I recently worked with the children in my class on BASE 5. I say BASE 5 because that was what I introduced the base work on. I was, once again, surprised how well this abstract concept, of using a different base, became something rather simple and logic for the children. How come?

I think it was the link to their well-known ‘base’ they work on- Base 10.

The sheer knowledge of how to do an exchange (carry over, what they all do on a daily-basis, is implanted in them, therefore, the act of using a different base is a simple logical frame-work.

I need to add that I do, meanwhile, work in 6th grade (elementary) yet 1st grade of the IBMYP programme. These two do overlap yet regarding heir age, 11 to 13, their reasoning mind is well developed (at least on an analytical side) therefore their wider understanding of the concept at hand is given and the time is right o confront them with this kind of lessons.

So I introduced the topic by readdressing the decimal system, making the link to the wooden hierarchical material, the families (simple, thousand, million) and directed them to the all known place values in the decimal system. A nice brief recap of what they know, bringing them back to where they come from. All felt secure and confident, that they remember all of this.

After the introduction was done, we went to the lace vales of base 5. Since the concept was understood within the decimal system, it was logic for them that instead of multiplying each number by ten, we multiply by 5;

1 – 5 – 25 – 125 – 625 = place values of base 5

All that was clear and the links were made.

The concet was understood and hence we established that in base 5, we only have 5 numbers. Vice versa, in base 10 we have 10.

Base 5 = 01234

Base 10 = 0123456789

All that was clear, and the addition exercise in base five presented no difficulty; Instead of exchanging at ten, we exchange at 5. Keeping in mind that five is an illegal number such as 6 7 8 9.

With some we went onto transforming base 5 to base 10.

There, all the knowledge of multiplication and division comes in action and need to be applied.

All in all, I need to say that this lesson was/is a fantastic manner o introduce something new yet all the known need to be applied and repeated; I can recommend to not wait too long to introduce to 11/12 year old children. It wraps it up very nice with something exciting and new.

Yours Chris



Geometry as a springboard to math

When there is a first combination … you will find a second combination.

I been thinking that these combinations are ideal ways to introduce a child in primary to various terminologies, words, language. One can apply terminologies found in algebra, explain the concept of variables with the pictures you see on the board. In that case the word sum could be brought to the child’s attention, that this word is linked to an addition, introducing the word quotient and product. For visual children this can be a good tool to give them these words. By experience a 10,  11 and 12 year old can by times struggle with word problems hence to a non-understanding of the terminologies they have in front of them.

These important words are often neglected because of the drive of having the right result or answer.

Of course there are millions of ways to give ‘the words’ to a student, yet within the Montessori material is so much that can be used for things, topics, facts and ideas but one doesn’t dare to do.

Another example…

I can explain (within the chapter of equations) what it means to maintain balance. It is visual, clear and attractive. ‘whatever is done on one side of the equal sign must also be done on the other side’;This board could be my introduction. Later one also can use a scale to let the children explore.

I will continue my investigation of the vabulous variety within the Montessori material, wher and how to apply the given in different topics of mathematics.


…. Identity

The question that I have had during the last weeks was how to actually define and explain identity? We all agree, that from a biological point of view, it’ s easy to define, explain or distinguish identity, your identity and the identity of another.

Yet, what intrigued me was to find a way to go further in finding the essence of identity.

First of all, I started to look for a simple way to express “identity” and ended up with the simplest way of communication… pictograms.

Would one be able to express oneself’ identity with the help of pictograms?


So first I need to find a way to understand, decide, decide, agree … where identity comes from and how it comes about.

I had the following thought…

Identity is linked to three basic and three additional factors.


Which create



I created n image to make it clear.



Based upon this guideline one can understand and classify ones own identity

Now coming back to my idea of pictograms.

If I follow these guidelines, I can in the simplest way show my identity.

On a historical note, Pictograms are the first way of communication in a “written” form to one and another.

To create an image with these guides, you eventually need to invent pictograms yourself, pictograms that meet or express your need. The list of the existing ones is long; there are many that could be used.

What I liked about this topic is that you have the opportunity to go back in time. To see where written communication had it’s beginning.

You probably think, where that has something to do with identity… Well, let’s say, it underlined and helped to be able to share, tell, explain and pass on ones own experiences that are linked to one’s own identity.

