Slow Learning

We often ask, what is learning?  Now let us ask, what is slow learning?

1. Slow

In Space and Time in Classical Mechanics, Einstein asks to imagine that he has dropped a stone while in a moving train.  As it happens he asks us to imagine that he has dropped it outside the train, from the window, as the train moved.

Inside a moving train, if we drop a stone we will see it fall down in a straight, vertical line.  If we are inside the moving train but drop the stone outside the train, we will see the same thing.  To the falling stone, once released from his hand, it makes no difference whether it is inside or outside the train.

An observer outside the train, on the platform, (or on the embankment, as in Einstein’s tale), will see the stone come down in a parabolic path.  As if it were not merely dropped but thrown.  To those inside the train, moving forward at the same rate as the stone itself moves forward, the forward motion of the stone is invisible.  We might say it is non-existent or cancelled out, like the motion of the earth – which we do not count we are sitting still.  Or when we drop a stone while sitting still.

Now the question Einstein asks us is:  What did the stone do?   Did it fall in a straight line or along a curve?

As Einstein goes on to explain in the rest of the book, Relativity: The Special and General Theory, questions of speed, distance and time become relative to the frame of reference.

Learning also takes many paths, perhaps all paths, as the quantum physicists say of particles.  Is one path longer than another?  Faster?

What parent or teacher is not familiar with this experience – in a conversation with a child, a flurry of ifs and buts arise, so that a simple point that that you thought you would explain in five minutes gets deferred for hours or days.  Meanwhile as you follow the tangents, further questions arise.  Is your original question forgotten?  No, it is still out there, drawing you towards it via this loopy, squiggly path.  Schools run like factories may not allow for such digression and yet the curiosity of children will keep these questions alive, patiently or impatiently awaiting their turn on the front burner.

If it takes two days to communicate a point that you thought would take five minutes, do you feel that time has been lost?  What about teaching complex concepts and skills – what if your child learns something months or years after the expected date?

Is this child slow?  Is s/he falling behind?  Will it be difficult to catch up later?  Will it hurt if I push her or him?  At what point should I intervene?

Many people have written about these questions with reasonable points supporting a spectrum of approaches.  Some offer suggestions to encourage progress, indicators for intervention when there is no progress, or reassurance that it will happen in its own time.

Some will say, “they will learn it when they learn it.”  Some will say, “they will learn it when they need it.”
But what is it?  Do we know?

Maybe we do.  Or maybe we only think we know.

Is my understanding, Wittgenstein asked, blindness to my misunderstanding?

2.  Learning

Let me tell a story about my daughter and the (suddenly glamourous) subject of arithmetic.

From as far as we can remember, our daughter delighted in number, shape, order, series and various mathematical concepts.   She would observe various shapes and patterns and then one fine day tell us something about them that would wow us.  She was equally thrilled to hear about math.  Indeed she heard math in places we would not have expected.  While listening to a Carnatic vocal performance in Pune, she looked up from her doodling to remark, “This music is very satisfying, like adding up the rows of numbers in a long multiplication problem.”

Everything reminded her of math.  She knew it too, and delighted in it.  While arranging her clothes in her shelves she referred to priority and order of operations.  While overhearing us refer to combinations and permutations in the context of tracing old classmates she immediately corrected us – “you can’t have permutations!”  Seeing our blank looks, she explained, “what would they do, enter the room in a different order?”

When it came to basic sums, though, she was adding on her fingers most of the time.  Would this be considered late?  Slow?

One day she arranged her dominoes in a pattern and called me to see that it served as an addition table.  I have described this in a comment posted on Peter Gray’s article, “Kids Learn Math Easily When They Control Their Own Learning” in his blog Freedom To Learn.

Had she memorized her basic addition facts, would she have devised an addition table?  Perhaps.  When?  Would that have been considered late?  Or slow?

What did she learn by making the addition table?  How was this learning facilitated by the fact that addition had not yet been ticked off her list of skills to master?

“Learn as if you would live forever,” said Mahatma Gandhi.  Not only will you be unafraid to learn something new, you will be unafraid not to know, and unafraid to say “I don’t know.”    You will not fake it, you will not be rushed to learn something when you are arrested by something more fundamental.  And as we approach the answer to one question we may again find our path slowed by still further questions.

For example – when coming across the phrase “first prime minister” (of India), my young friend was not interested in the name corresponding to this epithet.  She wanted to know what this phrase meant.  A question about what the “first” of a kind could be, how a given specimen could be “first” of a kind at all.

Her question:  So did they already decide to call the person a Prime Minister?

As I collected my thoughts to answer, there came another question – But who, they?

A question about the nature of authority itself, who vests it in whom.   (Is this history?  Or math?  Or politics?  Or philosophy?)

And then:  When did they call it India?

Those who “know” the answer to the question “Who was India’s first prime minister?” would probably answer the question, quiz-show style.

But how would they “know” such information?   And how would they “know” that one responds to a question with “the answer” rather than further questions?

Slow learning empowers the learner over the learned.   In the spirit of the movements for slow food, slow money and slow love, slow learning values the slow.

Of slow love, it is said,

“Slow love is about knowing what you’ve got before it’s gone.” – Dominque Browning, Slow Love, pg. 5.

You can look up the name of the prime minister.  But when you stop asking questions about first-ness and prime-ness, where do you go to tap into your earlier wonder about these concepts?