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"Using Fractals to Test for Learning"

On Education and Learning



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Have do you feel when you have to take a test? Anxious? Excited? Worried? Angry? This week, in our ongoing series on education and learning, we're going to take a first look at an alternative to statistically based academic testing, something I call, "fractal testing." Our goal? To find a non injurious direction we can take toward realistic educational accountability.

Fractal versus Classical - The Two Geometries Compared

Chapter Seventeen

"Plastic Flowers"

Even realize you've been fooled by something artificial, such as silk tiger lilies or a fake granite counter top? Feels bad, doesn't it? Ever consider what makes this feel so bad though? Or how in the heck you came to realize this thing was fake? If not, then know this. Within the answers to these two questions lies the thing most missing from our schools today. What thing? A real, blameless way to test kids for learning. And when I say "real," I don't mean that how we currently test is unreal. I mean that how we currently test kids measures mainly what these kids may have gained temporary access to; what they will remember and can access only while in the sequence of this learning and not afterwards.

What I'm saying is, the class ends and what you think you learned you forget. Has this ever happened to you? Of course, a better question might be, has this ever not happened to you?

My point is, the way we currently test kids for learning pretty much measures only what these kids can regurgitate while still in the glow of the class environment. More important, while learning to see these tests as invalid is important, what is more important is that we stop using testing methods which often do more to break kids' love of learning than they do to measure their success or failure to learn. Which makes the way we currently test kids in school as fake as artificial flowers. And as hurtful as well.

What is the answer then? I wish I could easily put it into words. In truth, I can't though. Why not? It turns out that anything really true; true "love" to true "justice," cannot be put into words. At least, not into words which contain the whole measure of this truth. Which means what, exactly?

Which means I'm going to have to find a way in which to show you what I'm saying which paints pictures rather than states logic. In other words, I'm going to have to follow the writer's maxim and "show, don't tell." And lest you see this disclaimer as a copout, please know that by the time you finish reading this column, you'll understand why I can't so easily put these ideas into words. And how this inability to put something true into words is what underlies our inability to define a genuine test for learning.

But if I can't put these ideas into words, then how am I going to teach them to you? Good question. And herein lies the heart of what we'll be exploring today. What defines something as being real? And how do you teach this real thing? In other words, how do you know if something is true or not. And how do you then teach this true thing?

The answer? Any truth which can manifest in our world has but two basic qualities. One, it cannot be put into words. And two, it can be drawn as a fractal shape. No fractal shape. No real truth. And yes, I realize what I've just said sounds very oblique and sci-co-babble-ish. It's not, though. It's just that what I've just said is a "meta-truth." And meta-truths are so concise and head banging that in order to understand them, you must completely reorganize what you know to be true.

How would you then do this? In fact, how do you even know for sure if something is worth the pain you'll endure during this process? Simple. You watch for the two criteria.

One, it cannot be put into words, at least not words which completely describe this truth.

Two, it can be represented by a fractal shape which completely encompasses this truth.

This is the nature of any real world truth. Including the nature of any true test for learning.

Now let's look at what makes these two things define what is true.

"Getting Angry" as a Proof for an Unlearned Truth

In one of our recent Emergence Master Teacher's groups, I tried to teach the teachers what we're about to discuss today; the nature of truth and how you can recognize it. Including how fractal geometry can reveal the degree of truth in something. The result. In at least one case, a teacher blurted out, rather angrily I might add, that what I was saying was incredibly BORING! Whoa, was she mad! And frustrated. And lost. Moreover, she was blaming all this on me.

What had happened to her? She had tried to keep up with the ideas I was presenting, got lost, struggled to regain her understanding, got more lost, struggled more, got more lost, and exploded. Ever felt this way yourself when you couldn't keep up with a teacher? I certainly have. Painful, isn't it?

All students experience this pain at one time or another. Good students feel this pain frequently. Some kids even feel this pain so badly they get lost, and stay lost, then flounder. Sometimes for a whole semester. Sometimes for the rest of their years in school.

Sadly, no one teaches kids that this painful feeling, which Emergence Practitioners call "hitting a dead stop," is the precursor to the biggest and best learning a person could ever do. Kind of like "the storm is always darkest before the dawn" kind of a thing.

Did she recover. Very well, think you. And her open curious face still rings in my mind. So how did she make this transition? I helped her to put her frustration into words, words which led her to the realization that she had no picture for what I was teaching. This then helped her to move from a "dead stop" to the state of learning we call, "unknown"; from hating her blankness to having a next question. Her next question? If she were to be able to picture this idea, what would it look like to her?

My point? That in order to learn things which hold the truth, we usually must experience great suffering. Including times wherein we get very angry at the very person who is trying to teach you this truth. Why? Because all humans have built into us a painful reaction to being in a "dead stop," meaning, to the experience of being unable to picture something.

