. The child who, as a small toddler, is allowed to help his mother in the house, and learns these skills from her, grows in intelligence, is deeply satisfied, and develops confidence and a good self-image. He knows he is doing useful work, and that his work is of value. He feels that he contributes to helping in the home. He knows he is independent and able to manage for himself.

In the Practical Life area of the classroom, the exercises and activities help children perfect their coordination as they repeat and become absorbed in an activity. Children gradually lengthen their span of concentration and also learn to pay attention to details as they follow a regular sequence of actions. Finally, through the exercises of practical life, the children learn life-long working habits: orientation to tasks, perseverance, self-directedness, satisfaction and a confidence they transfer to later academic work.

Practical life ideas help with developing motor skills, eye hand coordination, order, sequence, concentration, and independence. Most importantly, a child who can control his or her environment is a happy well-adjusted child. Constant uses of these ideas when cleaning, cooking, getting ready for the day, will let your child help become a real part of the family routine.

## Sunday, May 10, 2009

### Sensorial - study through the senses

Dr. Maria Montessori believed that there is nothing in the intellect which first does not exist in the senses. She based her method of teaching young children considering the fact that a child between two to six years passes through the ‘sensitive period for the refinement of senses’ along with the others and they can be helped in the development of the senses while they are in this formative period. In order to serve this purpose Dr. Maria Montessori introduced a subject called ‘Sensorial’ where the materials are specially designed to enable the children to use their senses to explore different attributes of the world. It is not fully correct to say that Dr. Montessori was the first person to realize the importance of sense training for a child. She was greatly influenced by the ideas of his two predecessors – Jean Itard and Eduoard Seguin. She took the idea of introducing didactic materials and the three period name lessons to the child in Sensorial curriculum from Seguin. In fact, it was Seguin who first followed the scientific method of teaching which was later adopted by Dr. Montessori in a more concise and modified form. She also took the idea of isolating one sense and highlighting it through one presentation from her predecessors.

Though the idea of didactic materials is taken from Seguin, Dr. Montessori modified them based on her observations of the children. By Didactic materials we mean the materials which are self-corrective and by the process of trial and error a child can achieve the end result without much assistance from the adult because of these didactic materials in Sensorial. This is basically known as ‘Auto Education’.

All the sensorial materials involve the use of the hands in a

classifying act. For example: visual classification of dimensions. The hand and the mind act together making a mental connection between an abstract idea and its concrete representation. The materials should be simple, direct aim being highlighted and the material is easy to understand. Children use these materials in spontaneous exercises. The sensorial materials are concrete bits of information which can be organized into meaningful patterns. The didactic nature of the material gives the children hands on experience with mathematical concepts. As teachers, we need to understand how children move towards understanding concepts and how different ways of using the materials match children evolving conceptual development.

An object possesses nine qualities as following:

By using his all five basic senses i.e. visual sense, tactile sense, auditory sense, gustatory sense, olfactory sense and also using the additional senses like baric sense (sense of weight), thermic sense(sense of temperature) and stereognostic sense (sense of shape and size of an object by holding it with hands) the child explores all the nine qualities of an object but in separate sessions and also with separate materials. For example: a child using his tactile and visual sense explores different dimensions of an object i.e. height, diameter etc. in the presentations like Cylinder Blocks, Pink Tower, Brown Stairs and so on. He explores different intensities of colours using his visual sense in Colour Boxes. His auditory sense is enhanced while exploring different intensities of sound i.e. loud and soft in Sound Cylinders while he can differentiate between tow textures i.e. rough and smooth using his tactile sense in Touch Boards. In Baric Tablets, he gets a clearer perception of weight – light or heavy using his baric sense and so on.

Young children like to explore experiment, tinker and try new things. They like to touch and feel and manipulate objects. They feed their minds through activities. They learn through their senses to satisfy their insatiable appetite for things to do. Dr. Montessori designed her sensorial curriculum area considering these facts. The first of the child’s organs to begin functioning are his senses. It is necessary to begin the education of the senses in the formative periods, if we wish to perfect this sense development with the education to be followed. The education of the senses can start from infancy and should continue during the entire formative period to prepare a child for his future.

