Maths teaching

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A busy winter’s day and a trip to Arad

January 14, 2024 by 0 Comments

I’ve had a busy Saturday, chock-full of lessons. Two maths sessions – two hours apiece – and three English ones. Everything from a creative writing piece about a murder and tactile Little Mermaid books to construction of perpendicular bisectors and probability tree diagrams. Marginally preferable to yesterday though, when I took five paracetamol for my sinus pain.

It’s been cold. Actual proper winter, like my first one in Timișoara, not the half-arsed stuff we’ve had of late. On Monday it snowed all day, making for a pretty sight, but getting around the city for lessons was quite a challenge. Today was the first time since then that the mercury – ever so briefly – touched freezing point. We’d been at (minus) sixes and sevens all week.

Last Sunday – just before the wintry blast hit us – I met Mark in Dumbrăvița and from there we went to Arad in his car. I hadn’t been there for six years. Arad is a fine city, with beautiful architecture much like we have in Timișoara. (Just like my home, it was part of the Austro-Hungarian empire for half a century until the First World War.) After a good wander, be both agreed that in some ways we preferred Arad to its bigger cousin. (Timișoara is roughly twice the size.) There were all kinds of photo opportunities. We managed to go inside the Palace of Culture, which reminded me of the larger one in Iași; the lobby and the concert hall were both superb. The Mureș, a much more substantial river than Timișoara’s Bega, runs through the city. The Christmas market was still running, but rather than grab overpriced food from there, we had a major feed at one of a clump of kebab shops at one end of the main drag. Kebab Alley, we called it. Unlike Timișoara with its three main squares, Arad has one long, broad main street where everything happens, though some of the side streets were impressive too. After our kebabs, we decided to go back home. Mark had parked in an area of town not far from the centre called Boul Roșu – the Red Ox – but despite seeing a sign depicting a red ox, it took us a while to find the car. Coming home from that very enjoyable trip felt like the absolute end of any kind of holiday-related downtime.

My record player – turntable, if you like – arrived yesterday. It’s still in its box. Getting that going will be tomorrow’s “thing”.

Here are some photos from Arad, and of the snow.

Above is one of those Roman numerals date word puzzle thingies that I mentioned on this blog some years ago. But did they have to make it so complicated? Someone must have really pissed off whoever made this in 1779 (if I haven’t gone wrong somewhere – I may well have).

Arad does have a square, and it’s in the process of being revitalised

On the left is the old water tower which I visited in 2016

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Grounds for optimism

January 1, 2024 by 0 Comments

It’s already 2024 in New Zealand. The last embers of the old year were still flickering when I called Mum and Dad. I thought I wouldn’t get them – they’d probably be at Caroline Bay for the fireworks and a spin or two of the chocolate wheel – but they’d had thunder and hailstorms and didn’t fancy it. The last time I visited Caroline Bay for New Year was with my brother eleven years ago. He was very subdued, having been through a nightmare few days. The next day we went to Methven – appropriately, it was completely dead – and saw a terrible Australian film at the cinema in Geraldine. Just like now, the darts was on TV. My parents had Mum’s old colleagues from Cairns staying with them; they really could have done without that. This morning Mum talked her elder brother’s daughter, who thinks the world revolves around her, and didn’t want anything to do with her elderly parents over Christmas. Having loving, caring parents hasn’t stopped her becoming a selfish arsehole.

This morning I went to the market in Mehala on the off-chance that there might be a cheap second-hand record player, but no such luck. There were quite a few records, though I didn’t buy any. It was nice to browse all the same, and take in the sights and smells on a sunny morning. The beer, the mici, the vehicles, the signage, the haggling. I had a particularly greasy langoș and then went home.

“You’ll find us on the street, between the langoși and the police station.”

A new footbridge being built over the Bega in the west of the city

No lessons today. Yesterday I had my 945th to 948th sessions of 2023, including my usual battle to get Matei to understand fractions. If you don’t know fractions, you’re screwed when it comes to calculating probability, and much else besides. Next weekend I’m going to spend the whole session on fractions. It’s what he needs. (His cluelessness about fractions is hardly his fault, as I’ve mentioned before here. He missed out under the Romanian system, and now he’s at the British school where they just assume he has all that knowledge.) After him I had the brother-and-sister combination. I normally spend two hours with him and one hour with her, but the boy said he had to meet some friends in town, so could they do 90 minutes each? She’s six. That’s an eternity with someone so young. Luckily I had a secret weapon: a rather tricky dinosaur maze (see below). I printed it off before our session, not realising how T-rex-like it actually was. Impressively to me, she persevered. (At her age, I think I’d have given up.) I tackled the start, she worked backwards from the end, and eventually we met in the middle. That ate up a good chunk of time. I had an online session with the guy in England when I got home.

