Little surprises

Yesterday I had a double culture-check.

The first came after I offered to help one of the girls in the house with her math homework. When I looked over her notes from her lesson at school, I was very impressed by their neatness and thoroughness. It looked like she was copying out an entire math textbook. She goes to and English-medium school, which means that everything is taught in English (for those like me who had no idea what the term meant).

When I asked her about the main content from the lesson, I noticed something interesting. She remembered the definition almost precisely as she had written down, but she omitted one word. To give some context, we were talking about relations, and in her notes she had written 

"Relation is simply a set of ordered pairs."

When I asked her to recall the definition without her notes, she remembered 

"Relation is simply a set of ordered."

What I found interesting was that she remembered exactly the trivial word "simply" but not the operative term "ordered pairs" without which the definition doesn't make any sense. The conclusion I drew, perhaps erroneously since it's based on little in the way of scientific evidence, is that she is highly trained at recall, which she does with near-perfect accuracy. (If quizzed on one sentence out of six pages of notes, I would never have remembered a superfluous descriptor like "simply".) However, her ability to apply the concept she had memorized the words for was essentially zero. My attempts to get her to recognize relations in any context outside of her copied-out example met with mute incomprehension.

After a few more minutes, I discovered another series of puzzling aspects of her education. She was perfectly capable of multiplying two or three digit positive integers, but she had very limited ability to add or multiply negative numbers. She could correctly subtract 7 from 6, but not 1 from 0. Half the time she correctly used multiplication for rewriting exponents, and half the time she tried to use addition. It was astounding that a smart, 17 year old girl who had good attendance at a good school couldn't do basic arithmetic.

I am somewhat familiar with the curriculum for her level of mathematics, having already tutored one student at the same level. I know that she will soon be taught functions, logarithms, vectors, and the quadratic formula. I fear it will do her little good without a thorough re-grounding in basic mathematic operations. I also suspect this is a chronic problem (I had also noticed it to a lesser degree with my previous pupil, who by the way had access to a much more expensive education). I'm worried that most of the content is completely inaccessible to students because they don't thoroughly understand addition, multiplication, exponents and so forth. Worse, this lack is covered up by their incredibly well-developed ability to exactly but uselessly recall things written on the blackboard*.

My second, unrelated shock came later that night when I went to visit a friend at his house. During our conversation he mentioned he was married, and I said that I hadn't known, so he pulled out a family photo album. He pointed out his wife, and his little baby, and then another photo where he has his arm around a very ancient Maasai gentleman, and he proudly said ".. and that's my father." I thought I had misheard him. Father and grandfather sound very much alike in Swahili: baba versus babu. So I asked "did you say father or grandfather?" It was his father alright, 90 years old even though my friend is only 26.

I didn't even think that was possible. On second glance, the man in the photograph looked more like a great grandfather, wrinkled and stooped but still with a bright, sharp look to his eyes. My friend went on to explain that his father had taken five wives over his long life, and I was proudly assured that "he is still productive now!"

Go figure.

*By blackboard, I am rather charitably referring to the front, concrete wall of the classroom that was, in some long-forgotten epoch, painted black.