Sensorial materials not only provide the refinement of sense but it actually prepares the child for many other subjects which the child encounters afterwards. Sensorial activities are indirect preparation for Maths. Because in Sensorial, we deal mainly with different shapes and seizes like what we do in Geometry. There is an excellent way of introducing Geometry to a child at a very tender age by the presentations of Geometry Cabinet, Geometry Solids etc. in every presentation a child thinks logically or compares the materials with other to achieve the final goal. This actually sharpens the comparative study skills and logical thinking of a child. It indirectly prepares a child for Decimal system because most of the materials are ten in number. Sensorial also prepares a child for different aspects of Languages like Adjectives, Opposites and also new words by the three period name lesson given on each material. We prepare a child to write with the presentation of drawing insets and the knobs present in the materials being the thickness of a writing pencil prepares the hand for holding it.

The education of senses makes men observers. The child who has worked with the sensorial materials has not only acquired a greater skill in the use of senses but also guides his exploration of the outside world. The aim of sense training is not only that a child shall know the colours forms and textures but also that he refines his sense through an exercise of attention and through comparison.

Though the idea of didactic materials is taken from Seguin, Dr. Montessori modified them based on her observations of the children. By Didactic materials we mean the materials which are self-corrective and by the process of trial and error a child can achieve the end result without much assistance from the adult because of these didactic materials in Sensorial. This is basically known as ‘Auto Education’.

All the sensorial materials involve the use of the hands in a

classifying act. For example: visual classification of dimensions. The hand and the mind act together making a mental connection between an abstract idea and its concrete representation. The materials should be simple, direct aim being highlighted and the material is easy to understand. Children use these materials in spontaneous exercises. The sensorial materials are concrete bits of information which can be organized into meaningful patterns. The didactic nature of the material gives the children hands on experience with mathematical concepts. As teachers, we need to understand how children move towards understanding concepts and how different ways of using the materials match children evolving conceptual development.

An object possesses nine qualities as following:

**1. Shape****2. Colour****3. Texture****4. Sound****5. Smell****6. Taste****7. Temperature****8. Weight and****9. Size**.By using his all five basic senses i.e. visual sense, tactile sense, auditory sense, gustatory sense, olfactory sense and also using the additional senses like baric sense (sense of weight), thermic sense(sense of temperature) and stereognostic sense (sense of shape and size of an object by holding it with hands) the child explores all the nine qualities of an object but in separate sessions and also with separate materials. For example: a child using his tactile and visual sense explores different dimensions of an object i.e. height, diameter etc. in the presentations like Cylinder Blocks, Pink Tower, Brown Stairs and so on. He explores different intensities of colours using his visual sense in Colour Boxes. His auditory sense is enhanced while exploring different intensities of sound i.e. loud and soft in Sound Cylinders while he can differentiate between tow textures i.e. rough and smooth using his tactile sense in Touch Boards. In Baric Tablets, he gets a clearer perception of weight – light or heavy using his baric sense and so on.

Young children like to explore experiment, tinker and try new things. They like to touch and feel and manipulate objects. They feed their minds through activities. They learn through their senses to satisfy their insatiable appetite for things to do. Dr. Montessori designed her sensorial curriculum area considering these facts. The first of the child’s organs to begin functioning are his senses. It is necessary to begin the education of the senses in the formative periods, if we wish to perfect this sense development with the education to be followed. The education of the senses can start from infancy and should continue during the entire formative period to prepare a child for his future.

Sensorial materials not only provide the refinement of sense but it actually prepares the child for many other subjects which the child encounters afterwards. Sensorial activities are indirect preparation for Maths. Because in Sensorial, we deal mainly with different shapes and seizes like what we do in Geometry. There is an excellent way of introducing Geometry to a child at a very tender age by the presentations of Geometry Cabinet, Geometry Solids etc. in every presentation a child thinks logically or compares the materials with other to achieve the final goal. This actually sharpens the comparative study skills and logical thinking of a child. It indirectly prepares a child for Decimal system because most of the materials are ten in number. Sensorial also prepares a child for different aspects of Languages like Adjectives, Opposites and also new words by the three period name lesson given on each material. We prepare a child to write with the presentation of drawing insets and the knobs present in the materials being the thickness of a writing pencil prepares the hand for holding it.