All in all, the topic identity linked with the story of writing is a unique opportunity to go back in time and investigate the creation of communication, writing and how it all came to be.

The story of the coming of life, the story of the hand, the story of numbers and writing are ideal stories to re-look upon again with children to lay a foundation to tackle the concept of identity. Additional you can talk about the fundamental needs of humans which will also open different paths towards a wider understanding of human evolution and development; reasons why and decisions that one has made, is doing or will do.

This is ideal for 6th grade elementary children, 1st and 2nd grade secondary.

Understanding and placing oneself in the global picture, is key and a nice eye-opener, helping children to ask the right questions about life, from the past to the present.


Spoken Language – in Montessori education

In the three to six class

Montessori never envisioned that children would be asked to work in silence. In her day it was exactly this that the children had been forced into by traditional education. She saw the children consigned to immobility and silence. And she completely rebelled against the structure. It was her vision that children should be set free. She believed that one of the essential human freedoms that had been taken form children was the freedom to communicate. She created a different environment for children one in which this freedom could be used and enjoyed by the children in a life affirming manner. Children need movement and interaction with the environment to become fully adapted human beings. In other words, if you set children down and command they cannot move, deviations will happen to the child. Children in the first plane of development are creating for themselves the language that surrounds them. It is the active intercourse of the absorbent mind and psychological  needs to be met through the child’s own activity within the environment. Children cannot merely listen to language being spoken they must be actively engaged with this language in order to develop the ability to use this human gift effectively. If their environment gives them this activity they can absorb and create for themselves many languages.

Montessori spoke of the atmosphere of a Montessori class as akin to the atmosphere of a hive or factory. There should be the constant hum of productive activity. Some Montessorians see normalization as the quieting of activity when actually it is only a quieting of any chaotic tendencies of mind. Silence on the classroom is far from the goal that Montessori had in mind. The children should be free to talk to talk about their work and to share experiences through conversation. The adult should encourage the children to discuss with and appeal to one another for help building a sense of community within. The children independent of the adult though guided by the adult who lends security to the interactions through showing techniques in grace and courtesy through modeling cooperative and respectful behavior and through being a safe haven for the child if the child’s own efforts are insufficient to solve the problem.

The children learn many techniques of interaction that involve many styles of verbal communication, appreciation for each others work learn how to be both teacher and pupil and learn various social graces applicable to the culture. The tone of voice that should be applied in the classroom is a low conversational tone of voice: do not ask the child to whisper, this is damaging and stressful to the vocal chords. If the voice level begins to rise too high a soft ringing of the bell should get the children’s attention. It is not useful to say things like, it is too noisy, and that gives the children no reason no real message except blame for displeasing the adult. If grace and courtessy exercises are done periodically, addressing tone of voice then what should be said when the bell is rung is something like lets have somewhat lower voices please. This is an empowering rather than blaming statement and carries with it the confidence that the children wish for the situation to be optimal. It is not a good idea to use a visual signal such as the turning off of the lights to signal something auditory turning the lights off is also disruptive and disrespectful tot their work.

At he children’s house level the child is creating language. The children must have the opportunity to use and appreciate language through speaking. The primary aim of the adult is to encourage the development of spoken language as a means of communication. The child’s development of spoken language enables an adaptation to the environment allows the child to fir securely into a group first the family second the group of classmates. The freedom to speak gives the opportunity for the expansion of vocabulary it also helps children build the self-assurance that is necessary for expression and communication with others.

Spoken language in the elementary class

Elementary children must continue this process of developing the skill of communication in their mother tongue they must continue talking. We add a new dimension to the development of spoken language. When we take into consideration the new physiological characteristics of the elm child for the tree to six year old, language is a set of facts: I can speak and understand and be understood; things have names, words are arranged in particular order etc.

With the advent of the power of reason spoken language becomes more than just a tool of communication it works to support and develop logical and reasoned through the individual. It aids the development of judgment arising form logic and reason. The child is exploring life in society and the reasons behind the existence of society. The child needs language based on reason to communication with society and to understand his or her own part in it.

