Issue 178: 2018 11 15: The Math Lesson

15 November 2018

The Math Lesson

Other eyes, other worlds.

By Richard Pooley

photo Robin Boag

What comes to mind when I say “African village”?

Lots of conical huts, reed-roofed and mud-walled, chickens scratching for food in the dirt, goats searching for something to eat among the few stunted bushes, children laughing as they play, a sinuous line of women walking through the Bush with pails of water on their heads, men sitting and chatting in the shade of a tree…  The truth is that there is no such thing as a “typical” African village.  A villager by the river Niger would paint a very different scene to someone in a village in the Ethiopian Highlands or another on the Kenyan coast.

Even so, the African village where I worked as a teacher in the early 1970s was fairly close to the stereotype.  Except for its size.  Molepolole is one of a string of huge villages which line the eastern edge of the Kalahari Desert in Botswana.  When I was there its population was around 30,000, dwarfing the country’s capital, Gaborone, 30 miles to the east.  A dirt road wound through it, numerous paths leading off on each side to collections of huts, often circled by a low mud wall or an irregular wooden palisade.  The road ended at the gates of the hospital compound built and run by Scottish missionary doctors – an oasis of mature trees, lawns and white-washed buildings.  To the west of the hospital the Kalahari scrublands stretched for hundreds of miles, empty of proper roads and peopled mostly by nomadic San.  To the south were a line of rocky hills and single kopjes sticking out of the flatness.

To reach the hospital the road had to pass between the village dam and the British-built junior secondary school.  If the November to April rains were good, the dam’s waters could spread as far as the road, covering the area used by many of my pupils should the school’s latrines not be working, a common occurrence.  In my first term the school consisted of a staff-room and library, a science laboratory, a hall, a single row of teachers’ bungalows, six classroom blocks, and an ablution block (as the latrines were called).  There was also a large area of open ground which though dubbed the “sports field” contained no grass, only yellow and red ochre earth, stones and the occasional thorn bush or aloe.  All the school’s buildings were rectangular, prefabricated and metal-roofed.  The walls contained asbestos, apparently as protection against bush fires towards the end of the dry season.  Inside them we baked for most of the year and froze on midwinter nights.

When I arrived in September 1970 I was just 18 years old.  I had been sent by Britain’s Voluntary Service Overseas.  Besides Eric, the Glaswegian VSO with whom I shared one of the asbestos boxes, there were American college graduates from the US Peace Corps, nearly all avoiding the Vietnam War, a couple from Canada in their mid-sixties who never stopped telling us that things were better “back home”, a one-eyed American adherent of the Baha’i Faith who preferred to proselytize than teach (perhaps because he had lost his eye while doing an experiment in the science lab.), a refugee from Lesotho, and several Batswana, only one of whom had got past secondary school.  Our youth and lack of teaching experience did not seem to matter.  What mattered was that we got as many pupils as possible, by whatever means we could, to pass the final Junior Certificate exam, the passport to a job in an office (boys), a good marriage (girls) or the one senior secondary school in the whole country (both).

I taught English, History and Geography and, because my sport at school in London had been rowing, Physical Education.  The fact that the nearest river of any size was about 200 miles away in South Africa did not seem relevant to the principal.  Mr Phalla had a dim view of the Peace Corps volunteers, all of whom he was convinced were sex maniacs and so could not be trusted to keep their hands off the many attractive teenage girls doing press ups, running 100 yards or playing netball in their invariably skimpy skirts and tight blouses.  It did not seem to have occurred to him that American male lust may have been fuelled by a simple fact: hardly any of the female pupils could afford to change their school uniform as they progressed from girls to women.  I saw no good reason to point this out to him.

English presented few problems.  History was much trickier.  Botswana had won its independence from Britain only four years earlier.  During colonial rule the capital of the Bechuanaland Protectorate, as it was called, was Mafeking in apartheid South Africa.  The history textbook of colonial times was only replaced at the end of my first term and had a decidedly Euro-centric take on the past.

“Teacher, sir, why is this book saying ‘Bartholomew Diaz discovered the Cape of Good Hope in one four eight eight’?”

“Fourteen eighty-eight, Tebogo”

“Yes, teacher. Eighteen forty-eight.  Why?”

“Why what?”

“Why ‘discovered’?  You are telling us last week that there are Hottentots and Bushmen that side.  Already there.  So long time.  What is this Diaz man discovering?”

But Geography was the toughest.  Try convincing even the brightest child that the Earth is round when she lives on the edge of the flat Kalahari and has never been further than 30 miles from her village.  Or that a meteorite streaking across the night sky is not God telling you a chief will die.  The latter belief became even harder for me to counter when a superb meteor shower was followed three days later by the dethroning of the chief of the local tribe (for being habitually drunk and, worse, failing to get married).

By the time the second term started in January 1971 Eric and I were considered experts on teaching Batswana children.  This was because staff numbers had almost doubled.  The new arrivals were American and British volunteers, new to teaching in Africa.  One of them was Jim.

Jim was from the Deep South of the USA.  His subject was Math (no amount of urging by us Brits would persuade him to add an ‘s’).  And he loved it with a passion which put his many other passions – sport and women and the Constitution of the United States of America – in the shade.  He was also good-looking.  And it was probably the latter attribute which least endeared him to Mel, the poetry-loving New Yorker who also taught Math, lived in squalor and was under the misapprehension that all women found him irresistible.  The latter notion had been proved to Mel’s satisfaction by the fact that he had managed to impregnate at least one village woman.  In short, Jim was competition.  There was no way that Mel was going to offer advice to his new colleague on how best to teach Math to Batswana children.  He wanted him to fail.  That’s why, three weeks after the beginning of term, Jim was asking for help from me.