The darts. There were three matches last night. First up was Brendan Dolan, the Northern Irishman who started as an underdog against Gary Anderson, winner of two world titles. Dolan, who uses Dropkick Murphys’ I’m Shipping Up to Boston as his walk-on song, raced into a big lead against Anderson who was misfiring at the start. Anderson then kicked into gear and went 3-2 up in the first-to-four-sets match. Dolan then made it 3-3 before hitting double three to pull off a dramatic and fully deserved victory, his third knife-edge win in a row. His wife’s face at various points throughout the deciding set was a picture. Next up was Raymond van Barneveld, an old hand who has been a top player since the nineties, against Luke Littler who is at the other end of the scale (though you wouldn’t think it by looking at him). Littler, who turns 17 next month, has been a sensation. The Dutchman played very well but Littler was unstoppable. The youngster won 4-1. I couldn’t stay up to watch the last match. Snooker, yes, but I draw the line at darts. A pity in a way, because it was one heck of a finish, with Luke Humphries beating Joe Cullen in a sudden-death leg, hitting the winning double at his tenth attempt. (Those outer slivers are pretty skinny, and even the best players miss them more often than they hit. All those misses ratchet up the tension.)

I managed to get the adminstrator to recalculate my catch-up water bill at the old rate, so this month’s bill ended up being a monster 983 lei instead of a gargantuan 1470.

I plan to see in the new year in town, where there will be fireworks and music. I’ve found 2023 to be quite stressful, with the exception of the period around Easter and (in grounds for optimism) the last couple of months. The early part of the year was bloody terrible. Simply put, I couldn’t cope. My “big thing” this year was spending a whole month in New Zealand. Stunning beauty around every corner. The stress my parents have been under became apparent when I was over there, and I’ve found it upsetting. I hope things become less fraught when their building work is done.

The word of the year for me is a depressing one: billionaire. I remember when billionaires were few and far enough between to be ignorable with the exception of Bill Gates and his Mr Clippy. Not any more. Every other article I read is about the antics of some mega-rich egomaniac fucking up the world for the rest of us just because he can. He, of course. Next year, with massively consequential elections taking place all over the world, their influence is unlikely to wane.

A couple of new year’s resolutions, both about writing. Firstly, this blog. I’d like to get back to more free-flowing writing such as I produced right at the beginning eight years ago. Hopefully being more relaxed will allow me to do that. Second, the book about my tennis-playing friend. I made progress last January, then things stalled badly. It needs to be a top priority again.

Family - Life :) - Maths teaching

A Christmas mishmash

December 27, 2023 by 0 Comments

It’s 5:20 on Boxing Day evening; the sun set half an hour ago. Once I’m done with this blog post I’ll dip into the ample leftovers from yesterday.

On Saturday the 23rd I had my full complement of four lessons. After an online English lesson, I had to get to Dumbrăvița by bike – a struggle on such a blustery morning. I was glad that Matei was finally learning probability. We went through various exercises. One of them asked him to imagine picking two letters, one at a time without replacement, from the word SCIENCE. What’s the probability that the first letter you pick is S? One in seven, he happily answered. What’s the probability that the second letter is S? Now he wasn’t so sure. Doesn’t it depend on what the first letter was? Well yes, but at this stage we have no idea about that. I did my best to convince him that the probability was also one in seven, asking him to consider a lottery draw (the second ball is just as likely to be 17 as the first, isn’t it?) and resorting at one point to tree diagrams. Probability messes with people’s heads.

On Christmas Eve I made salată de boeuf, which despite its name is a chicken-based salad, with potatoes, celeriac, carrots, parsnips and gherkins added to the mix, bound together by mayonnaise. I put a sliced egg, some olives and slices of red pepper on the top. Then I made salam de biscuiți: a pound of simple biscuits broken by hand, to which I mixed in milk, melted butter, cocoa, raisins and rum essence. I rolled the mixture into two salami-like cylinders and put them in the fridge overnight.

