If education is always to be conceived along the same antiquated lines of a mere transmission of knowledge, there is little to be hoped from it in the bettering of man’s future
— Maria Montessori (1870-1952)

It is a valid wonder the question, Why does the Montessori Method present the learning concepts to the children concretely before they have the expectation for the child to work abstractly. There is always the question: When is it the right time for children to work mathematics abstractly (paper only) as presented in traditional schools and concerns if the children are not going to be able to perform in a traditional setting.

First I would like to present the idea of concrete to abstract as defined by the Association Montessori Internacionale:

A progression both logical and developmentally appropriate. The child is introduced first to a concrete material that embodies an abstract idea such as size or colour. Given hands-on experience, the child’s mind grasps the idea inherent in the material and forms an abstraction. Only as the child develops, is she gradually able to comprehend the same idea in symbolic form.

The main idea to hold true to the Montessori Method is Dr. Montessori’s greatest belief that she expressed in everything she wrote and in every lecture she gave: “what the hand does, the mind remembers.” (M.M.) It is a hard rule she insisted upon, and it is feverishly given to the guides in training. We must trust the material to isolate a concept and through its manipulation the student will gain the full depth of the idea displayed in front of him or her. When is the child ready to move to pen and paper (work abstractly)? We understand this happens when the child demonstrates he or she has internalized the patterns, sequence, or logic of what is being presented and no longer needs the Montessori material to manipulate the concept to gain an accurate result.

In mathematics the material represents the abstract concepts of fundamental operations and assists in the development of the child’s “mathematical mind”. By manipulating the material the child has a logical, clear and visual way of grasping the concept. They can see and feel that 10 is more than 1 and that 1,000 is a quantity much larger than 1. Not just by the notion of memorizing a number or seeing it on paper but by the exercise of actually counting beads to internalize how much more counting is necessary to get to 1,000. This is extremely important when the child moves into dynamic operations (carrying the 1 to the next category). They get to visual and physically carry over to the next category. They see math and the manipulation of quantity and can then begin the process of analysis and working story problems, which brings them to the abstract of mathematic work. The most important gift the concrete material gifts the child is to bring order and sequence to the understanding of mathematical computations, theorems, and problem solving.

Language work provides a fantastic break down of each function of words and with symbols and colors children are able to compartmentalize language and truly get a since of all the Parts of Speech and their use in a sentence. Sentence analysis work is what outside of Montessori is called diagraming sentences. This material is also a gift to the child in breaking down syntax and sentence structure and physically moving words in a sentence to truly understand its position in a sentence and purpose.

The beauty of Cosmic Education lies in all the charts and timelines that lays out an amazing amount of concepts that are presented in a concrete way that can be manipulated, organized, replicated and recompiled in a way that is meaningful to the child in the intent to internalize the concepts and expand beyond what they know. Only until the information is internalized can the child truly express him or herself abstractly.

In our classrooms the children enjoy the freedom to work with Montessori concrete material, books, educational objects (globe, maps), specimens, nomenclature (information cards), art supplies and lots and lots of paper to express their acquisition of new knowledge.

A key to our work in the classroom is to follow Dr. Montessori’s Golden Rule:

Never give more to the mind than you give to the hand.

Peek to the Elementary classrooms:

AuthorDenis Samarin


Cosmic Education is primarily dedicated to the child in the second plane of development. Dr. Maria Montessori and her son, Mario after years of observations, carefully designed this method. Dr. Maria Montessori used the term cosmic education for children ages 6 through 12 years. As the children enter the second plane of development, the human tendencies continue to operate, while new physiological characteristics begin to assert themselves:  the emerging power of the imagination, the drive to know the reasons of things, a need for abstraction and intellectual activities, a drive to perform extended and elaborate work, and a focus on issues of morality. Each of these aspects of the child receives its own measure of attention as Cosmic Education is presented through the years. Even though in a physical classroom we usually see children grouped in ages 6 - 9 and 9 - 12, Cosmic Education and the approach towards the child does not change.


With this thought the child must begin to understand that laws are not oppressive, but rather are a natural part of life and enable us to maintain harmony and order. Cosmic Education reveals to the second plane children that all things in our Universe are connected.  This is how Maria Montessori manifests her concept of Cosmic Education. “The laws governing the Universe can be made interesting and wonderful to the child, more interesting even than things in themselves, and he begins to ask: ‘What am I?” What is the task of man in this wonderful Universe? Why we struggle and fight? What is good and evil? Where will it all end?”

All things are part of the Universe, and are connected with each other to form one whole unity. The idea helps the mind of the child to become focused, to stop wandering in an aimless quest for knowledge. He is satisfied having found the universal center of himself with all things.
— Maria Montessori, To Educate the Human Potential.

The Elementary Team has the amazing and forever exciting task to bring to the children a curriculum that offers the child the Keys to the Universe. The guide approaches any subject with a story that feeds the senses and opens the imagination. Coined by Mario Montessori as the Great Lessons, there are five: First Great Lesson - Coming of the Universe and the Earth, Second Great Lesson - Coming of Life, Third Great Lesson - Coming of Human Beings, Fourth Great Lesson - Communication in Signs (Alphabet), and Fifth Great Lesson - The Story of Numbers. These stories that reveal all the mysteries of the universe are the foundation for all academic learning in the child’s life span.


These lessons provide an all-encompassing, holistic vision of various disciplines combined where the children actively connect to many areas of study as the narration unfolds. They see how the whole relates to its parts and how the parts are responsible for the whole. The Great Lessons tell of how each particle, substance, species, and/or event has a purpose and a contribution to make in the Universe. Gratitude becomes second nature and expressed in the work of the child.


Dr. Montessori’s gift to the Elementary guides was a way to teach children ages 6-12 the beginnings of the Universe, concepts of the origins of life, the evolution of humans, the development of language, and the history of mathematics in a interactive method that crossed all disciplines. The Elementary teacher's goal is not to rely on a syllabus but the child, to be inspired by their curiosity and guide each student using lessons, materials, and providing experiences, both inside and outside of school to bring these great stories to how it is relevant to their life. Day to day the child experiences tangible sensory moments that stems from one of the Great Stories and becomes a part of the child’s past, present and future in relationship to the universe.