Children from ages 6-12 need to use language to explore functions purposes interrelationships and dependencies. Inside communication requires a particular low tone of voice. No one including the teacher should call across the room to another. In a room full of people there is also a lowered tone that is not the same as the tone of voice when one is alone with one other person. There is a way to interrupt one when necessary we need to develop grace and courtesy exercises to draw attention to these two factors of the tone of voice expected of the children and adult in the classroom. We also to need to draw attention as we do in writing to the norms of address and the varying styles of communication that should be used with different people. There are also forms for spoken language in the classroom that are either extensions of the types of verbal communication enjoyed by children of the primary or new forms of verbal expression in communication afforded by the increased reasoning capacity, knowledge base, and social maturity of the children at the elementary level.

Teacher reading allowed

Montessori thought that teacher reading was an important way to bring cosmic education to the children. You should read to the children from a varied diet of material as much as possible. Such as: different styles of writing, genre, books, magazines, newspapers, etc. Montessori also noticed that children will listen to most anything that you read to them but they are especially drawn to history, and stories about real people. Children may not get every nuance of complex things but they may pick up much more that you expect.

Help children figure out what helps them listen. Can they keep their concentration of their hands are busy or if they are doing nothing but listening. If they concentrate best with busy hands they could do metal insets, free drawing knitting, finger knitting etc. being read to is powerful this development the powers of attention concentration and imagination. Read allowed daily to the children preferably at the same time each day.

Children reading allowed.

Resist the temptation to have children read allowed in a 6 – 9 class. When you need to find out the reading level of a new child the question should be would you like to choose a book to read with me? The child can say no. Reading silently is hard enough to do that you have to be able to decode words and decipher someone else’s thoughts, reading allowed brings about more physical challenge, reading ahead to find out the stress, initiation and intent of the author is challenging there is too much to remember at once and their body is not ready for it yet. Ask that question in a private setting and have a private place to read with them. The children are prepared to read allowed in a number of ways. Conversation, thorough the command cards and grammar boxes asks them to say something allowed that is in print too. Interpretive reading helps too. Children also like to read poems memorize them and recite them. It can be fun on parent night or concert night.


Discussion is the opportunity for sharing discoveries and insights with regard to a particular topic. By its very nature it is open ended: each conclusion serving as a jumping off point for another discussion. We can never hope that discussion will evolve naturally in the elementary classroom if we discourage group work. We should be making our presentations to small and large groups. As the class grows and extends the group should evolve into mixed age level cooperative efforts.

It is important for the adult never to refer to first second or third level in our presentations or to refer to grade levels we must allow each child to precede as far as he or she is able regardless of age. By making them a member of a group are curtailing their possibilities by putting them into a box, and limiting their expectations of themselves. Invite the children as individuals: use their name, not a rank. This is a key lesson for the adult. It also brings about competition, vanity, and judgmental behaviors. We want a proud yet humble child who wills the good of another.

If we encourage group work in mixed age groupings we will have a natural forum where discussion about work can flourish. Children can learn more than the adult can teach them this is also the natural course of human learning and cooperation which takes place in a web of interrelationships and often rather than in a programmed and hierarchical fashion children with a solid foundation with a freedom of communication in the children’s house will have little trouble engaging in discussion at the elementary level. If they do not have this foundation we begin immediately to help them establish it.

We ask the children’s opinions about the material they are exposed to in presentations we elicit from them their observations about different phenomena and the reasons behind them. We also direct children to each other for information and assistance. The adult for the most part is the last resort. The adult should again provide a base of security rather than an ultimate authority on everything.

Since it is not of primary importance in most subjects that he child reach the right answer but that the child can formulate a conclusion based ion reason and logic. We can allow discussion to follow many courses. This does not mean we allow continuous incorrectness in the children’s work what it does mean is that we let the children reveal their thought processes to us. When we see how they are thinking we can then develop lessons to address any difficulties or incorrect reasoning when we see a mistake we offer the children source material but we must be careful to allow the children to hold different opinions based on their particular knowledge base and stage of development of reason and cognitive maturity.

Traditional education would have the structure of interaction as follows: the adult owns the information, the adult imparts the information, the burden of proof is on the child to prove that he or she has received the information properly, the adult gets to judge the child on performance. This is NOT part of the Method. Traditional education “I gave the lesson it is not my problem if they did not get it.” This is not the attitude of a Montessori teacher.

