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.


Geometry as a tool to strengthen logical thinking…

Geometry applied in the right way is a fantastic  tool to train logical thinking. already at an early stage, children can see and understand patterns. Often it is underestimated how a young brain can already understand structures infront of him or her.

So Geometry can help to train the brain. used in the right way, children will see this as something pleasing… geometry is esthetics. The eye likes symmetry and equal parts. One feels safe when the structure is even, balanced and logic. So children of all ages have comfort within geometry and if applied and shown right, it can be and is a springboard I.e. fractions.


One should n ‘ t be scared to use metal insets and let the children explore. What are they able to create? What kind of symmetries will they make? One can halp to givr certain guidelines, like no crossing lines, the iset needs to always touch another line that was drawn, etc. The younger, of course, the simpler and for older children one can add a compass or ruler,… the options are countless.

I personally think that geometry is not given the right amount of attention in a classroom. I think as well that often the right connections, the interdisciplinary links are not made, yet one clearly does not go without the other.

I do agree that math has a very high standing and that it is important, yet when one would allow the children to dwell for longer periods of time in the geometrical realm; they will, and I mean all, profit on the long run.


…. 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.



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.