Inside or outside the box

The majority of people would always like to think outside the box. In some way that is their way to be innovative or progressive. Generally, there is nothing against this way of thinking, yet often it is ending nowhere hence to the incapability of thinking inside the box. This might sound a little arrogant but that is not the intention. I just want to pin out the fact, that it is time to start thinking inside-the-box, to set the base to do the outside-the-box thinking. Why are all the solutions always to be found outside the box? Have we actually covered the ground inside it? People hat want to think outside the box obviously have covered all their options inside the box and are convinced that hey will find, whatever they are looking for outside of it. Or is this just a way to gain more time to look for something that is not yet in their vicinity? Why is no one saying that she/he is thinking next to the box. Maybe because that is to close to the inside and hence, not enough time available to do the proper thinking, that is needed to find the solution necessary. Maybe it is another way to say that one takes a step back, or actually outside of a ongoing thought process, to come back again after and having refreshed their thoughts…

Maybe that’s it…


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.


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.


Quote. Dr. Maria Montessori

Dr. Montessori said: “The aim is not to create a cultural mind, but a spiritual soul based on reality. Therefore, history should not be taught as a collection of dates and places. But rather be approched to arouse gratitude and appreciation. This gratitude should be aroused first to the law and order of the universe and the preparation of the environment into which human beings came.’