by When Mum was on the way to Christchurch to pick up Dad on Tuesday, she dropped in on her mother’s cousin Pat who now lives in a care home in Ashburton. Pat is 106 (!) years old – she was born during the First World War – and remarkably still has all her marbles. In this meeting Pat told Mum about her car journey from Christchurch to Dunedin at the age of four. A car journey of that distance would have been a mission back then, and something quite astonishing for a four-year-old; I can see how she still has a clear memory of it more than a century later. What was the car? Her family wasn’t wealthy as far as I know, so how did she end up in that car in the first place? What were the roads like? How long did it take? I’ll ask Mum the next time I speak to her; our conversation quickly moved on to the building work. Last year the local radio station had a phone-in where anyone who remembered Elizabeth’s coronation (in 1953) could call in and regale the listeners of their memories of the day. Pat called in. “I remember when she was born?” Um, sorry, what, you’d have to be at least a hundred. “Yes. Do you have a problem with that?” That might not have been exactly how it went down, but I know there was disbelief on the part of the host.
Yesterday I had a late finish – a face-to-face maths lesson between 7 and 9pm, followed by an online English session. In our maths lesson, among many other topics (her schoolteacher switches between topics at a maddening rate) I helped my 15-year-old student divide by decimal numbers smaller than one, without using a calculator. We think of division as sharing – that word was used at school, I remember – and sharing money or sweets or bottles of orange juice between two or three or ten people all feels natural. But sharing between half or a tenth or 0.08 of a person – what on earth could that even mean? When you divide by something less than one, you end up with more than what you started with, and that messes with people’s heads. It goes against what people intuitively feel that division does. By chance, earlier in the week I stumbled upon a blog post that used bottles of juice as an intuitive basis for dividing by small decimals. When I explained how to divide 24 by 0.08, I asked her first to imagine 24 litres of orange juice and (big!) 8-litre bottles. How many bottles would all that juice go into? She correctly said three. Now imagine the bottles are 0.08 of a litre. You know, tiny, the size that you could take through airport security. You’d need loads of ’em, right? Turns out it’s 300. Move the decimal point two digits to the right, or in this case add two zeros. I told my English student about my maths lesson – she’s an accountant and has a strong mathematical background – and she couldn’t understand how my student didn’t just know to do these division problems. She’s fifteen, for crying out loud. Can’t she just think of that decimal as a fraction and go from there? No. So much of being a good maths teacher is empathy. Just because you got it at a young age and it all seems obvious to you, that doesn’t mean they will. And I certainly wouldn’t want to introduce fractions into the problem – fractions seem to frighten the living bajeezus out of Romanian teenagers.
Earlier today I watched this video of somebody multiplying and squaring numbers showmanlike, faster than a calculator. His party piece came at the end: working out 37,691 squared in his head. I actually paused the video and tried to do this. It’s not the worst five-digit number to have to square. It’s 9 away from 37,700. The repeated 7 helps. All (!) you have to do is square 377 and tack on four zeros, then find 18 lots of 37,700 then take that away, then add on 81. Hey presto, Bob’s your uncle. But there’s a catch. You end up with a ten-digit number, and my brain is nowhere near capable of storing that many digits while also carrying out calculations. I gave up. He can also calculate the day of the week that a particular date falls on, which is something I saw people do at the autism groups I used to attend. I recently had a go at this 21-question hard mental arithmetic test. I tried to do the questions as fast as possible, and got 17 correct.
The weather is wet and nasty. I had to go out in it this morning, for a lesson with a 12-year-old boy who lives on the fifth and top floor of a block of flats with no lift. He’s a nice kid. We mostly did the simple past tense in all its glory.