We do need to aid the children in the thinking out and searching for their own answers. We offer them information on some of the techniques of discussion we help them with the ethics of discussion, letting people have their say, avoiding interrupting people, and respecting different positions we encourage the children to think of discussion as a non adversarial relationship.

The path of acquisition of knowledge is largely a path of trial and error. Of hypothesis experimentation and revision of hypothesis. We have to avoid looking at knowledge in our classroom as a product owned by some and coveted by others. The hierarchical and competitive view of achievement and knowledge is insidious in society. We as adults have a great responsibility to combat this assumption. We have to view education as process a continual act and an exciting journey with no particular goal but with many interesting and fascinating stops to make. The freedom to talk and discuss should entail the freedom to be wrong, to misjudge on the basis of imperfect knowledge the view of cosmic education is necessarily that at every step along the way human beings exert great effort to choose rightly. New knowledge brings new sets of choices and responsibilities. We expand the knowledge base, which should inform our choices.

There are limits to the freedoms to discuss. The classroom is not a place just for gossip and verbal repartee we must take the children seriously enough hat they begin to take themselves seriously, if we trivialize the curriculum or demean the children they will not take upon themselves serious intellectual tasks around there can be much discussion. Through grace and courtesy exercises we can inform the children of other limits those involved with listening, respect, and consideration for others and their ideas. There are few models for this type of discussion outside the classroom in society. Unfortunately the responsibility for aiding this development lies largely with the classroom teacher.

Report giving

Groups of children draw up together ad give reports about what they have been doing, this could be about a piece of work or an expedition. If a cooperative project has yielded information that can be shared with the class a summing up of the project can be done orally as well as in written form. We have to help the children with the various strategies for putting together oral reports. They need to structure their report to give enough information on a concise manner so that others will gain an insight as to what they have been doing and perhaps to be inspired to do something similar or related.

Oral reports can include descriptions of the aims of the projects, how the possess began, the materials used, the sources explored, the time taken, the people engaged, the procedures used, the difficulties encountered, the types of work used such as writing, illustration, model building, books, interviews etc. and the discoveries made. In this way, the children can share with each other the work they have done and they can teach each other.


This sharing through oral reporting helps the children to understand and appreciate the roles they play in society. The children also develop an ability to judge what types of work the class would benefit from hearing about. An oral report may be the outcome of serious extended cooperative work. It is a way of helping children develop a responsibility for what one says and shares with others. The children realize that they need not be satisfied with second rate subjects and poor expression. Anyone who gets up in front of a group to speak has a responsibility to that audience. A responsibility to choose meaningful and worthy subjects he or she feels excited about and wants to share. He or she must take time to prepare so that the allocution is thought out and exciting for the audience as well.

Those who wish to share should not interrupt the class in order to give a report have a time each eek for the children who ant to sign up and then do a report. However the entire class need not put away their work and gather. Those who wish to will come and appreciate what is being said. The group giving the report needs to be helped to understand and that not everyone is interested in the project, it is not required that everyone should do everything, nor that everyone should like all that others like.

The adult monitors the giving of reports in the beginning helping the children organize themselves so that the experience is productive for everyone involved. As children gain more skills exp and judgment they will also take on the task of monitoring themselves. Grace and courtesy lessons on how to give a report may include: be ready, have all necessary materials at hand and in order, face the audience and speak to them, do not hide behind your papers, use a tone of voice that will reach the person on the last row, use visual aids appropriately, acknowledge questions graciously, always acknowledge applause, grace and courtesy lessons on how to be a member of an audience may include: pay attention, listen attentively, ask appropriate questions, show your appreciation in an appropriate manner. These grace and courtesy lessons may be adapted to all of the following communication: speeches, children in the 6 – 9 class should net feel required to give speeches, however we prepare them for the giving of speeches through oral reporting which is less formal.

The 9-12 children can be helped with the process and delivery of a speech. The topic and outline need to be prepared before hand discusses organized and written out. Structural thing like introductory words can help, example: today we want to show you this picture of….. if you are interested in knowing more about you can find information in this book or you can talk with members of our group.

The subject of a speech can be the subject of anything that the group or child finds interesting. It can be something about the past they have discovered through their history of explorations or it could be a topical subject. But is should be something that the child should feel impassioned about. The speech can be short but should be cohesive. It can either be read to those who wish to listen or memorized and delivered form memory or notes. With older children you can discuss the different types of speeches that exist: the address an important and informal speech that nurtures a prepared and instructional speech. A talk, a less formal spontaneous speech an oration: eloquent and sometimes bombastic. A sermon: a speech with a moral or religious speech based on text. Children enjoy devising and creating speeches in those specific formats. Bring examples for them to read or you can read them and present them to the children.