In the next few months we will be exploring the depths of Cosmic Education as it unfolds in our classrooms. We look forward to sharing its beauty and wonder with the Creo Community.

Elementary Team

Peek to the elementary classrooms:





AuthorRuchira Fernando

We know when the child moves to the elementary classroom she is a different person. She has a different side of psychological characteristics operating so we must adapt our treatment of plants and animals.

This means it will not be enough for the child just to learn the names or the facts about plants and animals. She now wants to know the How and Why? What lies behind the characteristics and the behaviors of the plants and animals she is learning.  

Why is the plant drooping?  Perhaps it needs water!  

Why is the fish dead? Because...

What we also know about this child is that she has an imaginary mind that is aided by her reason. So in our treatment of plants and animals we have to appeal to that imagination and support our presentations with reasons for everything.  A mistake we don't want to make when working with this older child is to treat her as a primary child has been treated. If we do that we will bore the children and we will not meet their needs. So whenever we introduce an idea or a characteristic about plants and animals we always must give the function of the part (characteristic) because it is the function that explains the reason of the behavior of the plant or animal. Example: We know that leaves need light to make food. Since they need light they have a behavior of growing towards the light. We know that the roots have the task of collecting water that the leaves need to make the food. So the roots have the behavior of growing towards water. So from the children's experiences they see for themselves that the behavior of the plant or animals is related to the function that they perform in order to survive. 

Therefore we will use imagery and allegory in our presentations. They are delighted about stories of plants and animals. This means, that we do not teach them about plants and animals but we excite them about plants and animals through our storytelling approach. When we appeal to the children this way, they become curious about nature. They want to learn more about the fascinating aspect of life on earth. As they go through this process they develop a sense of wonder about all the wonderful ways life has created for their life and to meet their needs. Through these discoveries they become aware of that there’s diversity of life on earth. These great diversities on earth become an imperative for more discovery.

What we have from our approach is that to introduce the children to the world of nature through a storytelling technique. We inspire them to go out and explore what we talked about. We presented and though their own observation allowing them to discover many diversities of life that have developed. 

They become aware that all plants have the same needs but they meet these needs in different ways. That results in the diversities of life. Because we have inspired the children they are making more and more discoveries. Consequently they are building this storehouse of information. This is information they’re going to classify and organize just like when they were younger.  It's a satisfying method to the children because it allows them to order their knowledge and minds and by doing that they are meeting that natural tendency towards order. 

We give the children opportunities in the elementary classroom, to consciously classify different characteristics of plants and animals. First we do it through simple classification. Simple classification is where the children gather specimens that they will classify according to a pair of characteristics. This prepares them eventually for scientific classification.  How this works is that the children can take one specimen and know all of the physical characteristics that will put it in one group as opposed to another group that requires different characteristics.  

For example: This animal protects its body with feathers and his forelimbs are modified for flying. So we classify it in a group we call birds. This animal that protects his body with fur and walks about on four limbs we classify in a group called mammals. As the children participate in classification work they’re organizing the information they garnered. They are clarifying what they know and building their intellect. 

We allow the child to go out to experience nature because we’re helping her to develop her ability to observe carefully. When the children are fascinated by certain characteristics or behaviors of plants and animals, they want to find out more. They find out more by looking very carefully at the world around them. 

If they have a reptile in the classroom, and they notice that the reptile’s behavior has changed or perhaps been not as active as usual, they want to know why. Is it because it’s too cold? Or because he’s molting? The child is looking watching and observing. Through this process her powers of observation become acute. Then she can use this ability in relation to her whole life, not only to plants and animals. 

We know that the human being has a natural tendency to explore. Teachers provide opportunities for the children to explore not just the world inside the classroom, but also the world outside the classroom. Offering the cosmic education, we ensure that we have a method by which they can go out and explore. This is the going out program. 


Another human potential is having responsibility. Children learn responsibility by being able to take care of plants and animals. They also learn to be responsible when they go out, because they have to conduct themselves in a civilized manner. They have to be responsible to the choices they make around the classroom. Therefore,  responsibility plays an important role in the child’s development. It will be a feature or potential that they will use in relation to nature. They will discover that there is a delicate balance on earth between life and earth itself. 

This delicate balance must be protected and maintained. So biology is not treated just as a method of learning about plants and animals; it has a bigger role to play. We hope that our children come to understanding and love towards the plants and animals on the earth to the extent that they do what they have to do to maintain this delicate balance.  

They’re going to understand through work that every organism has a cosmic task, and whatever that task is, is important in the maintenance of that place in life. This means that they will never want to destroy but rather protect the earth.  It means they will want to become more aware of the impact that humans beings are having on life, and they will help to protect it when that impact is detrimental. When the children are confronted with decisions, we want to think they will make a responsible choice due to the exposure we have given them, which will be thoughtful and caring. 

AuthorRuchira Fernando

As children approach the age of six, Montessori observed that children change physically and psychologically. The Absorbent Mind fades, the Sensitive Periods disappear and an interest in sensorial exploration of the immediate environment faded, but not disappeared.

These children had what Montessori called "a hunger for knowledge and understanding." Exploration of the reasons for all of this surrounded them and became their new focus. These changes in the child necessitated a change in approach. Montessori expressed the situation in the following way:

Knowledge can best be given where there is eagerness to learn, so this is the period when the seeds of everything can be sown, the child’s mind being like a fertile field, ready to receive what will germinate into culture.
— Montessori, Maria (2007). To Educate the Human Potential. Amsterdam, The Netherlands. Montessori-Pierson Publishing Company
  • Such things as stars and molecules and distant places and times now attracted the child. These were things that could not be experienced directly.
  • The power of the child's imagination was required if these explorations were to be comprehended.
  • Maria Montessori called imagination the 'great power of this age'.
  • The imagination at work has brought humanity to its present state.
  • Besides its creative aspect, the imagination has been the chief tool with which humanity has been able to understand the nature of the universe. It is these two uses of the imagination that have enabled human beings to reach their present state and to stand poised to enter a new era of understanding. This understanding is exploration and creation.
  • What is the imagination and how does it come to be? How does it operate and what role does it play in elementary education?