Then in the evening I did something I hadn’t done for five years: attend a church service. Dorothy, a regular churchgoer, had invited me. To be polite I accepted, not knowing what I might be letting myself into. I cycled there and got my shoes all muddy as I found something to attach my bike to. I found the church, which didn’t look at all churchy, without too much trouble. Sfânta Treime – Holy Trinity. A Baptist church. I felt out of my comfort zone. Since Covid, I’ve found that any place where there are dozens of people, some of which I may have to interact with, will give me that feeling. It didn’t help that my muddy shoes came close to causing a scene. Mass kicked off at seven; I was amazed how young the congregation was. Many of them could speak English, and quite a few had good jobs in the IT field. At the front of the church, if it had a front, were a guitar, drums, and a viola. We sang several carols, many of which were the same tune as the English but with Romanian words. I must admit that the wordy Romanian version of Silent Night did little for me, though Away in a Manger was fine. (The Romanian for “manger” is iesle.) Some of the language was new to me; religious Romanian tends to be older and more Slavic-based than what you encounter day-to-day. In the middle of the service, the children acted out a short nativity play. There was a sermon in which the priest, dressed in civilian clothes, lost his thread on more than one occasion. The service took 1¾ hours. Afterwards there was lots of chitchat – I ended up talking to an Australian woman among others. Dorothy, who had gone to the church since 2001, was in charge of food and drink duties, as out came cozonac (a traditional Romanian cake which I’ve tried to make in the past) and non-alcoholic mulled wine. It was an interesting experience, but I was glad to finally get home at 10:15.

On Christmas morning I spoke to my parents who’d been over to my aunt and uncle’s place in Woodbury for dinner. I then called my aunt in England. I was happy to get through to her, but what do you say, exactly, when she’s stuck in a nursing home for what will almost certainly be her last Christmas? Have a good Christmas, I said. I think I’ll have had better, she replied. She got calls from Dad and my brother, and thankfully a visit from her son. I worried that she might spend the whole day alone.

I had a 45-minute walk to Dorothy’s place. The food and bottles of drink and (admittedly basic) presents were too much to carry on my bike. When I arrived, I was greeted by Dorothy and a 65-year-old man called Ionică who lives in the same apartment block and has recently retired from 44 years of working as a baker. A real job. He left school at 14, he said, and did military service which was compulsory back then. He had made enough apple tart for a dozen people or more, explaining that he either bakes in proper quantities or not at all. Ionică and I were tasked with decorating Dorothy’s (real) Christmas tree. When that was done, Gabriela (a woman who attends the same Baptist church as Dorothy) arrived. Although she has an 18-year-old son, she said she wasn’t yet born when Ionică moved into his flat in 1982. Her son didn’t come, apparently because he’d injured himself playing football. The food came out. I was slightly bemused by how gingerly Gabriela approached my salată de boeuf. What? A man cooking? A British man cooking? Romanian food? Despite being quite young and (you’d think) more open, that didn’t quite compute in her mind. In the end, she seemed to quite like it. Then came Dorothy’s roast dinner – chicken, stuffing, potatoes, parsnips, and so on. The British stuff, in other words. Finally we had dessert – the apple tart, my salam de biscuiți, and some Christmas pudding and mince pies that Dorothy had made. We had plenty of food left over. Ionică’s fact-free musings on mental health were interesting, shall we say. “I don’t take any pills,” he said with an inordinate level of pride. Lucky you. “Depression isn’t real. You shouldn’t have time to be depressed.” It’s all a lot more complicated than that, I’m afraid, I said. I’m glad I went no further. I found Ionică to be a very pleasant chap, but on that issue he was badly misinformed. Hardly surprising, because he comes from a time and place where things were simpler. Not easier certainly, but simpler. Probably the best thing about Christmas Day was how much Romanian I spoke. Pretty much all conversation was conducted in Romanian; a few more days like that and I might get reasonably good at it.

When I got home I spoke to my brother who showed me his son, dressed up in a Father Christmas costume. He has an outfit for every occasion, it seems. He’s just started walking and is a happy chappy whenever I see him. I’ve made up my mind to visit the UK for Easter, so it won’t be too long before I see him in the flesh.

Today I’ve finally got round to finishing George Borrow’s Wild Wales, including the interesting bit at the end on the Welsh language. We’re getting warm weather for the time of year, and tomorrow I’ll take advantage of that by going for a bike ride.

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Looking positive in Geraldine

December 12, 2023 by 0 Comments

Now Dad’s got Covid too. He didn’t look too clever when I spoke to him this morning (my time). Mum had already gone to bed by then. He told me that Mum had forced herself to do painting and other ridiculous DIY that day, despite being sick as a dog herself, and had been angry with Dad for not doing the same. It beats me how Dad has lived with Mum for half a century without ever (as far as I know) telling her to eff off.