Elocution or correct speech

If possible have an elocution teacher visit the class and talk about what he or she does. Have the children video one another as they practice then they can review and see how it is working. They can practice presentations in front of friends or in front of a mirror. They can also tape a presentation. How did the sounds come across?


Most poems are meant to be read or recited they are a good way of bringing the children to public speaking. We should read poetry to the children at least once a week. Read different types. Even if they are more complex and even if they do not understand, include different styles meters, rhymes, and look for different variations.


Debates are an extension of speech giving. Involving more people and a longer preparation period. They may be defined as a formal discussion or contest where opposing sides of a question argue the merits of the case. There is a definite question with a yes side and a no side. Debating requires that you know both sides for the question. That way you can anticipate what your opponent is going to say and have an answer to it before you can say it. We give lessons to the older children regarding the processes of preparing a debate. A topic is chosen by group consensus. We help the children decide on speakers and seconds. For those both for and against, we help the children in the preparation of the speeches. Research is done arguments assembled rhetoric polished. Speakers from the floor also prepare themselves.

We impress upon the children that the purpose of a debate is to explore issues thoroughly and find that which convinces all arguments used must spring form a process of reason and logic. Debating is generally something that does not happen in the 6-9 class, those children should be able to express their opinions but formal debating is more of a formal piece of work. The older class can visit a high school debate team so that the children know how a debate works. Look for debate books for rules and strategies.


We show children through small writing lessons how to write dialogue. We can also show children techniques of dialogue around a subject decided upon by everyone on the group. A dialogue is a more formal type of discussion. It requires that the children think through what they will say before speaking. The others question the speaker and ask for explanation and clarifications for each other’s viewpoints. Dialogues can occur around work, events, books, and philosophical, ethical and societal issues. The children can also research historical time periods choose characters that might have and a dialogue about something of that time and try to create that dialogue. This will require a lot of research and dramatic sensibility.


Drama does not fall narrowly into the subject of literature. It is concerned not only with words but settings, staging, actions, costumes, characterizations etc. The preparation for drama can be begun with the commands in the children s house. From the children’s work with these commands we can monitor their comprehension. We need not then question their reading or ask them to read aloud.  It can be observed.

As soon as adverbs are added to the commands the children are asked through actions or attitude the meaning s the meaning conveyed by the command. Interpretive reading cards are a work for the elementary class: The Advanced Montessori Method 2. Speech should only be used of called for. These are also an indirect prep for reading allowed, acting and the giving of speeches. The interpretive reading can help children to express from within their own persons what they have read. We let the children do this on their own without giving stage directions when groups of children work on these cards together, one child reads and acts out a card and the other children act as critics. The adult monitors this activity at first. Giving the children a model of how to be a critic.

First children need to give each other support for what they have done. Telling each other what they liked about the performance. Secondly, the children can ask questions that may lead the performer to revise or improve on the interpretations it is important to tell the children not to try and tell each other what should be done. The audience does not direct the actors. If the other children are confused they can ask questions. The responsibility and ownership of the process of revision should be in the hands of the child, the performer doing the interpreting. Constructive criticism does not really exist. That is a euphemism for telling other what you think they should do. That is not a valid form of aid. It promoted competition and division in the group. The adult must be very conscious of the language the children use when responding to each others work in general, giving them a questioning model which world lend support while still promoting the process of a piece of work.

Montessori discouraged reading allowed for all but the eldest children. The modulation of the voice and breathing indicating significance through the voice reading ahead with the eyes while the voice follows a bit behind and anticipation of changes in the flow of the mood of the voice.

The interpretive reading cards are a preparation for reading allowed they require the understanding of all of the implied action on the printed page. If a child were to be required to read the slips allowed too early he or she would most likely be unlikely indicate the dynamics. The delivery would seem flat but from the doing of the reading slips properly, that is interpreting through actions, the concept of dynamics is brought to the conscious awareness of the child thus serving as a preparation for reading allowed.