Imagination Builds the Mind and is Based Upon Reality

When Maria Montessori considered the imagination, she reached a similar conclusion, stating that imagination was the power to think of things not immediately present.

The imagination builds images; this implies 'something' from which to construct an image. Montessori considered the real-world as the source of images. It provides the raw material with which the imagination operates. She believed that when the imagination began contact with reality, it moved away from speculation and flights of fancy. Little would eventuate and was able to effect change upon the surrounding environment. By beginning with existing, observed facts, humanity and was able to achieve its own acts of creation.

Imagination can only have a sensory basis. The senses helps us to collect from the external world, the material for the imagination. The images that we gather come all of the creations of humanity. The creations of the artist are rooted in the observation of reality. The creations of the inventor find their roots here also. "No genius", Montessori tells us "...has ever been able to create the absolutely new."

It is with and upon images that our mind operates. The measure of these images, the manner in which our mind works with them, is the ultimate measure of the power. One does not carry real objects around in one's mind. All of our experiences are translated into mental images, which the mind is able to abstract.

Dr. Montessori clearly distinguished between imagination and abstraction. In her book The Absorbent Mind, she stated her belief that the human mind had the power to think of things not immediately present (imagination). To assemble and rearrange its mental content and extract an 'alphabet of qualities', from the numberless things that we meet in the outside world (abstraction).

In her view, imagination and abstraction played a mutual part in the construction of the mind's content. The human mind takes from the world through the senses and constructs images. This is the imagination at work. That same mind is also capable of working with the images of the mind; extracting from them common qualities, creating an abstraction.

Imagination in the Elementary Classroom

In the elementary, abstracted qualities are related. This is a new level of abstraction which begins in the Casa dei Bambini with matching games (What objects can you find can you find that are exactly this color?). Now, the abstract idea of 'division' is related to the abstract 'decimal' number and division of decimal fractions is explored. 'Convection' is abstracted through various experiments (Sawdust in heated water; patterns of flow that exist in magma under the Earth’s crust). The cooling of the newly born earth is comprehended as this concept is applied to the beginning of our planet.

By appealing to the child's imagination with 'Cosmic Tales', Maria Montessori brought the universe to children. These were the Great Stories. They incorporated grandeur and mystery in a conscious effort to strike the imaginations of these children. This idea of striking the imagination doesn't mean that the child is to be "excited" by the presentation, but that an impression is made upon his mind, as an impression is made upon clay.

The first of these, "God Who Has No Hands" utilized simple experiments and a series of charts to further feed the imagination.

Science experiments illustrated the various forces and mechanisms which were at work. Small pieces of paper are sprinkled on a bowl of water and amazingly, some clump together whilst others seem to avoid one another. This experiment gives a first impression of the behavior of atoms. Their attraction and repulsion of each other. Pieces of paper are not atoms (and for that matter surface tension is not nuclear force) so it is necessary for the child to move from this real experience into her imagination. Whereas, the atomic forces at work might be better visualized.

The charts utilized in this and many other presentations are also intended to appeal to the imagination. Many are 'impressionistic': They use personification and allegory in order to provide the child with opportunity to exercise the imagination. Hot particles rising above the globe as it formed, and cooler particles sinking down towards its surface, are represented as having 'angels' carrying them. The internal functions of a leaf are illustrated in the form of a factory inside a leaf, where minute workers carry out the various life-functions of a leaf.

In both of these cases, as it was with science experiments. The child must move from an illustration that catches the imagination, to a conception of the real processes at work. The imagination assists the child as the move from angel to convection is made. "It's as if..." the imagination says, to the actual process is brought more into focus.

The mathematics materials also help to develop the imagination. It is not possible, Montessori observes, to 'imagine' the number of animals in the ocean. But, if we express some of these numbers in decimal notation, we are able to deal with such quantities. By utilizing numbers and by building one number upon the other, the imagination is assisted in its task of bringing the universe to the child. It is not possible to visualize one billion or one quadrillion living things. Our minds do not possess the scope for this. It is numbers - 1,000,000,000 and 1,000,000,000,000,000 that help children to imagine such quantities!

Concrete representation of quantity and geometric representation of process contribute finally to an algebraic abstraction. It is not a difficult matter for the child to utilize arithmetic images and images of geometric patterns in order to make a final, generalized abstraction that we call 'algebra'. "That's algebra?" I have been asked by children time and again. "I thought that it was supposed to be difficult!"

The imagination, as we have seen, requires 'something' from which to construct its images. Access to the real world provides the best source for images. Now, as the children become interested in all that surrounds them, the contents of the classroom offer too little. Montessori recommended that we take the children out, showing them real things rather than made objects that are stored in cupboards. "Going Out" was viewed by Montessori as an important way to maximize the store of accurate images in the child.

For every new experience, the imagination is employed as it constructs new images,. It utilizes these new images, perhaps in combination with existing images, to construct novel images of its own. New ideas and concepts are thus built. The mind is further developed and organized, and the imagination is strengthened as its 'muscles' are exercised.

Moral and Social Development

Elementary aged children begin to explore morality and society as they enter the second plane of development. What is good? What is bad? Why does that person behave in that manner? What would I have done if I were that person? How might that person react if I do this? How would this person feel if I said that? How would I feel in the same circumstance? These are the kinds of questions that beset the second plane child, and as is the case with exploration of culture; it is the imagination that must be employed if answers to such problems are to be found.

Exploration of the moral field requires a grasp of abstract concepts (honesty and dishonesty, for example) and the ability to follow and to develop logical arguments. In order to determine what is good or bad, a standard must be introduced. This may be the word of an adult or of a peer. It may be the dictate of a holy book. It may be an agreement reached by a group. It may be measured by degree of contentment or dissatisfaction, or of health or sickness. Whatever the case, each specific must be related to the standard, and according to the standard, a conclusion concerning the moral nature of the matter is reached.

It is the imagination that we find hard at work as the children imaginatively place themselves in the shoes of another.

A similar need for the imagination is discovered when one examines the need in these children to associate with others. Organized activity is the order of the day, and this requires choice of a leader, and agreement as to rules and purposes of the group. As decisions are made regarding the order of action, consequences must be imagined and assessed. As the children develop their own moral codes, it is the imagination that enables them to steer a course. 'In the field of morality, the child now stands in need of his own inner light.' Rules and purposes must be invented. As problems are encountered, new avenues offering possible must be found. It is the imagination that drives these matters.