Last week I got an email from one of the other ex-owners in our Wellington apartment block. Ex. Thank our lucky stars that we’re ex. Still being embroiled in that misery (which about 650 owners in Wellington are) hardly bears thinking about. The email contained the words disproportionate, unfair and inequitable, which the whole situation absolutely is. (I spelt that out to letters I sent to Grant Robertson, my local MP, but they got passed on to the housing minister who was bloody hopeless.) The ball is starting to roll now, but up a depressingly steep hill.

Last week it was Boris Johnson’s turn in the hot seat at the Covid inquiry. He had aged, and at times he looked quite ill. The interesting bit came right at the beginning as some protesters were asked to leave during Johnson’s initial apology, and then Hugo Keith (the KC) pointed out that the UK had the second-worst mortality rate in Western Europe, behind Italy who were extraordinarily unlucky in the early stages and have a very high elderly population. “Look at the table!” the ex-PM protested. “Why are you excluding countries like Bulgaria [top of the European Covid death league overall] or Romania [fourth, I think]? When you include these vastly poorer countries full of anti-vax nutters, we’re slap-bang in the middle!” What a joke. After he’d got that apology out of the way, he spent two days justifying and normalising everything, including missing those five emergency Cobra meetings prior to mid-March. No, the toxicity in government at the time was not normal nor in any way desirable, and I seriously doubt it would have been like that had Theresa May or Gordon Brown or any of a number of former prime ministers had been in charge. This week the current PM Rishi Sunak, of Eat Out to Help Out fame, is stepping up to the plate.

Before my maths lesson yesterday, I met up with Mark at the beer factory. I had a pasta dish while he had a very Romanian combination: a slab of pork, some sausages, some mici, and mămăligă. I’ll go for that next time. Just one beer each; I’d soon be explaining algebraic fractions. We discussed various ongoings in his job which are making the experience rather less fun, and the possibility of my one day getting Romanian citizenship. Becoming actually Romanian and having triple nationality would be totally mad, wouldn’t it?

Talking of mad, someone else to put in the mad-but-good category is Luke Thompson, an English teacher based in Paris who has a long-running YouTube channel with over 850 episodes. I use his channel as a teaching tool for my more advanced students.

Five English lessons for me today after my initial Romanian one. Plenty of work, and with a welcome drop in my life admin, I’m not complaining.

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Accomplishments

December 3, 2023 by 0 Comments

I’ve just spoken to all the family. First I Skyped Mum and Dad. Mum had that pissed-off look. I didn’t entirely blame her. While she’d been painting the ceiling, Dad had been watching YouTube videos about Covid vaccines. The vaccines were useless according to the latest video he’d watched. “He’s a very creditable, highly qualified scientist.” Sure, he’s got a list of qualifications as long as your arm, but that doesn’t mean what he’s saying is true. At all. In fact you see people weaponising their qualifications all the damn time. YouTube is great if you want to find good music. Likewise if you want to know how to make sarmale or put up bookshelves or even solve quadratic equations. For “information” about Covid vaccines and treatments though, you should probably give it a pass. There’s a lot of nuance about the Covid vaccines. Maybe they were pushed out too soon. Some vaccines were clearly better than others. (Um, the Chinese one, anybody?) Side effects were real, to the point that maybe for a fit young person it was just about worth chancing their arm on getting the virus, from an entirely selfish perspective. The efficacy of booster jabs – fourth, fifth and beyond – is debatable. But to say that the vaccines were a waste of time is quite clearly ridiculous, when all the data points to vaccination massively reducing mortality. The more shocking a YouTube video is, the more eyeballs it gets, and that’s pretty much the story. Dad wants me to watch this latest (long) video, and I suppose I’ll have to, just to humour him.

After Mum and Dad, I spoke to my brother. He, his wife, and his son have been under the weather lately. The little chappy has had a bout of scarlet fever, which sounds like something from the Middle Ages. They’re almost recovered now though. My brother is going to St Ives in the next few days. It seems Mum and Dad have now considered paying for them all to come out to New Zealand (maybe after a comment I made, who knows) – that would be fantastic if it happened.

