Dedicated to NANCY LUKOSKI (Shoreham Schools) and PATTY FORBES (Springfield Schools), terrific Math teachers and teaching partners. They showed me how you  teach numbers with heart.

S. Wulfing, Der Kristall

This Old Man,
He played one.
He played knick-knack on my thumb.
With a knick-knack, Paddy whack—
Give the dog a bone.
This Old Man came rolling home.

His wise gaze penetrates you with all he has seen, eyes all the more brightly animated when he is listening to you. His leathery hands are amazingly warm and robust. How long has he owned that tattered Red Sox cap?

He taught ARITHMETIKE, undercover, to children in seventeenth century villages. Having been initiated by the ancient Pythagoreans, he practiced their art (tekhne) of numbers (arithmos).

He usually assumed the identity of some kind of itinerant trades-person, a minder and a measurer of material things— typically operating as a carpenter, merchant, or tailor.

And while he plied his trade, The Old Man would always be looking out for new children to charm, so he could practice the teaching craft on them.

This Old Man,
he played two.
He played knick-knack on my shoe
With a knick-knack, Paddy whack—
Give the dog a bone.
This Old Man came rolling home.

Once upon a time, the Patriarch of our Arithmetic Teachers loyally served a Queen who proclaimed him her Rabbi, her Sufi, her Sage, her Wizard. Then he applied for a grant so he could initiate the progeny of the ignorant and common people into left-braininess.

Into that particular generation, he was called to install the spell of counting out loud.

This Old Man,
he played three
He played knick-knack on my knee
With a knick-knack, Paddy whack—
Give the dog a bone.
This Old Man came rolling home.

One Two, Buckle My Shoe states a simple recitation of the sacred sequence of numbers.

This Old Man, however, narrates the very pedagogy that initiated the modern mind into mathematical syntax.

The sequence of the number line, installed into cultural memory, would serve as the mental architecture for left-brained, material-world concepts to come.

This Old Man,
he played four
He played knick-knack on my door
With a knick-knack, Paddy whack—
Give the dog a bone.
This Old Man came rolling home.

He appeared precisely when Evolution was urging the common folk to internalize a more rational mind, voiced from individualized, differentiated selves, each possessing his own given name.

The prevailing peasant consciousness when he arrived was like a gritty soup, thickened generation upon generation. Those folks perceived things very, very slowly— had only the most parochial impressions. They conceived only the most concrete concepts.

This Old Man came to synchronize the folk-soul to the steady tick, tick, toking of the Universal Clock. He set their minds into seconds, minutes, hours, days, months, and years.

This Old Man,
he played five
He played knick-knack on my hive
With a knick-knack, Paddy whack—
Give the dog a bone.
This Old Man came rolling home.

Old Mother Goose had come and gone, initiating Literacy into a prior throng.

She instilled rhymes and rhythms into the collective Nursery. She gently awakened the children’s soft, lyrical hemisphere into a sleepy self-consciousness.

This Old Man followed her with hard-headed, clear-thinking, linear-sequential
Rationality.

This Old Man
he played six
He played knick-knack on my sticks
With a knick-knack, Paddy whack—
Give the dog a bone.
This Old Man came rolling home.

From Buddha we have learned how the instrument of the body is imprinted by mental and environmental processes. The World tattoos itself onto our skin, it pinches our last nerve, it emblazons itself onto our organs, and then it comes to Mind.

one knick-knack on the thumb…
two knick-knacks on the shoe…
three knick-knacks on the knee….

Note his method of physically striking the pupil in progressive sequences.
The steady rhythm and the increasing count instilled the physical craving
to compute.

This Old Man,
he played seven
He played knick-knack up to heaven
With a knick-knack, paddy whack—
Give the dog a bone.
This Old Man came rolling home.

The Stranger practices his craft on young minds and meat. The guardian dog barks out his suspicions. Alas, Fido is easily distracted by a bone.

This Old Man,
he played eight
He played knick-knack on my gate
With a knick-knack, Paddy whack—
Give the dog a bone.
This Old Man came rolling home.

The antique “dunce cap” makes for an interesting collateral study of bygone instructional technologies.

You think of this quaint object of juvenile humiliation from the antique, black and-white Spanky and Alfalfa classrooms of the 1930’s, along with the hickory stick.