The moral and social development of the second plane child is founded upon the activity of the imagination.


The imagination is a key tool for elementary children as they explore their culture. Imaginative vision, which has 'no limits' is the only means by which the child may embark upon this new level of exploration. Whatever the interest of a child in the elementary class, it is imagination that provides the vehicle for exploration.

Imagination works in tandem with the other faculties of the mind, building concepts and refining abstractions. It is by working upon images, gathered from the world of impression surrounding each child, that the content of the mind is built and ordered. The work of the imagination brings the universe within reach of each child.

Why does the wind blow? Simple experiments and selected charts enable the child to extrapolate from the classroom, to the neighborhood, to the globe. Understanding is achieved through the action of the imagination. It is the imagination that enables the child to apprehend the marvels of natural phenomena, giving rise to a sense of wonder that encourages further exploration, and an appreciation for and gratitude towards the animate and inanimate elements of the world that contribute to the harmony of nature.

It is the imagination that provides opportunity for elementary children to originate their own creations and inventions. Work with the divided skittles and fraction insets enabled a group of children in my elementary classroom to develop their own abstract procedure for division of a fraction by a fraction on paper. Drawing from concrete experience, they had imagined the presence of the materials, imagined what the materials would do and show, but performed the calculation without them. They had then imagined a general rule/procedure that would replace the material! The Creative Imagination of Science had been at work in these children.

Other children imagined a painting that you could feel, and added sand and other materials to their paint. A three-dimensional, textured painting resulted.

As children learn new skills and develop artistically, they have no recourse but to their imaginations. Creative Imagination of Science, and Artistic Imagination play important roles in the on-going development of the elementary child.

If it is our aim to engender a love of learning in our children. If we want them to absorb to a maximum the knowledge available to them, then it is to the imagination that we must turn. The imagination brings life to what might otherwise be dry facts. If we take the children's love of stories as our starting point, as Montessori suggests, then we may find that there is a new enthusiasm and fascination for whatever we might introduce to them; for whatever they encounter. It is to the extent that the teacher frees and feeds the imagination that the student will learn.

Our aim therefore is not merely to make the child understand, and still less to force him to memorize, but so to touch his imagination as to enthuse him to his innermost core.
— Montessori, Maria (2007). To Educate the Human Potential. Amsterdam, The Netherlands. Montessori-Pierson Publishing Company

"Peek" into the Elementary classrooms:

AuthorDenis Samarin


Montessori and Mathematics

Dr. Montessori stressed that our first and foremost goal is to assist the development of the child, which entails supporting each child's progress along the path of self-construction. She believed that one section of that path was mathematical, and she worked to bring mathematics to children in such a way that they could understand it, and so that they could appreciate and enjoy it.

The mathematics introduced in the Montessori elementary environment includes arithmetic, geometry, and an introduction to algebra. For purposes of the adult's organization, arithmetic and an introduction to algebra are given as one sequence and geometry is given as another sequence.

Arithmetic: Numerical aspect of mathematics, or the science/art of computing. In the Montessori elementary the children study the four operations, fractions, decimals, numbers in different bases, measurement, etc.

Geometry: Originally a study of geodesy - Aspects of the earth (size, shape, weight of the earth). Today, a study of points, lines, planes, figures, solids, and an examination of their properties. In the Montessori elementary environment, the children are introduced to Euclidian geometry.

Algebra: A method for reasoning about numbers by employing symbols (usually letters of the alphabet) to represent them, and signs to represent their relationships. Algebra allows us to generalize and to symbolize. In the Montessori elementary, the children learn that algebra can also be used to solve problems, and algebraic expressions can be represented graphically.

Montessori intended that these three strands be introduced to the child simultaneously, and in a way that allowed them to reinforce and support one another:

Under the guidance of our experience with children, we have given these three together, and at an age almost incredibly early. Uniting the three has been found to be a great help and very effective; it is as if, instead of balancing the subject on a precarious pole, we placed it on three strong feet, which join together to give great stability.
— Montessori, Maria. 1963 Education for a New World Kalashetra Press, India

Mathematics and the Second Plane Children

Experiences given to the child in the second plane of development continue to be based in the senses but now sensorial exploration alone is insufficient to support the development of second plane children. The material of the elementary is sensorial, able to be manipulated. However, the work that takes place is now not just activity of the hand. It is also activity of the mind.

The materials invite not just further concrete steps with the hand, but the taking of further conceptual steps with the mind.

Second plane children now utilize their growing power to abstract, and they explore using their imaginations. This new level of work allows the children to identify a variety of relationships.

After each presentation, the children are generally introduced to some form of application or "follow up" work. This provides the necessary repetition for acquisition of the information or skill involved.


The Reasoning Mind

The absorbent mind of the first plane fades away as the child enters the second plane, and in the reasoning mind gains prominence. Second plane children must be left free to reach their own understandings via that store of facts built in the Children’s House, and the relationships discovered now through the use of the reasoning mind.

We must take care to support the children's explorations: We must treat their conclusions with respect, both for the conclusion itself, and for the intellectual process that allowed them to reach the conclusion in the first place:

"If this, then this." - "Furthermore, that is also true." - "This problem is just like that one."

These are constructions that reveal to us the development of a system of logic in the child's mind. We observe the child spontaneously developing syllogisms as they work on a problem, or construct an argument or defense:

A = B               B = C               Therefore, A = C

There is a great power of the intellect at the second plane. This great power will fade away as the second plane draws to a close. It is important, therefore, to provide the children with maximum opportunity to exercise this capacity while it operates.

Great Work

Second plane children responds best to challenging work that appears "difficult". Children of the second plane are drawn to the extremes and to the unusual. They tend therefore to construct extensive problems.

This characteristic provides a stimulating and exciting way to repeat, and to make independent discoveries.

The children should be shown how to construct their own problems. They will come up with problems that they can solve and they will create problems that they cannot solve, and therefore they come to ask for help. Learning occurs in both circumstances.