The education of senses makes men observers. The child who has worked with the sensorial materials has not only acquired a greater skill in the use of senses but also guides his exploration of the outside world. The aim of sense training is not only that a child shall know the colours forms and textures but also that he refines his sense through an exercise of attention and through comparison.

### Montessori Language Program

**Introduction**

Language is an organized system of symbols which human use to communicate. These symbols can be spoken or written down. It is an exploration through sounds which results in a medium of communication. Our ability to use language is one of the main things that separate us from the rest of the animal kingdom.

It is a human tendency to communicate with others and this could underlie the emergence of language. Dr. Montessori said, “To talk is in the nature of man.” Human needed language in order to communicate, and soon, the powers that come with language were revealed. The evolution of the human language began when communication was done through pictograms or pictures and drawings. It then developed into ideograms when pictures began to turn into symbols. Later, these symbols became words, words involved letters, vowels emerged, one symbol came to represent one sound, and an alphabet was created, and then came the alphabet we now use today. And just as language evolved hundreds of thousands of years ago, it also changes with each generation. Unneeded words are dropped and new words come into use. Language rose and continues to rise with the collective intelligence.

We know that the development of a young child's language skills begins at conception. An infant is born into a family with a unique communication style. Family members may be quite open, freely expressing their wants, needs, and feelings. Alternatively, communication may be reserved or even restrained. Babies listen to and absorb not only what family members say but how they say it because they are in the unconscious stage of the absorbent mind. They posses LAD (Language Acquisition Device) which starts functioning from birth and continued till 6 yrs. By this age, with almost no direct teaching, the child learns basic sentence patterns and has achieved considerable mastery in Phonology, Lexis (Vocabulary) and Syntax (order or words in a sentence). This doesn’t mean a child of this age has full language competence. He needs to acquire more complex structures during primary year. He should be given names of all the things in his environment for this is the period known as the ‘sensitive period for language’ where he learns things naturally. Later he will have to memorize them, which will be not only more difficult but not nearly so likely to stimulate a life-long interest in these things. It is equally important to surround him with the written words. A balanced environment, one that is open yet not chaotic or inappropriate, is the most conducive to language learning. We need to talk often and meaningfully with babies. Babies learn to trust their surroundings as older siblings and adults hold and cuddle them, engage them with smiles and coos, and most importantly, acknowledge their communications.

While talking about the child’s language development, we should name Naom Chomsky other than Dr. Montessori because he asserted that the capacity for language is genetic. The brain is pre-wired to understand and produce language. Chomsky found that all language contain the same elements like noun, verb, adverb, adjective, preposition, conjunction and interjection despite of cultural differences. He coined the concept as ‘Universal Grammar’.

When the child arrives in the Montessori classroom, he has fully absorbed his culture’s language. He has already constructed the spoken language and with his entry into the classroom, he will begin to consolidate the spoken language and begin to explore the written forms of language. Because language is an involvement in the process of thinking, the child will need to be spoken to and listened to often. The child will need a broad exposure to language, with correct articulation, enunciation, and punctuation. The child will need to experience different modes of language and to hear and tell stories. Most importantly, the child needs to feel free and be encouraged to communicate with others.

The most important preparation of the environment for successful development of spoken and written language in the child is the language environment of the home. It is never too early to speak clearly and precisely to the child. In fact the language of the caregivers in the first six years of life will literally form the spoken language of the child. Reading aloud to the child gives the message that reading is fun for everyone, and concepts and vocabulary words will be experienced which would never come up in spoken language.

The development of language in early-childhood classrooms is an umbrella for the entire Montessori curriculum. Often teachers and parents consider activities on the shelves of the Language area as the heart of actual language learning. Certainly these activities provide powerful opportunities, but language learning occurs most profoundly in the moment-to-moment life of interactions within the classroom.