Yesterday I had four lessons – three in Dumbrăvița, then an online session with the chap in London. My first session was maths with Matei. He’d been learning some basic stats and had no problems that I could see. At the end of the session, as I’ve done the last few weeks, I gave him a few short multiple-choice questions on a variety of topics, mainly to get his mathematical brain working. They’re designed to be answered in under a minute. One of them was this:

He stared at it for a good five minutes, maybe more. He eliminated A (“it can’t be smaller than 36”) and D (“too big”), but was unable to choose between B and C. The question clearly says (perhaps unfairly) that you can’t use a calculator, though I don’t think it would have helped him. If I was tackling this question, I’d immediately see that 75% is three-quarters. If 36 is three-quarters of our number, then 12 is a quarter, so I’d just add on 12 (the remaining quarter we need) to get the answer. It would take me ten seconds or so, without any recourse to algebra. Just for a laugh, I gave Mum that question on our Skype call this morning, without the four options. She got the answer impressively quickly, using the exact same method that I did. As soon as I read out the question, Dad blurted out, “is it a hundred?”. Ha! But how do I teach the method that Mum and I use? Between us we’ve been fiddling with numbers for over a century, and in that time we’ve developed all kinds of hard-to-teach tricks and time-savers that we use without even thinking about them.

After Matei I had English with Octavian. We looked at yet more poems by Ted Hughes, such as The Thought-Fox, a poem about writing a poem. By the time he does his IGCSE in the summer, he’ll be beyond sick of Ted Hughes’ poems. I wish I could focus on his pronunciation, which could be greatly improved, rather than poetry which while interesting is of far less long-term benefit. Then came his little sister – after last week’s horse-heavy session, this time I gave her loads of sheets with dinosaurs. Next time she wants stuff on Christmas. When I got home I had my online session – we went through two articles, one on AI, the other on consumerism.

Friday was Romania’s national day, and a much warmer day than we’ve had of late. I met Dorothy in the centre of town – my old stomping ground – and we watched the parade of military and emergency vehicles. Unlike previous parades, this one was disappointingly short. When I sent my brother the pictures of the vast crowds, he likened it to Red Square victory parades. In truth there was little of that kind of vibe, but in Ceaușescu’s time they were just like what you saw in Moscow, or what you see now in North Korea. When the parade was over, I suggested to Dorothy that we walk through Central Park as I did countless times when I lived there. We walked by the busts of the great and the good of Timișoara – all men – and read some of the inscriptions. Some of them were ex-mayors. Many of them were writers. One was Béla Bartók, the famous Hungarian composer, who had links to Timișoara. When we reached Ioachim Miloia’s bust, I noted that he was my age now when he died. Look what he accomplished in that short time!

An art-history guru, a library founder, a writer on all matters related to local history, and painter who helped to restore numerous churches in Timișoara and its environs. And then look at me! Wouldn’t it be nice to say I’d accomplished something? Dorothy was taken aback by my comment, and I explained that I’d probably feel quite different if I had a family. My biggest accomplishment is, without a doubt, coming to Romania and making a life for myself here (and having a job where I help people, at least in a small way). In early 2015, a few months before I started this blog, I had the realisation that nothing would happen unless I did something drastic. Visiting the US that year – seeing the big wide world out there – gave me the impetus to actually do it.

Here are some pictures from the parade. The main square is being done up nicely.

Piața Unirii, 4:30 pm last Sunday
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Bamboozled

November 25, 2023 by 0 Comments

Yesterday I got a phone call from Florin, the guy I play tennis with. They’re seeing in the new year at the same place as last year. They already need numbers. Do I want to come? Of course I don’t, but it’ll only be a few hours and won’t it be good to at least show my face? It couldn’t have been that bad last time, surely? Luckily I have this blog to remind me, and there it is, in black and white and orange. It really was that bad, and I even vowed not to put myself through that again. The difficulty is finding an excuse. A way out. There’s also the prospect of Christmas in the UK. A horrendous time of year to go there or be there. My brother doesn’t particularly enjoy Christmas with his wife’s family because they really go to town with party games and other activities he can’t stand, and I totally sympathise with him. I hope if I decide not to travel there for Christmas and instead go over at Easter, he won’t think I don’t care. Sometimes I really miss Covid.

The UK Covid inquiry resumed this week. Patrick Vallance, the Chief Scientific Advisor, spoke unflatteringly of Boris Johnson. The former prime minister didn’t get the concept of exponential growth, or a heck of a lot else by the sound of things. In Vallance’s words, he was bamboozled. I liked Vallance’s comment about the heavy bias in government towards people with humanities backgrounds at the expense of science and maths. He said that it should be a 50-50 split, emphasising that a bias towards science and maths wouldn’t be a good thing either. Next week should be an absolute doozy – twat-in-chief Matt Hancock will be making an appearance, among others. The inquiry, or the bits I’ve seen so far, have thrown into sharp relief how dangerous the ministers and senior advisers were. The contrast between them and the general public, who were extremely compliant, could hardly be starker.