Adults should wait until help is needed or requested. Do not under-estimate the ability of second plane children and the remarkable results that emerge from their independent effort. Real learning may come from the making of errors, from righting those errors, and then by moving closer towards success.

This is the time when the children need and are capable of completing, an enormous amount of work. If they are not given work to do, to construct themselves as their nature demands, then the result is that they will assert themselves in less desirable ways. The evidence will be various less desirable and less acceptable activities.

Mathematics and History

From time to time, Maria Montessori referred to the "Mathematical Mind" of the human being.

Our human tendencies to abstract, imagine and then to make exact leads to this conclusion that we have this Mathematical Mind. History demonstrates that we symbolize what we discover. Human beings are able to generalize from particulars, and can then apply their discoveries to many new particular situations.

We use mathematics every day in a practical sense as we count our money, or as we attempt to fit various objects into certain spaces. Mathematics helps us to keep records of dates and amounts and measurements. These are activities that we can trace back to the earliest civilizations!

History brings mathematics to life. It allows children to glimpse some of the very real uses to which mathematics has been put, and it connects the children to the many fascinating individuals who have been instrumental in developing our mathematical knowledge. This in turn connects mathematics to society, and it also invites the children to contribute in their own time.

Elementary children are able to apply mathematics to their own daily lives, and to see it in action in the world and society in which they are immersed: "What are proportions of ingredients in the recipe for the dessert will I need to make enough for 100 people, rather than myself. Is there a formula that I can create that will work for 1 person, 10 people, 100 or 1000?"; "What is the shape of this leaf, or this wing, or this galaxy?"

In the history of our numbers and of mathematics and mathematicians the children see that people of the past have each made a contribution that led to the present state of our knowledge. Without them, we would be in another, less advanced place. They also see that these heroes of the past were simple people like themselves, inviting them to strive to make their own contributions in the future.

AuthorDenis Samarin

As the child constructs the adult that s/he is to become, successive levels of independence are attained.

From 0 - 3, the child constructs the ability to move independently. Opportunity to practice the associated skills (crawling, grasping etc.) must be provided. At this age also, the child is constructing an ability to communicate through language. A need to talk and to listen arises.

The immediate environment of home and family is all that is required. In the family home security and safe limits for this physically and psychologically dependent child are found.

From 3 - 6, the child refines independent movement. The Montessori Children’s House answers this need with the Exercises of Practical Life. The senses must be refined and ordered. The child finds an aid to this process in the Sensorial materials of the Primary classroom.

In the second plane, Practical Life continues as new levels of independence are achieved, but many of the skills that are important cannot be learned in the classroom.

The intellect is also very active, and although sensorial experiences are important, now pieces of material in the classroom are not enough – The child needs sensorial experience from the wider universe.

Now, family and home are not enough. A wider environment is required, and the prepared environment of the school becomes a second environment in which the child is able to exercise developing skills and concepts.

In the second plane (6 -12), children construct the ability to function in society. An interest in everything is manifested! Going Out provides an avenue for the development of this self-construction. It is now time to move beyond family and school. Physically and mentally, the child is capable of a great deal. The doors to the universe are now thrown open, and the children begin to explore all that surrounds them. At this stage they are guests and observers of the society.

Going out allows children to discover and satisfy their curiosity. Although we do plan lessons to spark interest and excitement, going out and classroom work must come from the questioning of the reasoning mind of the child. The children must be participating and experiencing society to some extent and this starts indoors: navigating and contributing to the classroom community. (Examples: setting up lunch/snack, baking, taking care of the animals and plants, etc.)


We cannot expect children to be able to navigate society successfully if they're not exposed and not given an opportunity to practice.

The closed society in the classroom is not enough for the second plane children. The children are exploring the Universe and trying to figure out how he or she is going to take place in the world of work. We must give him or her the opportunities to get out into society, to communicate with various people in different environments.

People are the essential ingredients for this. Human exchanges are fundamental to the child's experience. Children will come across adults who are helpful and not helpful. They will have to learn with the guide's support how to gracefully handle both situations. When others make poor choices, we shouldn't react to their negativity. That's a lesson we must teach the children.

What is the difference between a Going Out and a Field Trip?

The Montessori Elementary Curriculum has two types of Going Outs:

1.    Guide-inspired Going Out: How this works is, when a lesson given to a small group of children, sometimes their interests peak and they become interested of knowing more about the subject. Then it is the Guides responsibility to provide them with opportunities to explore those ideas first hand. This is usually small groups, as most Going-outs should be.

2.    Child-inspired Going Out: When a lesson given to a small group of children, sometimes their interests peak and they become interested of knowing more about the subject. Some children may choose to explore options outside of the classroom to gather more information. There is a clear set of guidelines that the child/group must follow in order to attend on Going-Out. The guidelines are reviewed with the Guide and should all aspects be complete, the Guide approves the Going Out. The Guide, Assistant or School Assistant will attend on the Going -Out.

However, these Going Outs are different from Field Trips. A Field Trip has something we do as a whole class to gain experience. For example, an event that is rare to Arizona such as going to see the Russian ballet performance, special Art exhibit or even more expansive such as an overnight exploration within the State.

Each child’s educational experience is individualized, which means that not all children will attend all Going Outs or Field trips. In most cases, all children will experience similar types of opportunities over the three-year period. Some children are not ready or are prepared for certain activities. 

One of the daily goals is to assist all children in grace and courtesy, time management, and following directions so that they are prepared for the various experiences that are provided in the Montessori Elementary. 

Kinds of Going Outs


Guide-led going outs:

Our lessons should open the doors and appeal the imagination and get the reasoning mind working. But children should not get all the information they need in the classroom, they should get just enough to get started. The only way they will develop their potential is by getting out to society. If we spark their imagination and allow the children to go out they will be unlimited with seeking of knowledge. If we stir up the children they will wonder "What else is there to know?", and "What else is there to find out?". True learning takes place when there is interest and the person has the tools to find out. The function of our stories and presentations is just to open the door.

