Cosmic Education – nourishment for a lifetime


I recently gave the first great lesson – the story of the universe to the elementary children. This is a period of great excitement, questions and ponderings for the children and well, for me too.  I am always especially excited for the children who are hearing this epic tale for the first time. An entire universe is unlocked and ready for their explorations.

The entire Montessori ‘curriculum’ during the elementary years is dubbed as ‘Cosmic Education’. Cosmic Education connects all players in the Cosmic Drama, both animate, as well as inanimate. It is an opportunity for the child to unify themselves with the very cosmos!

Lofty ideals these, but Montessori is ALL about lofty ideals. The primary aged child has the gift of developing a ‘unified self’, the elementary aged child has the gift of ‘unifying with the cosmos’ and the adolescent, ‘unifying with ones fellow beings’.

Each and every year I see these stupendous ideals fleshed out into practical experiences that guide the children on their path.

This year, soon after I presented the story of the universe to the children I saw the movie ‘Agora‘. It’s the fictionalised story of the life of Hypatia– the Alexandrian mathematician and philosopher who lived during the 4th century CE. Living through times of religious strife, Hypatia managed to hold on to her beliefs and till the very end dedicate her life to probing the secrets of the universe. At a time when the mere thought that the workings of the cosmos was anything less of pure perfection was considered heresy, Hypatia anticipated that the earth went around the sun in an elliptical orbit. Now an ellipse was considered an ‘impure’ shape – a base figure as compared to the ‘perfect’ circle, where the centre is constantly equidistant from its diameter. Hypatia was a woman far beyond her times.

While viewing the movie (which had it’s good and bad points, but this is not a film review) I couldn’t help but see a parallel between Hypatia and the elementary child. Both probe the secrets of the cosmos and ‘touch’ it with their gift of imagination, are sensitive to issues of fairness, cannot help but ask BIG, philosophical questions and attempt to find answers guided by their reasoning mind.

I often meet adults who have completely lost touch with the child they once were. Philosophical questions, the awesomeness of the universe and all the many splendours out there, leave them unmoved while they plod along life’s path miserable in their day-to-day existence.

My hope is that children who have received cosmic education will, no matter how old they get, always have the child they once were alive in them. No matter what difficulties life throws in their path, and there surely will be many challenges, they will never cease to feel wonder at this truly majestic universe that we inhabit, never cease to ask questions bigger than themselves and never fear to look for answers.

In short, my hope is that the Cosmic Education they receive will last them a lifetime.

“Cosmic Education is intended to help each of us search for our cosmic task as a species and as individuals. To do this, we must understand ourselves in context. It is only against the background of our place in the universe, our relationships with other living organisms, and our understanding of human unity within cultural diversity, that we can attempt to answer the question, ‘Who am I?’”

~ Micheal Duffy and D’Neil Duffy – Cosmic Education – Children of the Universe

To see a World in a Grain of Sand
And a Heaven in a Wild Flower,
Hold Infinity in the palm of your hand
And Eternity in an hour.

~ William Blake

The Long Bead Chains Cabinet

The elementary finally has the long bead chains rack to show off this beautiful material!

It took a day and a half to put the cabinet together and I could not be happier!

What a far cry from storing them in boxes like we have up until now.

What’s more it was made at a fraction of the cost of those available with the material manufacturers.  Also we used better quality wood to do justice to this superbly elegant material .

Once all the chains were hooked, squares aligned and cubes neatly placed in a row, Violet, one of our ancillary staff commented, “This looks like a jewellery shop”

The children are going to LOVE it!

PS: For those of you who are wondering what the long bead chains actually are : the material allows a child to build an arithmetic square (10 x 10) and then an arithmetic cube (10 x 10 x 10) for numbers 1 to 10!

For example, 10 bars of 10 beads in each bar, fold in together to make a square of 10 (ie 10 x 10 ); the child continues folding in the squares and ends with 10 squares of 10 bars of 10 beads.

She replaces the folded bars for actual squares and when she stacks them up one on top of the other.

Lo Behold! the 10 squares form a cube of 10 (10 x 10 x10).