Maths last night. Plenty of bamboozlement there, as I started teaching my 15-year-old student the basics of probability. There are very few things in this world that I get, or that I’ve come somewhere close to mastering. Probability might just be one of them though, so you’d think I’d be on pretty firm ground. But there was one snag – this is Romania, and probability involves a whole ton of fractions. She really doesn’t get fractions, even at the most basic level. A half plus a quarter? Huh? I learnt about basic fractions when I was six or seven, before I ever touched decimals, but Romanians obviously didn’t, so when they join a British school where fractions abound in their maths classes they face an uphill battle. I’m in the middle of making a fractions worksheet (or workbook, as it might end up being). These things are all over the place online of course, but they’re (understandably) targeted at rather younger age groups.

Romania won their final qualifier against Switzerland 1-0 to finish their group in first place, with an impressive haul of 22 points from 10 games. It’ll be Romania’s first appearance in a major tournament since I arrived here. It was funny to watch the game against Israel on TV, where the local commentators didn’t even attempt to appear impartial.

A nippy start to the day as I had my lesson with the boy on the fifth floor. The lesson went well, though. Next week I’ll be starting lessons with her husband (a total beginner, she says, but I’m always skeptical about that).

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Why is English so dominant? (And can I face a British Christmas?)

November 20, 2023 by 0 Comments

I managed 32 hours of lessons last week. I was my first time over 30 for a while. I always think of 30 as a good benchmark for a full, productive week, but cancellations had kept me below that level. After I got home from Dumbrăvița on Saturday I emailed Mum a logic problem about odd and even numbers that I’d given to Matei. She replied with the right answer. (It wasn’t immediately obvious to Matei that if you multiply two whole numbers and you get an odd number, both the numbers must be odd.) I thought about the night classes in maths she took when I was little, half her lifetime ago. She’d show me her book full of xs and ys. It would be nice if she could do something similar now.

At the weekend I read an article about the rise of English. It is undoubtedly the dominant language in the world, and is likely to remain so for some time. Most of this is down to American culture. Just look at Romania. As the country develops, slices of America keep popping up everywhere, with “Drive-Thru” and “Wash & Go” spelled out in English. Twenty-year-olds grew up on Cartoon Network. Teens (and even pre-teens) are all over TikTok – Chinese-owned but loaded with American popular culture. There were plenty of comments on the article, and some people said that the dominance of English isn’t only due to America, but also because it’s simply easier to communicate in than most other languages. “Me no like the cats” is very wrong but perfectly understandable to a native speaker. They’re partly right – English has few inflections, it lacks grammatical gender, and English text takes up less space than most other languages that use the Latin alphabet. But that’s only a small part of the story. Bad English is easy for us to understand precisely because we’re used to non-natives speaking English, or attempting to. We even simplify our language in return. I remember in Bali 30-plus years ago, where the locals often knew English but at a very basic level, Dad would say things like “Many motorbikes here” or “Takes long time?” It’s not the same with less widespread languages. If I utter a very bad Romanian version of “I don’t like cats”, my Romanian listener won’t have heard anything like that before in his life. He’ll be thinking WTF? So that puts a barrier in place to anyone trying to learn Romanian – you have to get to some kind of reasonable level before you can even start using the language. Its very pervasiveness is what makes English one of the easier languages to learn; in 2023 you’d have to be living under a rock to not know like or love or stop or OK. You get a lot of English for free, and that gives you a heck of a head start.

I don’t often watch football these days, but on Saturday I watched Romania’s Euro 2024 football qualifier against Israel, played in Budapest. It was originally meant to be played in Israel, but got moved for obvious reasons. If Romania avoided defeat, they’d qualify for next summer’s competition in Germany. Israel took the lead in only the second minute, then Romania equalised in the tenth. That dramatic start set up a very watchable game. Romania took the lead midway through the second half and held their advantage until the end. They probably should have won by more – a player by the name of Mihăilă missed a sitter and then got himself sent off just before the end. Romanian football, and sport in general, has been in the doldrums for a while, so it’s nice that they qualified. Beneficiaries of a pretty easy group it must be said, they’re unbeaten in nine games (five wins, four draws) and if they can get at least a draw against Switzerland in Bucharest tomorrow night they’ll top the group and in theory have an easier ride in the final tournament.