Going out is not an activity that occurs spontaneously. The children must be prepared to Go Out and this process can take some time. Going Out involves a number of stages, and each of these requires a different set of skills. These skills should be built piece by piece, and it should not be assumed that children have already acquired them. This process may be considered indirect preparation for Going Out, and an extension of Grace and Courtesy and Practical Life exercises from the Children’s House, and from lower-elementary classrooms, in case of upper-elementary classrooms

To guide the children through this process in the beginning we organize guide-led going outs to build a solid foundation so later the children can start organizing going outs on their own. When an interest sparks child goes through the materials in the classroom and still the thirst is not exhausted. In this case, we offer them to go out to find out more. The choices are trip to a library, to a store, nature walk or hike in the surrounding environment. That would be a first step in building that foundation. When the children are acquainted with the process with these initial going outs, when the skills are solid we can proceed with more structured going outs to build the next level skills: going outs to museums, art galleries, historic sites, etc.

In case of preparation for a field trip we organize a school sleepover where we are able to mock a field trip in a more controlled environment – the school. On the sleepover there are activities organized by the guides that can happen on a field trip. The children are guided and participate through the whole process. That allows us to assess the maturity level of each child and the community as a whole.

This forms the grace and courtesy of the elementary community. We need to prepare them on how to act, behave, greet, get someone’s attention, react in a challenging situation as well as they must know how to ask questions and thank the people. The Guide prepares the children by introducing particular tools they need (through modeling). Children go out to learn more and gather information. This starts in the classroom, it's not a trip to the park. Going out is work related, it’s about digging deeper “what else can I find out?”, “Where can I find more?”, “Is this something I need to find out on my own or as a group?”, “When?”, “With whom?”, “Where?”, “What preparation should I be making?”. There is a thinking through process to going outs. The reasoning mind is planning for going outs. This helps the child to develop critical thinking and problem solving. The children will need explicit presentations on what to think through. What we need to be considered when planning a going out. We are in the end simply fostering independence for their thinking and action.

Child-led going outs

When the children are exposed to different types of guide-led going outs and have all the necessary skills to organize a going out on their own the guide gives them more responsibility with freedom to make a going out on their own. It doesn’t mean that there are no adults to accompany or supervise them. On the high-level child-led going out there is always a chaperone who can be a school assistant, or prepared trained adult from the community of parents.

So the whole process of preparation looks like that:

  1. Guide-led going out – Skills development.; Children assist with different steps, using the skills that they have developed.
  2. Child-led Going Out – Guide assists and supervises closely.;
  3. Advanced Going Out (sometimes out of state or country).

AuthorDenis Samarin

A glance at typical geometry text might lead to the conclusion that geometry is far removed from daily life. Nothing could be further from the truth. The world that surrounds us is composed of shapes, lines, curves, and angles. There is geometry in nature - In the angles and planes of a mineral crystal, and in the symmetry of a butterfly's wings. 

An inborn, intuitive understanding of fundamental geometric concepts exist in all human beings. Geometry also is to be found everywhere in the world created by humanity. Bridges, iron girders and the design of a chair all have their roots in geometry. This is something that children begin to absorb early in their lives. Impressions, which may not yet have names to them, are gathered by the child in mind and stored for later use. If correct names are used the child is able to add this vocabulary to the growing store of impressions that is being used. 

Whatever the case, the child encounters geometry everywhere. It is a part of the world in which children live, and this must be reflected in the environment that is prepared for children.

 In the Montessori classroom, geometry is part of a three-pronged approach to mathematics. When combined with arithmetic, algebra, and geometry it offers a stable and mutual reinforcing approach to mathematics. The binomial square is a good example of this. It explores an algebraic expression (a + b)^2 = a^2 + 2ab + b^2, and this expression appears in a geometric form (squares and rectangles) Arithmetic is incorporated as numerical and hierarchical values are assigned to pronumerals. The algebraic expression is easy to internalize through the geometric pattern that it produces.


The elementary child has an interest in analysis and the finding of relationships. Constructive triangles, for example, were used in the Children's House for work in construction. Now in the elementary, concepts such as equivalence and the Pythagorean theorem are explored using this material. The Geometry materials and presentations of the Montessori elementary classroom invite intellectual activity, which is attractive to elementary children.

The absorbent mind of the first plane disappears as the child enters the second plane. As the child encounters new terms, another avenue for internalization is required. The need for second plane children to know "How?" and "Why?" provides a new vehicle. Etymology additionally provides a fascinating new way to approach the learning of such nomenclature, for example, why is this shape called a pentagon? (Its name comes from the Greek word for five: pente.) The child's fascination with reasons makes the memorization of terms less onerous than it would otherwise have been!

The idea of Cosmic Education is thus realized as a study of geometry results in a survey of the history of our language. History is suddenly related to geometry, and the lives and work of various innovators in the field of geometry - Thales, Pythagoras, and Euclid for example - offer new fields for exploration for the child. It is in this way that the child is brought into contact with humanity, as Dr. Montessori desired.

The materials allow the children to explore a variety of the basic ideas of geometry. The creative aspect of their developing minds is also nurtured as unique answers to the challenges provided by the materials are found. Many of the geometry activities are open-ended. There is no one correct way, nor one correct route to an answer. Many equivalent shapes may be created for one base figure, for example, with the geometry insets or constructive triangle. Constructions using only a straight edge and compass provide many challenges that draw on the creative talents of each child.

Peek into the elementary classrooms:

AuthorDenis Samarin

When it comes to language, we focus on helping the children understand their place, the place of our species in this world. Language is, of course, connected to our species deeply. If we think about the human tendencies, there is a tendency to communicate, and that takes language. 

With stories and key lessons we try to make the children become aware of the fact that all languages were first developed by early human beings and passed on. Over the years, our language has developed and been built up. As we bring in words from other languages, it has become enriched. Language responds to the needs of human beings. It’s a function of society, built by cooperation and agreement, an agreement of sounds, an agreement of order. Language also is vital to pass on information and knowledge; one of the characteristics of our species is that we can communicate with each other.

Language may be used for good or for evil. It may be used to express truth or falsehood. It may be kind and healing, or cruel and damaging. The use of language is a personal responsibility in terms of accuracy and intent.  Language can create feelings of fear, love, excitement and happiness. It can escalate a confrontation, or it can defuse that same confrontation, whether the confrontation occurs between individuals, groups, or nations.