There are corresponding tickets of multiples that the child lays out and thereby the arithmetic value of a square and cube is also worked with.

Building the basic frame.

Building the basic frame.

Measure measure measure

Measure measure measure

Checking the hooks

Backing - check; hooks - check; shelves for squares - check; shelf for cubes - check; symmetry - check!

Backing – check; hooks – check; squares – check; cubes – check; SYMMETRY – CHECK!



Story Of The Universe

We are a month into the new academic year and the children who have recently joined our elementary environment have received their first great lesson – THE STORY OF THE UNIVERSE. The story is accompanied by many experiments, including a show stopper – blasting a volcano! This year around, we used ammonium di chromate in the volcano for some real BANG, instead of the tame baking powder and vinegar routine. Needless to say it was all very exciting.

Along with the younger children, the older children too had the benefit of receiving the story again and like every year, it has sparked off great work!

Today, one of the many projects undertaken by the children after the telling of the story was completed.

After reading the awe inspiring book, ‘Born With A Bang – The Universe Tells Our Cosmic Story‘ by Jennifer Morgan and Dana Lynne Anderson, two boys decided to make a timeline depicting some of the major events in the Universe’s history.  There is a concise page at the back of the book that lists some of these major events and was just the right morsel for the boys.

Here is the long and short of their timeline.

They did some finger knitting and converted its length into a timeline. Each foot on the length of their finger knitting accounted for 1 billion years.

The timeline in our library corner, above the light box. Below is the much loved volcano. The timeline goes all along the wall ….

… and wraps around …

… to the other side …

A brass bell signals each major event. With it is a card that explains what happened at that point in time. The first two events are so close together that they have been strung one on top of the other – but – true to the need for precision that characterizes the elementary child, they are just ever – so – slightly, askew.

BIG BANG – less than 1 second old – In a fraction of a second the universe went from the size of a dot to the size of a galaxy …1 second to 3 minutes – the universe cooled down to 3,000 degrees and that was enough for the neutrons and protons to form …300,000 years after the Big bang it cooled down enough for the first atoms to form. The first atoms were of Helium and Hydrogen … 

1 billion years after the Big Bang galaxies formed. Mother stars were born. After stars die their stardust makes new stars that have complicated elements …

2 billion years after the Big Bang the Milky Way formed. Older star clusters joined new star clusters

7 billion years after the Big Bang our mother star might have exploded. There might have been more than one mother star that might have created our solar system …

8 billion years after the Big Bang our sun formed from clouds of gas and dust which came from a supernova of our mother star. Gravity made the clouds squeeze together. Atoms of Hydrogen joined to make Helium. This made the cloud shine. It was now a star…

8 1/2 billion years after the Big Bang the planets formed. One planet was perfect – not too hot, not too cold.

For the sake of convenience the timeline has now moved to a new location – above the science material.

“let us give him a vision of the whole universe. The universe is an imposing reality and an answer to all questions. We shall walk together on this path of life, for all things are part of the universe and are connected with each other to form one whole unity.” ~ Maria Montessori (To Educate The Human Potential)

Materialized Abstractions

The Long Bead Frame (via good tree montessori homeschool)

Two days ago a boy was busy sliding and counting beads to help him subtract numbers in millions. Each time he borrowed or exchanged a bead, I observed him stare at the subtraction problem on his paper and mutter, mutter, mutter.

He came to me saying, “I think I’m doing this without material … just with my mind”, so I suggested that he put the material away and check.

He brought over his paper. Neat rows of numbers with a precise difference recorded.

The boy had abstracted subtraction!

“I want to do another subtraction problem. A l-o-n-g one in quadrillo’s”

Now, quadrillo happens to be a number name invented by one of the children in class, for a hierarchy after googol (10100).

I asked if he wouldn’t mind starting with a number belonging to the quadrillion hierarchy (1015 ) first and then moving on to one in ‘quadrillo’ and he agreed.

He did two precise subtraction problems. The strips of paper he had used, inspired him to make a flag out of them.

He went outside and found a stick and stuck his subtraction problems, front and back to make a ‘subtraction’ flag.

