Why INSIGHT is a key in an atrium or classroom.

by David Fleischacker

Though the modern educational world has developed thousands of techniques for dealing with this or that situation in the classroom, there is something central that has never changed in the core of education.  That unchangeable reality is that true education generates insights, and all insights spring from patterned images or what Saint Thomas Aquinas, following Aristotle, called phantasm. 

The examples that one finds throughout history to illustrate the relationship between phantasm and insights are taken from math, usually geometry. The reason for this is that the connection between image/phantasm and insight is so clear. 

Take the example of a circle. One can describe a circle as being a perfectly round object on a page.  But to get an insight into a circle more has to happen.  One has to find the key parts and then grasp how these parts are patterned into a whole.  But how do we get to those parts?  This is a real challenge, and the key in the challenge is that the imagination has to playfully walk toward those parts.  

Let me illustrate this with a bike wheel that has spokes. Notice how the spokes are arranged. They are all attached to a hub at the center and a rim that goes around the perimeter.  With the hub and the spokes and the rim, one has an image.

Now for the playful walk.  Let us say that we keep decreasing the hub in its size, reducing its diameter smaller and smaller.  Notice that the spokes attached to the hub will get closer and closer to each other. They are approaching the very center of the hub.  Of course physically, getting the spokes to the very center will not be possible because the materials will stop one from doing so.  But that will not stop the creative geometer’s imagination.  This mathematical mind will say, lets decrease that hub until it has no diameter, no magnitude.  Hence, it has no depth, width, or height.  But notice what has happened.  The hub has disappeared, and yet one knows what it is. It is now a location with nothing in it.  That mere location with no magnitude is called a point.

To keep the spokes attached to that location though, something strange must happen to the spokes.  One must reduce their width.  Let us say that you keep adding more spokes as you reduced the width. Soon one has moved from 50 to 100 to 1000 spokes and more.  Still, one will not be able to get all of those spokes into the point unless the line itself decreased to a width of zero.  The spoke still has length, but it has no width. That is a line.

There is another feature of the spokes that needs to be highlighted.  Notice that in the bike wheel, the spokes are the same length.  If they were not, or at least is could not be adjusted to the same length, the rim would become warped, and if you have ever hit a curb head on with a bike wheel and bent the rim, you know how disturbing that can be.  I ruined many rims when I was young.  The spokes must be the same length from the hub to the rim.  This is also true as one playfully moves the imagination in getting an insight into the circle.  The spokes must be the same length. Thus, as the width decreases, the length of each spoke must remain identical to the others, lest the wheel loose its round shape.  So, all the lengths of the line must be absolutely equal to each other.

In addition to the lines having no width and equal length, the bike wheel suggest one other element. They need to be laying side by side, or relatively so.  They must be attached to the hub on one end, and the rim on the other.  Now, as we have reduced the hub to a point, what happens to the rim?  Our goal in the end has been to explain why the whole thing is perfectly round.  In the case of the rim, there really is no need to keep it to reach our goal.  Let’s get rid of it, and let the end of the lines form the new perimeter.  But for these lines to be “perfectly round” they must line up side by side, with perfection.  In other words, they must all be on the same plane from one end to the other, from the perimeter to the central point.

And now for a last note.  How many lines are there?  The imagination can keep expanding spokes, making more and more of them.  But the geometer is going to realize that one can say that there can be an infinity because there is no width.  Furthermore, the geometer is going to say there must be an infinity if the perimeter is to remain continuous like the rim. 

Now we have discovered the circle. But everything in the old bike wheel has literally disappeared. And we can understand the circle, which when we started we only “saw” it from its appearance as a perfectly round object.  

It is important that we notice something here.  The object at the beginning is the same as the one at the end, but what has been added is an insight into its nature, into its being as a perfectly round object.  The center point, the infinity of equal lines, all of which are on the same plane are key parts that have been discovered. However, they were only discovered through the playful walk with the imagination.  Without something like a bike wheel to start, there would be no insight. 

Though this connection between phantasm and insight is clear in geometry, it is true of all areas of life.  Montessori instinctively knew this, which is why the playful walk is so prominent in all of the materials and activities that she discovered.  Practical life requires an insight that discovers a solution to some need based on the materials and resources within one’s experiences (sensory and motor images).  Music involves insights into patterns of sound that express meaning.  Science discovers patterns in data (notice the need for charts and diagrams and symbols – all of which are playful walks of the imagination). Architecture is like art in that it requires insights linking patterns of materials, colors, and spatial order to create spaces that also have practical uses. Beautiful clothing and style at heart also are rooted upon insights.  In everything, the human senses and motor experiences  are key for begetting insights.  And with an insight, comes the great joy of discovery.  Children leap for joy when they have had insights of their own.  In reality, no teacher can give insights. Teachers prepare the imaginative experiences a child can have with the hopes that the child will have insights.  This is why the four dimensional environment of the Montessori classroom and atrium is so rich and fruitful when setup properly.

[Though for another blog—another key discovery in Montessori is how to allow the child to become aware of their own insights so that they realize this gift that happens within them—and only then do they leap for joy].