Less Is More

montessori-resources-pink-tower-04

Having made several visits to various Montessori material manufacturers over the last month, I have noticed a marked increase in the range of ‘supplementary’ material that is on offer.

Most of these materials are inessential, silly baubles that serve to detract rather than enrich the child’s work. Moreover, they seem to be carelessly made, using uninspiring material. Often times they also convey misleading information.

In addition to the ‘supplementary’ material, there are a host of materials that were previously hand made by the teacher – reading material, nomenclature cards, math charts and so on. Though the store bought materials are ‘shiny’ and so much more convenient for the adult, I couldn’t help but observe that the connection between the hand and the material had been instantly severed.

The teacher made material is a slow cooked meal, while the store bought materials are fast food!

From what little I know of market economics, there is obviously a demand for this supply, which I have observed steadily increase over the last few years. Take it one logical step further and it means that there are many Montessori schools out there that are placing these materials on their shelves and having children work with them.

I am a Montessori purist. I haven’t always been this way, but as my understanding of the child and the method grew and as I gained more experience, I found myself becoming more and more of a purist. The open ended nature of the material and the connections between them are so cohesive that it is only rarely that I find the need to ‘create’ a material. When this happens it is usually in response to an individual child or children rather than to the whole group.  These materials rarely, if ever, stay on the shelf through the year. Again, these materials are more often for the elementary aged child.

This is not to say that the method and our understanding does not change. Of course it does and should. Montessori always said that her work had come only so far and it is was now for the others to take it forward. And I believe it has changed. These changes however need to be guided by the deeper principles of child development and need to be well thought out, improvements.

Every material that is added has the potential to take away from another. Also, as Barry Schwartz discovered a complete lack of choice leads to demotivation and reduced involvement, while on the other hand, excessive choice serves to decrease satisfaction and happiness.

There is a golden mean. It serves us well to remember the Montessori principle – ‘give only what is necessary and sufficient’

Here is an article by Angeline Lillard, “How important Are Montessori Materials” that reflects on staying true to the original Montessori material vs adding supplementary materials into the classroom.

 Excessive quantity of the educative material; may dissipate the attention, render the exercises with the objects mechanical and cause the child to pass by his psychological moment o f ascent without perceiving it and seizing it.  … such objects are then futile.

Over-abundance debilitates and retards progress; this has been proved again and again by my collaborators.

~ Maria Montessori (Advanced Montessori Method I,   Kalekshetra 1965)

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!

BEAUTY!
BEAUTY!

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! 🙂