For example, say you are looking to buy a new vacuum cleaner. If I get you to picture how my super-duper vacuum can suck a golf ball through a garden hose, in all likelihood, you'll jump at the chance to fork over your dough. But if I deliver you a vacuum which couldn't suck a gnat through a soda straw, you'll probably feel like killing every person in my company. And in my family.

What I'm trying to say is, all new learning requires you feel the pain of being unable to see something. Moreover, each time we attempt to refine what we already believe is true, we not only feel this pain but also the pain of giving up an already visible to us idea. Which is why we often feel ready to defend even what are obviously illogical ideas.

Real students frequently do this. They go to war over their beliefs. Why? Because completely reorganizing one's beliefs requires that we experience great amounts of suffering. Moreover, because our beliefs are rooted primarily in what we picture, we are very vulnerable to being fooled by visually similar things. And very angry when we are forced to admit that what we saw was never there.

Why make such a big deal out of these kinds of reactions, including that we frequently feel angry at our teachers? Because it turns out, feeling this kind of anger is one of the best indicators we have that something we believe to be true is probably not true. At least, not completely. And that something we are currently being told is probably more true.

What's so odd about all this is simply that, whenever we hear things we believe might be more true than what we already know, we either blow them off or grab onto them for dear life (the two ends of the teachability index; arrogance or naivete). But when we see things which we feel may be more true, while we immediately sense this truth, at the same time, we usually fail to value this truth.

For instance, take oak leaves. How many words would you have to be told in order to be able to recognize an oak leaf? Given you'd never seen one, that is. Contrast this with how many oak leaves you'd have to be shown in order to learn to truly recognize oak leaves. Even if no one spoke a single word to you.

People can learn to recognize an oak leaf simply by being shown one single leaf. Yet most of what teachers use in classrooms relies more on logic and words than on literal examples. And on numerically high samples.

Now ask yourself the same questions about cumulus clouds. How many words would it take to enable you to recognize a cumulus cloud? Given you'd never seen one, that is. Contrast this with how many cumulus clouds you'd have to see in order to learn to recognize a cumulus cloud. Even if no one spoke a single word to you.

Here again, most people can learn to recognize a cumulus cloud simply by seeing a single example. Yet most teachers rely more on logic and words than on literal examples.

Now let's tie this together. Ever get mad at someone for showing you an oak leaf? Or a cumulus cloud? Or a snow flake? Or a pot of boiling water?

Contrast this with how you have probably reacted to people who have tried to get you to put into words things like the nature of oak leaves, or of cumulus clouds, or of snow flakes or boiling water.

Witnessing truths feels wonderful. Trying to describe this beauty in words usually feels empty and lacking in substance.

These tests for truth are build into our natures.

Schools ignore they even exist, let alone how valuable they are.

Using Geometry to Test for Truth

Now we come to this week's diagram, a drawing entitled, "The Two Geometries." What does geometry have to do with testing for truth? It turns out, everything. You see, while no truth in our world can be completely told in words, all truth can be described with one of the two geometries. Classical Geometry describes perfect truths, those which can never manifest in our world. And Fractal Geometry describes imperfect truths, those which can only manifest in our world.

Are you getting lost? Angry at me perhaps. Please do not disregard these feelings. They are very important. Moreover, they are the signals built into your psyche which tell you that what you're hearing holds a great amount of truth. Certainly more truth than what you currently know how to say.

Still don't believe me? Well, let's try to make this truth a bit more visible. By doing a little "show don't tell." By exploring a few examples.

All squares are perfect truths. All plant leaves, including oak leaves, are imperfect truths.

All trapezoids are perfect truths. All gaseous clouds, including cumulus clouds, are imperfect truths.

All circles are perfect truths. All crystals, including snow flakes, are imperfect truths.

All spheres are perfect truths. All water surfaces, including that of boiling water, are imperfect truths.

Why say that squares are perfect truths? Because nothing in our world can be a perfect square. And because we can use words to completely describe a square; "a shape which has four equal sides and four equal angles."

Try doing this with any leaf, including an oak leaf. What words could you use to completely describe this leaf? Obviously, there are no words. We simply cannot do this, regardless of how well we write or speak. Why not? Because words cannot describe imperfection. Why not? It is simply too complex. (Which makes me think they should rename "complexity theory" to "imperfection theory." They never will though. Too honest. And unscientific. Which is just another way to say "too honest.")

At the same time, we human beings can pretty easily know whether an oak leaf is real or not. Simply by looking at it. And herein lies the simple fact which we could use to design genuine academic tests for learning. All truth in our world [1] cannot be put into words and yet, [2] can be completely described by fractal geometry. Recognizing this geometry is, after all, our built in, natural truth test. It is the thing we use every time we need to see if something is true or not. Tiger lilies, to granite counter tops.

Don't believe me? It's easy enough to test this out for yourself. Try describing, in words, anything which literally exists in our world. A blade of grass. A fallen log. A curl of smoke. A flaming match.

Can you do it? Of course you can't.

At the same time, can you tell the difference between a real blade of grass and a fake one? Or between a real fallen log and an artificial one?