From this arises the idea that we should think before we speak or write. This is an important idea for children. Communication carries with it responsibility for effective and morally sound interactions with others. Language is much more then just reading and writing; language is visual, through senses, and auditory. 

Language discoveries happen consistently but appear differently between the first plane and second plane of development.  The use of and the need of language through the first plane of development in the children's house are not silent. Conversations happen naturally with much reasoning, questioning and asking. Four examples of discoveries that happen in the first plane of development might be:

There are more words than what I know right now. - Ex: nomenclature materials 

I can make my language visible. - Sand paper letters / Movable Alphabet 

I can know what someone else is telling me without hearing them speak. - reading

Words have a function. -  We give seven parts of speech in primary.


Language in the Elementary class:

What’s significant to the second plane child is the difference between spoken and written language. Spoken language needs clarity of thought at that given moment. With writing, there’s a different time factor involved, you have time to think. You can go back over to edit your writing. With spoken language, one can be easily misinterpreted if we’re not careful. If we’re not clear we can cause confusion and trouble. This is the idea we want to help the children understand.

When Dr. Maria Montessori started her work, she wanted to ensure that the children were not in a traditional classroom set up. She wanted the children to move freely and be able to talk to one another. This is why she suggested the arrangement of the room more of a 'home-y' environment rather than row of desks. A drawing room idea where there are different tables and chairs with different shapes and she said, these rooms should not be silent. 

She compared her environment to traditional environment; she was product from traditional teaching, where only with permission children were allowed to speak. What classrooms need to see and hear is the sound of human beings having a relationship with one another.  Groups of children should not be getting fed information by the adult sitting quietly, rather instead having conversations, greeting one another, collaborating, open discussions, blending into the environment as a community.  

We know that when children get to the second plane, they have new characteristics and we have to appeal to the new child. That's why language is presented as an imaginative exploration, otherwise children won’t be very interested.

If we expect the child to write a reportanalyze and dissect every book they read, we will kill the love for reading. Reading should be encouraged and fostered and it should be for pleasure. Reading should come out of a child’s interest and be something a child wants to do to satisfy the unrest in her mind.

That's why when giving a new lesson we do a recap of the previous work, or a connection to something we’ve already done or talked about. We’re building on what the child knows. Sometimes we pose a question or another way of helping the child to focus on what is going to be in this presentation. The presentation will give a new concept or an idea. Sometimes we tell a story. Sometimes we show a material. For example: The noun in our grammar work is seen as a black pyramid and the verb is identified as a red ball.  We also give an experience or concepts before (Oral introductions) we give terminology, often with the use of etymology. 

Getting the children interested in literature is important. During this time we expose the child to many types of books. We also encourage children to write imaginatively, creatively and factually. They should be doing research and reporting in subjects they are excited about while learning grammar and syntax.  

Picking up on writing from Children's House, where we encouraged the child to put his thoughts down on paper or with the movable alphabet. All of the writing in both the Children's House and the Elementary class could be illustrated and decorated by the children. In Elementary, we’ll talk about illuminating some of the letters. We’ll see that written compositions can be beautiful as well as interesting and factual.

By the time children come to the end of the second plane, they should be able to use language in an almost limitless way. It should be an exciting aspect of exploration and a useful and usable tool.

Children are human beings to whom respect is due, superior to us by reason of their innocence and of the greater possibilities of their future.
— Dr. Maria Montessori

Language Discoveries in Elementary:

  • language is a human creation
  • language helps people to satisfy their needs
  • language has probably existed as long as there has been people
  • language is the vehicle for transmission of human culture
  • language changes
  • language has forms that should be used for precise communication


"Peek" into the classrooms:

AuthorRuchira Fernando

When we talk about a study of many aspects of the physical world we combine it under the general heading of Geography, which is the area of work that has a central place in the Montessori elementary class though for the children it is life and physical reality, in which every fascinating thing under the sun and beyond it appears.

Geography in the Montessori context concerns all things connected with the earth (from Greek: geo = earth, graphein = to write). Geography is a description of the earth and all that occurs physically upon it. Second plane children have a consuming interest in everything. The everything is the universe. In the Montessori elementary classroom one of the children's earliest lessons introduce to them the story of the universe! Arising from this introduction are myriad lessons and activities, many of which fall under the general heading of 'Geography'.

Major subjects included are: Astronomy, physics, chemistry, meteorology, climatology, and geology. Topics selected are chosen for their ability, in the first instance, to provide an aid to children in their quest to understand the physical world, past and present. In the second instance they are selected to enlarge upon initial interests sparked by the teacher's presentations. The children see, for example, that the earth revolves around the sun. Arising from this are such ideas as solstices and seasons, and climatic zones, which, relate to vegetation and fauna to be found in particular regions.

In the elementary, the child focuses upon the nature and reason for things: "Why are the seasons different in the Northern and Southern Hemispheres? What made the Grand Canyon?..." The focus is plainly more upon environment, and elementary children respond to this as they encounter the order and harmony of the universe, and the relationships that exist between all things.


Children entering the Montessori elementary classroom at the age of 6 have undergone great transformation. Their physical and psychological characteristics have changed. Where previously they explored their immediate environment sensorially, now they are suddenly ready to study what is not readily accessible to their senses.

The Human Tendencies continue to operate. Their focus has changed: Work (with the hands) continues, but with emphasis on finding reasons, on developing understanding. The child wants to know why, to discover relationships and functions, not just facts. Exploration of the extreme, the outstanding fascinates the child. They are drawn to the very large and the very small. Why? What for?... How is this related?... These are the types of questions that this child asks, and as hero worship features in the children’s interests we introduce to them the explorers and inventors of our history cultivating this characteristic.

In order to cater to this all-embracing thirst for the reasons of everything, to satisfy the Human Tendencies, Maria Montessori suggested that we begin with the universe, which contains the answers to all questions. The universe, Montessori tells us, gives the child a reference point, something with which any new information can be integrated, as opposed to 'bits' of disconnected knowledge:

If the idea of the universe be presented to the child in the right way, it will do more for him than just arouse his interest, for it will create in him admiration and wonder, a feeling loftier than any interest and more satisfying. The child’s mind then will become fixed and can work. The knowledge he then acquires is organized and systematic; his intelligence becomes whole and complete because of the vision of the whole that has been presented to him and his interest spreads to all, for all are linked and have their place in the universe on which his mind is centered.
— Montessori, Maria (1973) To Educate the Human Potential Kalakshetra Press, India

Much of the information that we seek to give to children makes no sense unless it has a context. Cities and ports and the lives of peoples only make sense, for example, when connected to the geography and environment of a region. It is the nature of hot air to rise and carry moisture, which drops when cooled. Water, by its nature, moves sideways and downwards, forming rivers, lakes and seas which affect plants animals, cities and people. The reasons behind things are the issues that matter!