Incidents similar to this occur in every montessori environment and ours is no different. I can picture the other montessori teachers who are reading this nodding their heads in agreement.

Often I am asked the question if abstraction  really happens so naturally –how and when and indeed if at all, children leave the material behind and work mentally, without being explicitly taught?

To answer how and if at all the child moves from the concrete to the abstract, we need to look at the materials presented to the child.

The montessori materials that children work with are  ‘materialized abstractions‘.

The materials are the concrete forms of an abstract concept.  Through hands-on work with material, the child internalizes the concept or abstraction that it houses.

Working in ‘abstract’occurs as a result of an internalization of the concept embedded in a material, and repetition of many parallel activities that serve as ‘passages to abstraction’.

It isn’t just one long vertical line, but also a horizontal one, where the child discovers the connections between things. For example, the connection between addition and subtraction or addition and multiplication and so on. (mathematics overflows with patterns and the list is endless)

To answer when will a child reach absraction, we must bear in mind that this takes time. It comes after much work and and each child has her own timetable. Rather than push a child, the Montesori guide protects the freedom of each child to reach the abstraction on her own. Aah! to witness the delight expressed at the discovery of a connection!

But most important of all, is to remember that the materials  are not presented with the sole intention of having a child internalize a concept. This is not just a ‘different’ way of ‘teaching’. Their purpose is far greater than that … it is one of development. The materials satisfy a need of not just what is still to come but what is NOW! Through active involvement and freedom of choice, the child builds upon her ability to concentrate, self-direct and gain successive levels of independence.

But now I am digressing, let’s go back to the boy we spoke about earlier.

Looking at the paper on which he did the subtraction problems, I was struck by the neatness. There were no strokes and loops showing the borrowing and changing of quantities, like this:

Instead his paper looked like this:      826 , 251 , 450 , 622 , 368 , 274

                                                                  – 673 , 529, 046 , 241 , 111 , 647


                                                                     152 , 722 , 404 , 381 , 256 , 627


And I remembered my school days.

If I had shown up with subtraction problems completed like the one above, the teacher would have assumed only one thing – that I had copied it from a friend. If it had been on a test, I would have been knee deep in trouble!

The very same thing that we are celebrating in this post, would have  been the source of ridicule and shame.

The boy deciding to convert his work into a flag brought to mind Montessori’s words. In one of her books she spoke about a child being anchored to his age. Though he might be working on something that we would consider beyond his years, when he goes out to play he is just like every other child his age.

The boy may subtract in ‘quadrillo’s’ but in the end he wants a flag! 🙂

Platonic Solids

Our school is tumbling with 3D solids constructed by the children. They are EVERYWHERE! Hanging from the ceiling, sitting in the lawn, decorating the tops of shelves, sitting quietly on a table and peeping out of lonely window panes. The children can’t seem to get enough of constructing solids out of paper, straws, sticks – anything that will work!

The children have explored these geometric solids in a variety of ways – they have made them in clay and then cut them up to observe the shapes of their faces, they have explored the environment for these solids and made comparative charts recording their edges, faces and vertices.

One day they ran each face of the solid in sand, tracing it’s path. They observed the pattern of shapes left on the sand. On another day they copied the pattern onto paper, using the actual solid to trace the faces.

They had arrived at making their own geometric nets!

The environment was buzzing with activity!

“How do we make cones and cylinders with circles and rectangles?” “Is it possible for me to make the sphere with paper too?” “”Look! there is more than one way to make a triangular pyramid!”

And then…one of the them discovered the Platonic Solids.

It was love at first sight.

The enthusiasm caught on and each morning there were a few of them trying their hand at making these symmetrical solids that have inspired so many great thinkers, like Plato (who they are named after) and Kepler who believed they held the secret to the orbits of planets.

The child who first discovered the platonic solids has moved on to more complicated 3D solids – the cuboctahedron, the cantellated tetrahedron and the decagonal antiprism … what’s more he’s constructing the nets using a protractor and compass!

Our aim is not only 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.- Maria Montessori