To help the child in his development in language, the Montessori classroom is designed to help the child. Because the learning of language is not done through subjects as in a normal classroom, the child is learning at his own rhythm. This allows the child to concentrate on the learning of each important step in language so that each progressive step is done easily and without any thought on the part of the child. The special material also plays an important role in aiding the child develops the powers of communication and expression, of organization and classification, and the development of thought.

But the most important tool in the child’s learning of language lies within the directress. She must support the child in his learning; give him order to classify what he has learned, to help the child build self-confidence, and to provide the child with meaningful activities. The directress is the child’s best source in language development.

As the child leaves the Montessori classroom after the age of six, he will have become an articulate person, being able to communication his feelings in well-formed sentences and in writing. He will be able to write these thoughts and feelings in a skillful handwriting. He will have the ability to write in different styles and about a variety of subjects.

For success in language a child needs confidence that what she has to say is important, a desire to relate to others, real experience on which language is based, and the physical abilities necessary in reading and writing. There are several things that we can do to help.

We can listen and talk to the child from birth on, not in baby talk, but with respect and with a rich vocabulary. We can provide a stimulating environment, rich in sensorial experiences and in language, providing a wealth of experience, because language is meaningless if it is not based on experience. We can set an example and model precise language in our everyday activities with the child. If we share good literature, in the form of rhymes, songs, poetry and stories we will greatly increase the child's love of language.

If we help our children with the physical preparation of the body and hands, listen carefully to our children when they talk to us, set an example of loving to read, and approach giving our children language with the same spirit of fun with which we play other games, we will be doing the most important things to prepare for a successful life of reading and writing.

Each new concept can be presented in a multisensory, hierarchical procedure matched to the child's level. Each activity can be broken into reduced levels of difficulty or increased levels of abstraction as fits the student. For this reason the child, having difficulties in grasping language may move more slowly than another child but will not suffer complete confusion.

## Monday, March 16, 2009

### Montessori Maths Program

A young girl's small hand grasping beautiful objects, sensing the world around her – shapes, dimensions, relationships, amounts - all represented by concrete objects that prepare the mind for a deep understanding of the principles of mathematics. Maria Montessori discovered that children understand the world, through all their senses which she referred as the ‘Sensitive Periods’, and that only by making use of this knowledge can their understanding be developed to its fullest potential. Nowhere is this more evident than in the Montessori mathematics curriculum. As the child progresses from early childhood through the elementary years, the Montessori Math curriculum moves from the concrete, to increasingly abstract concepts of mathematics. As with all Montessori materials, the mathematics curriculum is performed by the individual, using self-teaching and self-correcting materials. These materials are presented to the child as interest is expressed or observed and then the adult moves away, to allow exploration through repetition, until the concept is mastered. In small sequential steps, each learner develops a mathematical mind at his or her own pace.

The Montessori sensorial materials form the foundation, in preparing the child for the abstract world of numbers. Montessori gave the Sensorial equipment the credit for helping the child explore his environment and also for developing the mathematical mind - the mathematical structures necessary for the order, sequencing and precision of mathematics. During the day-to-day manipulation of concrete objects the child builds her concepts of numbers and the ability to concentrate. Montessori emphasized that all materials must be beautiful, and stimulating to the senses, inviting children to take them from the shelves to explore them again and again. Small children naturally love repeating activities and thoroughly absorb the intended concepts. The Sensorial work is a preparation for the study of sequence and progression. It helps the child build up spatial representations of quantities and to form images. When a child starts working with the sensorial material the first numbers he deals with in most of the apparatus are from 1 – 10 like in 10 cylinders, 10 cubes, 10 prisms etc. As the basic numbers of the decimal system are from 1 – 10, the child unknowingly starts to deal with mathematical concepts through sensorial materials. Other than the numbers, geometrical shapes, their names and complex mathematical concepts like one-to-one correspondence, seriation, sorting & grouping are also initiated with the sensorial materials in a concrete way where the child is actually experiencing them visually or using his muscular memory. Along with these, the Long rods in Sensorial being same in the length as the number rods in maths lays the foundation for the child to receive Maths program in Montessori environment.

