4/1001 Bradburian Nights

 

An excerpt from 'The Mathematican's Lament'

Short Story: 'Brooksmith' by Henry James

Essay: "A Mathematican's Lament" by Paul Lockhart (available to read here) recommended by my friend Kelly Cumbee.

What an essay! So much applies to Charlotte Mason's approach to education. Lockhart makes some incredible statements right off the bat:

"...if I had to design a mechanism for the express purpose of destroying a child's natural curiosity and love of pattern-making, I couldn't possibly do as good a job as is currently being done [by our present system of mathematics education] -- I simply wouldn't have the imagination to come up with the kind of senseless, soul-crushing ideas that constitute contemporary mathematics education."

Well, at least we can't accuse him of holding anything back.

There is a lot more where that came from. It's not merely an essay; it is truly a lament, a lover’s lament. It is an elegy as well as a scathing accusation against the way the standard institutional educational system has handled - or, to quote Lockhart, how it has “openly and cruelly tortured” - mathematics. See the quote above as well as quotes like this:

"...it is so heartbreaking to see what is being done to mathematics in school. This rich and fascinating adventure of the imagination has been reduced to a sterile set of "facts" to be memorized and procedures to be followed."

And this:

"Now let me be clear about what I'm objecting to. It's not about formulas, or memorizing interesting facts. That's fine in context, and has its place just as learning a vocabulary does -- it helps you to create richer, more nuanced art. But it's not the fact that triangles take up half their box that matters. What matters is the beautiful idea of chopping it with the line, and how that might inspire other beautiful ideas and lead to creative breakthroughs in other problems— something a mere statement of fact can never give you.
"By removing the creative process and leaving only the results of that process, you virtually guarantee that no one will have any real engagement with the subject. It is like saying that Michelangelo created a beautiful sculpture, without letting me see it. How am I supposed to be inspired by that? (And of course it’s actually much worse than this— at least it’s understood that there is an art of sculpture that I am being prevented from appreciating).

"By concentrating on what, and leaving out why, mathematics is reduced to an empty shell. The art is not in the “truth” but in the explanation, the argument. It is the argument itself which gives the truth its context, and determines what is really being said and meant. Mathematics is the art of explanation. If you deny students the opportunity to engage in this activity— to pose their own problems, make their own conjectures and discoveries, to be wrong, to be creatively frustrated, to have an inspiration, and to cobble together their own explanations and proofs— you deny them mathematics itself. So no, I’m not complaining about the presence of facts and formulas in our mathematics classes, I’m complaining about the lack of mathematics in our mathematics classes."

And this about teaching:

"If teaching is reduced to mere data transmission, if there is no sharing of excitement and wonder, if teachers themselves are passive recipients of information and not creators of new ideas, what hope is there for their students? ... Teaching is not about information. It's about having an honest intellectual relationship with your students. It requires no method, no tools, and no training. Just the ability to be real. And if you can't be real, you have no right to inflict yourself upon innocent children. …
"Teaching means openness and honesty, an ability to share excitement and a love of learning. Without these, all the education degrees in the world won't help you, and with them they are completely unnecessary."

Let's take  moment to catch our breath.

A Mathematican's Lament is an impassioned plea to give math - actual mathematics, the "art of explanation" - a chance. As much as I love an eloquently phrased jab at industrial education, I love even more to hear an amateur (from Latin amator ‘lover’, from amare ‘to love') - even an expert amateur (amateur expert?) - wax eloquent about what they love, and at length, if possible. To hear an amateur speak about their passion is to risk being convinced that you have seen whatever it is they are praising all wrong - that maybe you have never actually seen it at all - and to find that you are not only intrigued but that you want to learn more for yourself - indeed, that you must, you need, to learn more as soon as possible! The entire essay is an ode in praise of the Beauty of Mathematics, a meditation on the loveliness of this much-maligned art, and a call to reconsider our entire approach: "The first thing to understand is that mathematics is an Art.... Mathematics is the purest of the arts, as well as the most misunderstood." It reminds me of Cinderella, and Lockhart is the prince who sees through the insitutional rags we've made her wear to the beauteous and virtuous maid waiting patiently beneath.

To read Lockhart's lament is to become convinced that you have never experienced Mathematics at all and to find yourself lamenting your loss. I think that now, I might understand Edna St. Vincent Millay's sonnet a bit better:

Euclid alone has looked on Beauty bare.
Let all who prate of Beauty hold their peace,
And lay them prone upon the earth and cease
To ponder on themselves, the while they stare
At nothing, intricately drawn nowhere
In shapes of shifting lineage; let geese
Gabble and hiss, but heroes seek release
From dusty bondage into luminous air.
O blinding hour, O holy, terrible day,
When first the shaft into his vision shone
Of light anatomized! Euclid alone
Has looked on Beauty bare. Fortunate they
Who, though once only and then but far away,

Have heard her massive sandal set on stone.

Poem:

An excerpt from "For the Time Being: A Christmas Oratorio"

by W.H. Auden

Well, so that is that. Now we must dismantle the tree,

Putting the decorations back into their cardboard boxes --

Some have got broken -- and carrying them up to the attic.

The holly and the mistletoe must be taken down and burnt,

And the children got ready for school. There are enough

Left-overs to do, warmed-up, for the rest of the week --

Not that we have much appetite, having drunk such a lot,

Stayed up so late, attempted -- quite unsuccessfully --

To love all of our relatives, and in general

Grossly overestimated our powers. Once again

As in previous years we have seen the actual Vision and failed

To do more than entertain it as an agreeable

Possibility, once again we have sent Him away,

Begging though to remain His disobedient servant,

The promising child who cannot keep His word for long.

The Christmas Feast is already a fading memory,

And already the mind begins to be vaguely aware

Of an unpleasant whiff of apprehension at the thought

Of Lent and Good Friday which cannot, after all, now

Be very far off. But, for the time being, here we all are,

Back in the moderate Aristotelian city

Of darning and the Eight-Fifteen, where Euclid's geometry

And Newton's mechanics would account for our experience,

And the kitchen table exists because I scrub it.

It seems to have shrunk during the holidays. The streets

Are much narrower than we remembered; we had forgotten

The office was as depressing as this. To those who have seen

The Child, however dimly, however incredulously,

The Time Being is, in a sense, the most trying time of all.

For the innocent children who whispered so excitedly

Outside the locked door where they knew the presents to be

Grew up when it opened. Now, recollecting that moment

We can repress the joy, but the guilt remains conscious;

Remembering the stable where for once in our lives

Everything became a You and nothing was an It.

And craving the sensation but ignoring the cause,

We look round for something, no matter what, to inhibit

Our self-reflection, and the obvious thing for that purpose

Would be some great suffering. So, once we have met the Son,

We are tempted ever after to pray to the Father;

"Lead us into temptation and evil for our sake."

They will come, all right, don't worry; probably in a form

That we do not expect, and certainly with a force

More dreadful than we can imagine. In the meantime

There are bills to be paid, machines to keep in repair,

Irregular verbs to learn, the Time Being to redeem

From insignificance. The happy morning is over,

The night of agony still to come; the time is noon:

When the Spirit must practice his scales of rejoicing

Without even a hostile audience, and the Soul endure

A silence that is neither for nor against her faith

That God's Will will be done, That, in spite of her prayers,

God will cheat no one, not even the world of its triumph.

Our tired tree, still standing but beginning to droop