It was a late Sunday afternoon and the heat of the summer sun had waned.  Jim and I were walking up into the low ridge of hills near the village.  Jim was not his usual positive self.  He hardly spoke.  It wasn’t until we got to the top of a hill and were gazing down at Molepolole sprawling below us that he began to unburden.

“Hey, Rich, are these guys stupid?  I know I’m not supposed to use that word but… I just don’t get it.  Or rather, they don’t get it.  Number seems alien to them.  Even simple adding and subtracting.  And forget Geometry.  They… they just can’t draw anything correctly.”

I empathised.  I told him that I had given up trying to get my pupils in Geography to draw a map to scale.  The concept of a map was beyond most of them, let alone reducing the landscape to something which could be drawn two-dimensionally in their exercise books by using some abstract formula.

We continued in this vein for some time, reinforcing each other’s reluctant conclusion that our pupils were lacking intellectually in some areas.  We tried to find reasons.  Periods of malnourishment in early childhood?  Lack of sleep?  The smoke-filled air in the interior of their huts?  Anything but what we did not want to admit: black people are not as bright as white people are.

Suddenly, Jim jumped up.  Later, I would pretend to myself that he shouted “Eureka!”.  But I think it was a quiet, head-shaking “Holy Shit!”  What he said next I can definitely recall.  “We’re the stupid ones, Rich.  It’s the teaching which is stupid.  We’ve got it all wrong.  What’s right in your British schools and in the US is all wrong here.”  I had no chance of finding out what he meant.  He began running downhill, occasionally sliding in the scree or jumping from rock to rock.  “See you later!” was all he called back up to me.

In fact, I did not see Jim again until the next morning.  He had just finished the second of two Math lessons and walked into the staff-room, a bundle of exercise books under one muscly arm and doing a Black Power salute with the other.

“Both classes.  They got it.  I did Geometry.  Walked in and asked them to imagine they were an eagle flying over the village.  Told ’em to look directly down on their family compound… on their huts.  ‘Open your exercise books and draw what you see, you eagles’, I said.  Thought I’d gone crazy, of course.  Wanted to know if this was in the exam.  Jesus!  But they did it.  Here’s the best one.  The lovely Lerudi.  What did she draw?  Look!”  He opened an exercise book and stabbed at a page covered with almost perfectly drawn circles.  One of them had a line showing its diameter.  At right angles to the line was another just touching the circle’s edge.  There was a number too: 3.14.  “See what I did differently?”

I couldn’t.

He shook his head.  Now I was the stupid one.  “Think back to when you did Math in First Grade.”  I assumed he meant my first year in an English primary school.  “Geometry.  What did you start with?  Lines and angles, right?  Squares and triangles and right-angles, yes?  Simple to you and me.  Why?  Because that’s our world, Rich.  Look at this building.”  Everyone in the staff-room had been listening and we all began to look around the room.  “It’s a rectangle.  Straight lines.  90-degree angles in every corner.  Think of our students.  They are sitting in a rectangular building at a shared rectangular desk drawing on a rectangular piece of paper in their rectangular exercise books.  They’ve got right-angles all around them.  Yet they can’t draw… they can’t conceive of a right-angle.  Why not?”

“Because it isn’t their world,” I said.

“Right on, brother.  I looked down yesterday… Yeah, brother, from the mountain top.  And what did I see?” Jim had gone into his impersonation of Martin Luther King, something which had made me uncomfortable in the past but which was making all of us, black and white, smile now.  “I saw the whole of Mo…lep…o…lole spread out below me.  I saw many things.  But there was one thing I could not see.  A right angle, brothers and sisters.”  He was addressing all of us now.  “And not a single straight line.  Until… until I looked left and there was this British school and the Scottish church and the Scottish hospital.  Right-angles, rectangles, straight lines.  In our world, brothers and sisters.”  He stopped channelling King and spoke softly as if just to me.  “So, I started with their world.  Huts equals Circles.  No problem.  Then I asked them to imagine they had eagle eyes and could see through the roof of each hut.  Where was the pole holding up the roof?  A dot in the middle of the circle.  Draw a line to the side of the circle.  That’s a radius.  Diameters.  Tangents.  Jesus, tangents!  And right-angles.  And then pi.  They got it.  All of it.  Even the dumbest of them.  As teachers we have to start seeing the world from our students’ point of view and then bringing them to ours.”

Actually, Jim did not say that last sentence either then or in that way.  But it summarises the conclusion that Jim, Eric and I reached after further discussion that evening.  We agreed that it did not just apply to teaching.  If you want to persuade anyone to do something, including changing their mind, you have to first step into their shoes and see how they see the world.

There is a coda to this story which I may have imagined but which recent research makes me think really did happen.  A few weeks later one of Jim’s pupils invited him out to his family’s cattle post.  These were the places, sometimes 50 miles or more from Molepolole, where the villagers kept their cattle, every family’s most precious possessions.  The first evening Jim watched as the boys rounded up the cattle and brought them inside the thorn-fenced kraals for the night, safe from hyenas and even lions.  He listened too.  As the cattle were being driven inside, he heard his pupil counting them in.  He was not counting to the base ten.  He was using a binary numeral system, he was counting to the base two.


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