By the age of three and half to four, the child is ready for the receiving mathematics. A series of preparations have been made using other areas of Montessori

1. The child has established internal order.

2. The child has developed precise movement.

3. The child has established the work habit.

4. The child is able to follow and complete a work cycle.

5. The child has the ability to concentrate.

6. The child has learned to follow a process.

7. The child has used symbols.

8. The child is informally introduced to the primary numbers.

All of this previous development has brought the child to a maturity of mind and a readiness of work.

Montessori math curriculum is designed to support children's natural interest in math and provides a strong foundation in numbers through the use of specially designed, hands-on/minds-on math materials. Through concrete mathematical experiences, the youngest children learn about dimension, size, number, shape and sequence. Then, with the use of increasingly abstract materials, children make the transition from concrete experience to paper-and-pencil exercises. Each math concept is taught with corresponding materials.

The Montessori maths program is divided into parts to facilitate a sequential and gradual progress in the maths concepts starting from simple to complex. During circle time, informal activities or games are introduced to initiate complex maths concepts like seriation, one-to-one correspondence, sorting and more in the simplest way. Without counting or even uttering a number name, the child is actually introduced to maths through preliminary maths activities.

Then he is actually introduced to the basic numbers of decimal system through the presentations in ‘Early maths in separate sessions or depending on his personal cognitive development level. Using the sensitive periods of order, manipulating small objects and locomotion the child is able to grasp the basic number concepts from 1 – 10 easily. In early maths program, a child needs to know numbers to 10, in order to be able to work in the decimal system. The long rods introduce the concept of comparative length. Through laying out the rods one-by-one, the child learns, at the most basic concrete level, how the numbers one to ten relate to one another. The red and blue segmented rods add the concept of one-to-one correspondence and allow for the memorization of the 1 through 10 counting sequence. Each rod represents a given number and the relative difference between each number is clearly seen. Then Sandpaper numbers are traced by the child one at a time to associate number names with the fixed quantities they have experienced with the number rods. When both the number rods and the number cards are merged together in a single presentation, the child then & there associates loose number names with fixed quantities which gives them absolute clarity in the accurate association of number and quantity. ‘0’ being an essential and probably one of the most important fundamental concept of maths are taken in isolation with the presentation of ‘Spindle Box’ to make the child understand the meaning of ‘0’ i.e. ‘0’ on its own means nothing but when it is associated with a number, it certainly indicates a bigger number. Some number games and ‘0’ games are played during early maths program to reinforce the concept of ‘0’ and also to make the child experience the bigness and smallness of basic numbers from 1 – 10. Next the child is introduced to the cards & counters where the level of abstraction requires the child to demonstrate that he recognizes the numbers one through ten, knows the order of one through ten, understands one to one correspondence, and can relate the proper quantity to the numbers. The basic four operations – addition, subtraction, multiplication and division are shown in simple yet in an interesting way using only the number rods highlighting the importance of 10, which make the child familiarized with the four operations we need to use in our daily lives probably in every step of it. The whole early maths program reinforces the importance of 10 as the base of introducing the formal demonstrations of Decimal system.

Once the child has developed a secure knowledge of numbers to ten, the exciting world of the static golden bead materials comes to her. This part is known as the formal introduction of the Decimal system i.e. a number system based on ten in which numbers are expressed by combinations of the digits from 0 -9. In this system, all the derived units are the multiples of 10. With the introduction to the Static Golden Bead Material, the child learns to handle numbers till 1000 without being introduced to the traditional number names. From this stage, he gets absolute clarity in each and every hierarchies of the Decimal System and his thorough understanding of the primary numbers (1 - 10) helps him to understand the interrelationship between the hierarchies. While working with the static material, the child forms quantities with the concrete and then with the abstract to gain a considerable mastery in associating both. Like in early maths, in this stage also when the child is comfortable with the concrete, abstract symbols of the hierarchies with the importance of the number of zeros are introduced to him. A number of activities are shown with the concrete golden beads and the static cards to reinforce the child’s concepts of hierarchies, sequencing of numbers, each hierarchy is 10 times than the previous one and the column concept of maths which leads to a natural transition to the complex tasks with the dynamic material.