This song popped up on YouTube – Sleeping Satellite, Tasmin Archer’s one-hit wonder. It came out in 1992 and was the very first song on Now 23, one of the first tapes I ever had. A complex song, unique in many ways, with levels of rhyme adeptly woven into the lyrics. It brings back memories of a more optimistic time.

Last night I watched the first episode of the new series of Charlie Ottley’s Flavours of Romania. It’s on Netflix; I thoroughly recommend it. I hope to get a few ideas for road trips, for when I finally do own a car. I also watched Noel Philips’ trip from Amsterdam to Paramaribo (the capital of Suriname) – a nine-hour flight on an Airbus A340.

My brother called me on Saturday. My nephew was bouncing around, on the verge of walking. A very happy chappy. He’s fascinated by the cat, though the cat seems less fascinated by him. I’m thinking of going over there for Christmas, but can I face it? What I’ll really want are about four days with little risk of having to see or communicate with anyone.

Family - Maths teaching

A talking time machine and the great divide

November 17, 2023 by 0 Comments

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.

Family - Language teaching - Life :) - Maths teaching

Play time

November 13, 2023 by 0 Comments

I’ve just had an argument with Dad on his last full day in the UK. We talked about him and Mum possibly making the trip in six months’ time. “We have to consider the cost.” No, Dad, you really don’t. I’m fully sympathetic to all the factors that make the trip difficult for you, but the cost isn’t one of them. It isn’t even close to being one of them. Dad will visit his sister later today – it might be the last time they meet.

Last night I saw a comedy play at the theatre with Dorothy and Sanda. I got wet on my bike ride to Scârț, a place that houses a bar, a museum of communism, and an amateur theatre company called Auăleu. (Auăleu is a Romanian exclamation, used similarly to “Oh my god”.) The theatre sat 50 people; I was on the front row (of two) next to Sanda, but wished I was on a hypothetical tenth row. Being that close to the stage was rather intimidating. The play was called Grand Hostel Timișoara. Guests of various nationalities booked in, and the comedy came from all the national stereotypes as well as local jokes about Timișoara in 2023 (supposedly it’s the European Capital of Culture, though you wouldn’t know it) and other in-jokes, only some of which I got. After the interval the guests came back to the hostel having visited the city and suffered all kinds of mishaps. Some of the actors could clearly actually speak the native languages of the guests – German, French, Hungarian, and so on. The play was partly improvised and was very clever and well done, though it wasn’t quite my thing. Being in Timișoara for “only” seven years didn’t help, and political jokes about Schengen or neighbouring countries’ accession to the EU left me cold. I’ll happily go back though and see something else if the opportunity arises.

Plenty of interesting lessons last week. One was with a woman who is always ever so busy in her work as a middle manager at a large bank, to the point where she often has to cut short her meetings with me. I still haven’t figured out the purpose of our sessions. Business English? Well, she’s got that down to a tee already. A simple chat? Maybe, but our discussions rarely stray from the corporate world. Last Tuesday she talked about how good it felt in her previous job to be given so much power; in that job she was the sole determiner of who got what access to vital IT systems at a company she didn’t even work for. With no sense of irony, she said “I felt like a rock star.” That responsibility would terrify me. I could, like, accidentally press something that shut down everyone’s access at a stroke. Then on Friday I helped a woman prepare for a job interview in English, which she has tomorrow. The first thing I did was browse her CV. She, like many Romanians, uses an automated CV system which produces personality-free walls of text in a tiny font. Her first inscrutable wall of text related to her current job. “So, what do you actually do?” Robots. Directing robots. Fixing robots. Ordering new robots. “Why, then, are there over a hundred words in this paragraph and not one mention of robots?” Robot is a fun, eye-catching word, even if it’s a bit scary. (Incidentally it comes from a Czech word meaning “forced labour”.) But I couldn’t persuade her to move away from that dreadful vagueness. I then saw that at the bottom of the CV she said she was at a C1 level in English listening, but B1 in all the other disciplines (reading, writing and speaking). Why the big gap, I wondered. (C1 is miles better than B1.) I can understand anything anyone says. That’s why I’m C1. I suggested that she visited a British pub and tried to follow a conversation – jokes, regional accents, people arguing and talking over each other. It became apparent during our interview practice that she didn’t really know what she’d be doing if she got the job. Not her fault – the job description was hopelessly vague. I’m so glad I’ve left the corporate world behind.

Another highlight was an 11-year-old boy’s piece of creative writing, in which he said there were “cloudy clouds” in the sky. Then yesterday I had maths with Matei. Fractions reared their ugly head again. He can add, subtract, multiply and divide them, but conceptually he hasn’t the foggiest, and that’s starting to cause a problem.