Particles 'obey' as all of the cosmos follows an orderly course, coordinated with others by the laws of nature. And as each element of the universe follows its nature and its personal laws, the balance of nature is maintained. Harmony arises through obedience of natural laws. So laws and rules are not restrictions, and the child's mind becomes aware that without these rules, there would be disorder.

These ideas are first encountered in the story of God Who Has No Hands, not as theories, facts and theologies, but in the form of a cosmic tale. The aim of the story is not to create 'understanding' in the children, but to touch their imaginations, enthusing them to their innermost core. This, and the other stories that we tell, are designed to strike the child's imagination, opening new fields for exploration. As a cause and effect and pattern is grasped by the children, their intellect takes over and the teacher helps them to locate more facts and to study the chosen subject in more depth. Once interest is sparked, facts can be given to children hungry for them.

Topics forming the body of Montessori elementary Geography include: Space, Earth and Universe; Composition of the Earth; States of Matter; Sun and Earth;  Work of Air;  Work of Water; Life on the Land; Interdependencies; Economic Geography.

These areas are to assist us to effectively structure the classroom environment and to better prepare lessons. For each topic we provide aids to the imagination in the form of stories, colorful, impressive charts, and a variety of experiments, many of which have been selected to provide impressions, not facts. The children are offered opportunity to reconstruct reality in their own minds! The aim of our presentations is to create an unrest in these children's minds, so that they will want to find out more.


What attracts the children first or last is not really important. What is important is diversity... As many groups of children as possible doing as many different things as possible, reflecting the diversity of the universe! Then, as a culminating presentation, the children are led to see that all are interrelated via the Chart of Interdependencies.

Geography, a living segment of Montessori's Cosmic Education plan, generates spontaneous, active, self-renewing interest! A love of learning blossoms in the children, and lifelong fascination with elements of Geography may evolve.

And our usual rubric - Peek into the classrooms:

AuthorDenis Samarin

Cosmic education is primarily dedicated to the child in the second plane of development. This method was carefully designed by Dr. Maria Montessori and her son, Mario after years of observations. Dr. Maria Montessori used the term cosmic education for children ages 6 through 12 years. As the children enter the second plane of development, the human tendencies continue to operate, while new physiological characteristics begin to assert themselves:  the emerging power of the imagination, the drive to know the reasons of things, a need for abstraction and intellectual activities, a drive to perform extended and elaborate work, and a focus on issues of morality. Each of these aspects of the child receives its own measure of attention as cosmic education is presented through the years. Even though in a physical classroom we usually see children grouped in ages 6 - 9 and 9 - 12, Cosmic Education and the approach towards the child does not change. 

Dr. Maria Montessori stated, We claim that the average boy or girl of twelve years who has been educated till then in one of our schools knows at least as much as the finished high school products of several years seniority, and the achievement has been at no cost of pain or distortion to the body or mind. Rather are our pupils equipped in their whole being for the adventure of life, accustomed to the free exercise of will and judgment, illuminated by imagination and enthusiasm. Only such pupils can exercise rightly the duties of citizens in a civilized commonwealth.  

 With this thought the child must begin to understand that laws are not oppressive, but rather are a natural part of life and enable us to maintain harmony and order. Cosmic Education reveals to the second plane children that all things in our universe are connected.  This is how Mari Montessori manifests her concept of Cosmic Education. “The laws governing the universe can be made interesting and wonderful to the child, more interesting even than things in themselves, and he begins to ask: ‘What am I?” What is the task of man in this wonderful universe? Why we struggle and fight? What is good and evil? Where will it all end?”

Cosmic Education invites second plane children to see themselves as part of a whole, as they are assisted in the task of building their own personalities. They are led to place themselves in relation to others, both animate and inanimate, and to understand that they have responsibility towards others, that they do not exist for themselves alone. They gradually come to an understanding of the cosmic task of humanity: Humanity continues the creation and has a responsibility for maintenance of the balance of nature.

With the Cosmic Education children find their answers for "the reasons of things" as they are focused on how and why things were and are as they were and are. They are invited to find links between the disciplines as a study of one specific object inevitably leads to all the other disciplines. Relationships and connections fascinate the children and as they ascertain these interrelationships they achieve a state of calmness and repose, become normalized.

The Content of the Cosmic Education

When Maria Montessori observed the needs of elementary-aged children she recognized that their interest covered all areas of knowledge and that their studies would tend to lead them from one area to another. She found out that they need something about all areas and would allow them organize any new peace of knowledge around it. And the answer for both was the presentation of the Universe, the story that is given at their entry into a Montessori elementary classroom and bring an impression of the immensity and wonder of the Universe by exploiting experiments and colorful charts.

Then follows the evolution of plants and animals which flows to the story of humanity with all its love, imagination, continuing achievements, and actions on and in the environment. The study of humanity through time leads to contact with such creations as art, idealism, music, language, and mathematics.

The first great story, God with No Hands, introduces children to the universe and sets the stage for everything else. Maria Montessori said, “Let us give him a vision of the whole Universe. The universe is an imposing reality and an answer to all questions.” If we start with the universe, we have something broad enough to answer all of the children’s questions. “We shall walk together on this path of life, the teacher and child, for all things are part of the universe and are connected with each other, to form one whole unity.” 


Onto the stage set by the first great story comes life: plants and animals. The second great story is The Coming of Life with the Timeline of Life. With just the first two great stories, a vast field of exploration opens in the classroom. Plants and animals, even in all their diversity, were not enough to carry out the totality of the grand plan that lies in the Universe. The furnished environment of plants and animals needed an agent for its total fulfillment. This sets the stage for the third great story: The Coming of Human Beings.