The dynamic material facilitates the change at 10 in maths. While handling and working with the dynamic materials repeated times, the child is able to understand clearly that when a number reaches 10, it goes to the next hierarchy. The child practices hierarchies changing at 10 many times with the dynamic material and cards. It should be noticeable that without being introduced to the traditional number names, the child easily handles bigger numbers in thousands and hundreds while doing all types of operations with or without change just because he has a clear concept of the primary numbers from 1 – 10 from the beginning of the maths program. All the operations concepts are reinforced and the child handles bigger numbers but still he is counting in tens.

In the later part of the maths program, traditional number names are introduced again with forming quantities with the concrete material first and then associating with their written symbols through the ‘Seguin Board’. Addition, Multiplication, Division and Subtraction Boards are used to reinforce the valuable concepts of these basic four operations. The child is introduced to multiplication tables with interesting materials like Multi-coloured bead bars.

It is clearly visible with the break ups of the Montessori maths curriculum, that all the maths material are graded from simple to complex and from concrete to abstract. Montessori took the idea that the human has a mathematical mind from the French philosopher Pascal. The mathematical mind tends to estimate, needs to quantify, to see identity, similarity, difference, and patterns, to make order and sequence and to control error. By comparing all the facts that a mathematical mind should have, we can say that the Montessori maths curriculum is beautifully designed to suit the child’s need for growing up with a mathematical mind

The Montessori sensorial materials form the foundation, in preparing the child for the abstract world of numbers. Montessori gave the Sensorial equipment the credit for helping the child explore his environment and also for developing the mathematical mind - the mathematical structures necessary for the order, sequencing and precision of mathematics. During the day-to-day manipulation of concrete objects the child builds her concepts of numbers and the ability to concentrate. Montessori emphasized that all materials must be beautiful, and stimulating to the senses, inviting children to take them from the shelves to explore them again and again. Small children naturally love repeating activities and thoroughly absorb the intended concepts. The Sensorial work is a preparation for the study of sequence and progression. It helps the child build up spatial representations of quantities and to form images. When a child starts working with the sensorial material the first numbers he deals with in most of the apparatus are from 1 – 10 like in 10 cylinders, 10 cubes, 10 prisms etc. As the basic numbers of the decimal system are from 1 – 10, the child unknowingly starts to deal with mathematical concepts through sensorial materials. Other than the numbers, geometrical shapes, their names and complex mathematical concepts like one-to-one correspondence, seriation, sorting & grouping are also initiated with the sensorial materials in a concrete way where the child is actually experiencing them visually or using his muscular memory. Along with these, the Long rods in Sensorial being same in the length as the number rods in maths lays the foundation for the child to receive Maths program in Montessori environment.

By the age of three and half to four, the child is ready for the receiving mathematics. A series of preparations have been made using other areas of Montessori

1. The child has established internal order.

2. The child has developed precise movement.

3. The child has established the work habit.

4. The child is able to follow and complete a work cycle.

5. The child has the ability to concentrate.

6. The child has learned to follow a process.

7. The child has used symbols.

8. The child is informally introduced to the primary numbers.

All of this previous development has brought the child to a maturity of mind and a readiness of work.

Montessori math curriculum is designed to support children's natural interest in math and provides a strong foundation in numbers through the use of specially designed, hands-on/minds-on math materials. Through concrete mathematical experiences, the youngest children learn about dimension, size, number, shape and sequence. Then, with the use of increasingly abstract materials, children make the transition from concrete experience to paper-and-pencil exercises. Each math concept is taught with corresponding materials.

The Montessori maths program is divided into parts to facilitate a sequential and gradual progress in the maths concepts starting from simple to complex. During circle time, informal activities or games are introduced to initiate complex maths concepts like seriation, one-to-one correspondence, sorting and more in the simplest way. Without counting or even uttering a number name, the child is actually introduced to maths through preliminary maths activities.