The children may be encouraged to read form their own reading cards, making them up or borrowing them form passages in literature. Eventually the children will begin to explore skits and plays. They may or may not want to act them out the children can write these dramas about almost anything daily life historical plays imaginative plays drama should be the children’s work not put on them by the adult. As the children become more experienced with drama we can help them with aspects of scenery costume, makeup staging etc. drama is group work requiring tremendous individual control and cooperation among people. It requires a lot of trust and a clear understanding and agreement on a common goal. It is not therefore advisable to bring in drama specialists to train the children in drama. they need to come to the realizations involved in the writing acting and production of drama through their own discoveries.


G´day y´all,

This is a book that was offered to me by a friend at school. I need to say that it is a interesting and fascinating booklet. “Practical Geometrical Constructions”. Indeed the things you are shown are flabbergasting and have a solid ´WOW`effect. It is an interesting guide for Nomenclature, that you can use additional to your Nomenclature that is available in a Montessori classroom. I need to say that for a lower elementary child, the handling of a compass is often challenging enough (and that  does by times last until secondary) yet this could be something that the teacher can construct, next to a small group of children, like a presentation, to show what is possible to construct.

I think it is fascinating. It could be a springboard for exploration along regular polygons, equilateral triangles etc. The designing of shapes with a compass can and is indeed a special sort of art. Plus, there is no better way to explore and learn those different names of shapes and all the additional terminologies that need to be known within the geometrical realm.

I can recommend that little book. It is a sweet little addition to your albums and other resources.

bildschirmfoto-2016-12-04-um-19-53-22Here you can see the ISBN number in case you are interested.

Are we going far or not far enough

After all these years as a Montessori teacher I came to the understanding that the albums that one creates, studies and internalizes are after all a base to build upon.

In this particular case I am talking about upper elementary 5th or 6th grade.

If children decide to execute a study on i.e. electrical energy, renewable energy, end up with wind power and want to read, learn or study more about wind turbines, where do they start?

Well there are various factors to look upon, such as, how does the motor work, how is it set up etc. But these are technical facts. That is one side. The other side would be, where are they placed  and what are the reasons for that?

I actually want to make the link to the Montessori Albums and look upon the chapter of air and wind. By simply focusing on these chapters, the children have a preliminary introduction to the source of the power, why it actually is renewable.

Along, they will see how winds function upon the planet and how the interfere around the planet, are once more introduced to the seasons, northern and southern hemisphere etc. Thanks to these facts and figures,  the question of where you can mainly find wind turbines will be answered automatically and can  be checked after to verify if these realizations and observations fit with the reality.

This way, the step to ask Google is taken away in the first instance  and that whole process is slowed down.

We should avoid that a study is commenced with the visit of a computer. This is one example yet there are more. Especially in the science and geographical area.


Musical Intelligence

What Is Musical Intelligence?

Musical intelligence is the capacity to think in music and rhythm. People possessing musical intelligence are considered to have a strong appreciation for music, can easily remember songs and melodies, have an understanding of timbre and composition, can identify differences between musical pitches and generally enjoy being immersed in music. The ability to play instruments comes naturally to this type of person.

Informative sites:

The Four Planes of Development 6 – 12, The “Social Self”

In the second plane, the six – twelve year old is in a stage of consolidation and relative stability. It is a time of great energy. It is generally a hard and strong period.
Exploration out into the nature and society can begin. It is a time of loosing teeth. At nine some children loose their molars. New teeth allow the child to eat bigger food. The power to abstract and the intellect grows tremendously.

All other factors sink into insignificance as compared to exploring the world by feeding the intellect. It is during the second plane that a sense of time develops. This plane is when the child makes collections. It is also the time of the herd instinct, an indication of a growing social self. This is a time of moral development and fairness is a big issue. It is a time for teaching children how to work things out and how to cooperate. It is also a time of hero worship and a time when maximum effort is put forth in the physical, mental and social area.
The children have still a deep connection with the family.

The Human Tendencies

Montessori education is in its essence a study of the “nature of a human being”, a process of a formation and conception throughout life.

Two unique gifts are given to the human being

  1. The intellect – reasonning mind
  2. The will – love

These two gifts allow the tendencies to construct the human uniqueness. The tendencies are factors that operate the vehicles of the intellect, enabling the human to learn about and understand his environment.