The truth. You know you'd know it. Moreover, you could discern this difference easily. Even if your eyes were making it hard for you to tell. Just by listening to your gut as well as to your eyes.

Toward Real Educational Testing

My whole point is, we know truth when we see it. Given we listen to our eyes and hearts. Which is why, if we are really honest with ourselves, we know already that most tests in schools are close to worthless except as tests for temporary learning.

How temporary is fractal learning? It's not temporary. It's permanent. Which is what makes Shakespeare's words; "a rose by any other name," so profound. You see, he knew, at least intuitively, the very thing which I've been trying to put into words today. And can't. He knew how to tell if something was true or not.

He also, like Socrates, knew that truth, beauty, and goodness could never be seen separately, and that for something to be true, it must simultaneously be all three.

What we teach in schools should be all three. And how we test kids for having come to know all three should be the criteria by which we know kids have indeed learned these things.

Roses are fractal geometry. Roses are beautiful, good, and true. Like Socrates and Shakespeare, we know this to be accurate both in our eyes and in our hearts. The same with puffy, cumulus clouds. The same with iced over winter lake surfaces.

We also know we can never put this beauty, truth, and goodness into words. At best, we can do what Shakespeare did. We can indirectly refer to that this can't be done, simply by referencing the fractal nature of this thing, as in, "a rose by any other name ...."

So how could we use this knowledge to design authentic academic tests? My honest answer? As far as how to design fractal tests for individual children, I don't as yet know enough of the details to pragmatically describe this process. I do, however, have one example to share with you before I go. Before I do, let me just say this.

Until we can pragmatically define a process with which we can create authentic tests for learning, our academic experiences will continue to more resemble tests for artificial flowers than for any true learning. As well as contributing to our children's skepticism regarding that we have anything of value to teach them.

Now consider what this means about way we use grades to test children. And why these grades hurt children so badly. Even the kids who get high grades.

Why do they hurt so much? Because grades can test only a kid's ability to parrot someone else's ideas. They cannot test for truth. Why not? Because grades are never, in and of themselves, fractal. They're not even visual. Except, of course, when taken in high enough measures as to enable one to plot these numbers on a bell shaped curve.

No coincidence that bell shaped curves are fractal geometry.

My point?

Using grades to measure learning in individual kids is a spurious endeavor. Not just some of the time. Every time.

Similarly, using numbers to test for an individual's IQ, or for a person's personality, or for a human being's honesty are all equally spurious tests. As are tests which try to match us to a romantic partner, or to a genetically sound mate, or to an appropriate profession.

Now consider what this means if I am right. It means our three hundred year old obsession with scientifically designed studies is entirely spurious. At least, it is at the "individual" person level. Which would mean that things like "trait theory" (a theory of personality), which attempts to reduce a human being's personality to descriptions of five words or less, is an insanely ridiculous waste of time. As is computer dating. As is anything which attempts to use mere numbers and words to comprehensively measure something in the real world.

Put into simpler words, all learning, and tests for learning, require we come to consciously be able to know a personally meaningful example of this teaching when we see it. In effect, we need to have acquired a "reference visual experience" in order to have genuinely learned. Moreover, we can never reduce these reference experiences to mere words or numbers. However we can, with certainty, know these experiences as true when we visually experience them on the screen of our mind.

Closing Comments

Now, lest you think I've forgotten my example of fractal testing in schools, allow me to tell you about one currently in existence. No surprise, this example involves my friend Scott, the English teacher, and his ongoing project to bring Emergence into the classroom.

What is he doing that involves fractal based testing? Simply this. He is having his kids, 7th and 8th graders, pair off. Then he is asking that one of them be a reader, and that the other watch, and keep a count of, the times the reader's eyes go blank.

In essence, the child who has been designed the "watcher" simply watches for a fractal pattern present in all human eyes, a visual-intuitive cue which allows us, with high degrees of certainly, to know for sure if someone is picturing the words they are reading.

Observing blankness in the eyes of a child while this child is reading. A simple fractal pattern. It is also as recognizable to human beings as oak leaves or snow flakes.

How is this project working out? From his reports, simply amazingly. In fact, his class aid recently told his department chair that she has learned more about teaching reading in the few weeks she has been in his classroom than in the whole rest of her education.

So now. How about Hallmark Valentine cards? Are they okay? Or would you rather get a handwritten note on a beautiful letter paper scented with your sweetheart's perfume?

And how about if the words in the card were the same words written on the letterhead? Would this make the card any more real?

How about buying some fake Gucci shoes, or a $10 Rolex, or a replica Shelby Mustang. Any buyers?

Perhaps it's time we stop buying our kids bargain educations. Including statistically based testing.

Statistically based educational testing is no bargain. Moreover, it hurts our kids chances to learn so badly, most kids come out of school simply glad it's over.

Don't our kids deserve more?

Until next week then. I hope you're all well,

Steven

P. S. And for those wanting to see how open they may have been to this week's ideas, here's a link to fractal test; Teachability Index Worksheet.


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