An errant pupil was ordered to sit, isolated, on a stool, facing a corner of the classroom, wearing  this conical cap. Branded a “dunce,” he was terrorized into self-consciousness by the righteous teacher’s rally to ridicule.

The dunce cap’s positive instructional purposes have been lost for generations, and its pedagogy for mental development has long been forsaken.

In former times wizard and witch wore such as antenna over the skull cap. They utilized pyramid power to sharpen their wits, no doubt amplifying their meditative transmissions.

Properly placed on the head, applied in a corner of the room’s solid architecture, the technology of the dunce cap was supposed to provide focus to a vague spirit, centering him in his own corporeal body and physical space.

This Old Man,
he played nine
He played knick-knack on my vine
With a knick-knack, Paddy whack—
Give the dog a bone.
This Old Man came rolling home.

Today, our Mystery Teacher’s ultimate successes are omnipresent.

Behold these children raised in an increasingly materialistic, mathematical, and man-made environment. New souls are exposed to abstraction, quantification, and sequence at earlier and earlier stages of their earthly life.

A child conceptualizes a glass of milk independent of any Momma. Numbers and letters lie flush up against her daily bread.

Babies are initiated into the number system by fluorescent, even grotesque picture books on supermarket shelves, on high definition television sets, and from the unearthly humanoid voices looped into computers.

This Old Man,
he played ten,
He played knick-knack
all over again
With a knick-knack, paddy whack—
Give the dog a bone.
This Old Man came rolling home.

Not within a university Mathematics Department, but at a cottage in the woods up the mountains, you’ve come to find him, now retired.

You see that the villagers know him very well, but not as the Master Arithmetic Teacher of your sacred quest.

They know him, rather, as a gifted ornamental horticulturist and landscaper. You’ve noticed the neat, orderly fields of flowering shrubs and leafy things, not unlike cultivated rows of desks and seats in certain old- fashioned classrooms.

He’s in there, of course. You can see him through the window, hunting and pecking and fuming on the keyboard. He’s shooting an angry email off to a neighboring farmer whose plants have withered from neglect, and to the Commissioner of Education for doing likewise.

You knock timidly on the door.

“Come in! Come in!” he bellows, transferring to you his irritation with the errant Commissioner, or neighbor.

Suddenly, you are thunderstruck!

In the presence of The Master, your heart goes wild. It’s him! It’s him! You feel so lightheaded, even dizzy.

You suddenly want to bolt out the door and run away. But you must stay. You must ask the question you have been sent to ask, not just for yourself, but for a whole new generation of Math Teachers. Now, you have been told, is the final opportunity to get his answer.

A flourish with the mouse and he is done expressing himself electronically.

A few more clicks and the impressions on the screen are routed through cyberspace into the virtual mailbox of either negligent farmer or negligent Commissioner.

The Master suddenly pivots to you and swallows you up in his gaze. Instinctively, you close your eyes tightly, and just blurt out your question:

What is the best thing we can do to teach Math to today’s kids?

With that ever-ready wink on his crafty old eye, he says the answer is simple:

“Teach them to play with their own digits first!”

He holds out both hands, wiggling all his fingers, then he performs:

Little fingers dance with me—
One, two, three, four, five.
Little fingers dance with me,
You are quite alive.

One goes up and
Two goes down,
Three goes up and
Four goes down.

What do we do with little Five?
Little Five shall take a dive.

Little fingers dance with me,
One, Two, Three, Four, Five.
Little fingers dance with me
You are quite alive!

He exits his little characters to behind his back, and then he boyishly bows.

That done, he changes into his maroon Aloha shirt with the 23 hula dancers, grabs his Red Sox hat, bolts out the door— suddenly stops, turns, smiles to you, waves goodbye to everyone— then delights in taking off his hat and making his final bow.

With a nod, he tumbles and chuckles— giggles and tumbles.

He creates a whirlwind of air and dust, and summons you to “take a spin” with him.

But before you could—or even would— you see him with your own eyes. He is rolling out of corporeal matter, submitting himself to transcend into pure energy.

First a wave, a beam, a steady flash, a zap, a certain glow— and then he’s gone.

You are flabbergasted.

In the distance, there’s Fido barking all over again.

Something, he smells— is Unreal.

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