I’ll soon be playing tennis for the last time in 2023.

Family - Life :) - Maths teaching - Tennis - The UK

Maths, newness, and unwanted grub

October 23, 2023 by 0 Comments

Yesterday I went to tennis but nobody showed up. As I was waiting in vain, Dad called me. He’d just come back from my brother’s place in Poole, and was tired after a seven-hour bus journey full of traffic jams. He said he wouldn’t want to live in the UK again. New Zealand is on a human scale, he said. I see what he means. I remember seeing a road sign around Wanaka: “Christchurch 424 km”. In Romania you see signs showing similar distances. But travelling through southern and central England, you rarely see much above 60 or 70 miles, or 100-odd kilometres. Everything is on top of each other – there are no gaps that allow you to breathe. Dad enjoyed seeing the family – he had nothing but positive words for his grandson – but his (and my brother’s) mental energy was taken up with sorting out his email and phone; he’s always got some tech issue. As soon as he got back, he saw his sister who was surprisingly chatty.

Yesterday I made a cottage pie (something British!) and quince crumble to give to Viorica and Petrică, the couple in their late sixties who live on the top floor. Viorica has been so helpful to me. Without her, I’d be having cold showers all through winter. This is too much, she told me, and spooned half of the food onto some plates, leaving me with the other half. A few minutes later my doorbell rang, and she handed me back almost all of the half that she’d originally taken. “I appreciate the gesture,” she said. But not the food, obviously. When I gave her the pie she asked me where the beef had come from. Kaufland, I said. Maybe she sees supermarket meat as poor quality or something. Older Romanians have these ideas, I’ve noticed. Oh well.

On Saturday I only had one lesson – two hours of maths with Matei. He’d just got an A grade in a test, which will allow him to take the extended GCSE maths paper. He only needed a C for that, so in other words he smashed it. That’s obviously great. I still think he can improve though. He’s good at following processes – move this over to the other side of the equation, now square both sides – but still lacks a good understanding of how numbers fit together. When I say numbers, I mean fractions, decimals, percentages, roots, powers, the lot. He reaches for the calculator at the first opportunity. Funnily enough, one thing that helped me with this when I was growing up was a crappy calculator with an eight-digit display, which my maths teacher called a “Noddy calculator”. Tap in 1 + 2 x 3 =, and it would tell you 9, not 7. So I’d learn about the order of operations, which at the time we called BODMAS. My Noddy calculator preferred SAMDOB. Divide 2 by 3 on that same calculator, and you’d get 0.6666666. Multiply that by 3 and it spat out 1.9999998. As the real answer is clearly exactly 2, that taught me something about the perils of rounding. A handy feature was being able to quickly repeat an operation over and over again by mashing the equals button. If you started at 1 and repeatedly multiplied by 2, you’d see that (a) the final digits cycle through 2, 4, 8 and 6, and (b) the numbers get very big very fast – just like the grains of rice on a chessboard – until they got too big for the screen. Dividing by zero was an immediate no-can-do. Why was that, I wondered? On fancier Noddy calculators with a square root button, you’d see that repeating square-rooting brought you closer and closer to 1. Now kids have better calculators – even the ones on their phones are way superior to Noddies – but the old Noddies gave you a better idea of how numbers fitted together. Plus you could tap in 5318008, turn your screen upside down, and have a giggle – this doesn’t work on your phone. After maths on Saturday, I really did play tennis. This was singles again with the other Florin. I lost two games out of the 23 we played.

I’ve now been in Romania for just over seven years. In my head, I split that time into four phases. Phase one was from the moment I arrived (October 2016) until the summer of 2018, when everything was new and exciting. The sights, the sounds, the smells. The regular trips back in time. That proper first winter. Living in the centre of such a beautiful city and trying to build my teaching business (all those phone calls, when I could hardly speak the language!) was like nothing I’d experienced before. I look back at that time with great fondness. Then came phase two. Timișoara and English teaching had become normal. Routine. The newness had gone. That lasted until the outbreak of Covid. Terribly scary, and horrific for many people, but (and this probably sounds awful) at least it was something new. I enjoyed the quiet of the lockdown. The parks in the springtime with the birds and the flowers. The focus on the simple things. That third phase lasted two years until we clambered out of all the lockdowns and restrictions into a world of having to achieve again, and in my case a move and feeling unable to cope. I’d really love phase four to be over. New Zealand – that feeling of newness, of something different – was wonderful, but it was just a temporary respite.