Then he is actually introduced to the basic numbers of decimal system through the presentations in ‘Early maths in separate sessions or depending on his personal cognitive development level. Using the sensitive periods of order, manipulating small objects and locomotion the child is able to grasp the basic number concepts from 1 – 10 easily. In early maths program, a child needs to know numbers to 10, in order to be able to work in the decimal system. The long rods introduce the concept of comparative length. Through laying out the rods one-by-one, the child learns, at the most basic concrete level, how the numbers one to ten relate to one another. The red and blue segmented rods add the concept of one-to-one correspondence and allow for the memorization of the 1 through 10 counting sequence. Each rod represents a given number and the relative difference between each number is clearly seen. Then Sandpaper numbers are traced by the child one at a time to associate number names with the fixed quantities they have experienced with the number rods. When both the number rods and the number cards are merged together in a single presentation, the child then & there associates loose number names with fixed quantities which gives them absolute clarity in the accurate association of number and quantity. ‘0’ being an essential and probably one of the most important fundamental concept of maths are taken in isolation with the presentation of ‘Spindle Box’ to make the child understand the meaning of ‘0’ i.e. ‘0’ on its own means nothing but when it is associated with a number, it certainly indicates a bigger number. Some number games and ‘0’ games are played during early maths program to reinforce the concept of ‘0’ and also to make the child experience the bigness and smallness of basic numbers from 1 – 10. Next the child is introduced to the cards & counters where the level of abstraction requires the child to demonstrate that he recognizes the numbers one through ten, knows the order of one through ten, understands one to one correspondence, and can relate the proper quantity to the numbers. The basic four operations – addition, subtraction, multiplication and division are shown in simple yet in an interesting way using only the number rods highlighting the importance of 10, which make the child familiarized with the four operations we need to use in our daily lives probably in every step of it. The whole early maths program reinforces the importance of 10 as the base of introducing the formal demonstrations of Decimal system.

Once the child has developed a secure knowledge of numbers to ten, the exciting world of the static golden bead materials comes to her. This part is known as the formal introduction of the Decimal system i.e. a number system based on ten in which numbers are expressed by combinations of the digits from 0 -9. In this system, all the derived units are the multiples of 10. With the introduction to the Static Golden Bead Material, the child learns to handle numbers till 1000 without being introduced to the traditional number names. From this stage, he gets absolute clarity in each and every hierarchies of the Decimal System and his thorough understanding of the primary numbers (1 - 10) helps him to understand the interrelationship between the hierarchies. While working with the static material, the child forms quantities with the concrete and then with the abstract to gain a considerable mastery in associating both. Like in early maths, in this stage also when the child is comfortable with the concrete, abstract symbols of the hierarchies with the importance of the number of zeros are introduced to him. A number of activities are shown with the concrete golden beads and the static cards to reinforce the child’s concepts of hierarchies, sequencing of numbers, each hierarchy is 10 times than the previous one and the column concept of maths which leads to a natural transition to the complex tasks with the dynamic material.

The dynamic material facilitates the change at 10 in maths. While handling and working with the dynamic materials repeated times, the child is able to understand clearly that when a number reaches 10, it goes to the next hierarchy. The child practices hierarchies changing at 10 many times with the dynamic material and cards. It should be noticeable that without being introduced to the traditional number names, the child easily handles bigger numbers in thousands and hundreds while doing all types of operations with or without change just because he has a clear concept of the primary numbers from 1 – 10 from the beginning of the maths program. All the operations concepts are reinforced and the child handles bigger numbers but still he is counting in tens.

In the later part of the maths program, traditional number names are introduced again with forming quantities with the concrete material first and then associating with their written symbols through the ‘Seguin Board’. Addition, Multiplication, Division and Subtraction Boards are used to reinforce the valuable concepts of these basic four operations. The child is introduced to multiplication tables with interesting materials like Multi-coloured bead bars.

It is clearly visible with the break ups of the Montessori maths curriculum, that all the maths material are graded from simple to complex and from concrete to abstract. Montessori took the idea that the human has a mathematical mind from the French philosopher Pascal. The mathematical mind tends to estimate, needs to quantify, to see identity, similarity, difference, and patterns, to make order and sequence and to control error. By comparing all the facts that a mathematical mind should have, we can say that the Montessori maths curriculum is beautifully designed to suit the child’s need for growing up with a mathematical mind

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