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What are we reading? 17 April 2023
Morning all.You will not be surprised to read that I am interested in the maths talk today. In this instance he is right to hold this ambition. The opinion that it is socially acceptable to be bad at Maths is widespread. How often we hear people on the television and radio boast about this failing.
I foolishly ventured to write that I agreed with him elsewhere on the G when this was first mentioned and there were several rather nasty replies saying how they had always managed with the very basic, not realising that they rather proved the point.
people often equate Math with arithmetic and disregard all the other areas of the subject. It’s that breadth and the logical reasoning involved in the subject which make it so important.
You may be aware that I taught all ages, from a four yr old class of Infants through Junior, Secondary, Further Ed and lectured at Uni.
If I were to advise on this panel that they are trying to set up I should say loudly concentrate first on Primary Maths and make sure that every Primary teacher is more mathematically able.
The greatest stumbling blocks I found was when certain techniques were introduced badly, fractions for example, or too early, decimals , that perennial misunderstanding of place value which so few master………..once put off in Primary ……oh I had better be quiet.,
Morning allSoft spring air rising with Ash, Rowan, Sycamore and Horse chestnut starting to bud or leaf, the skyline is that flecked green against bare trees that signals mid spring, birdsong loud..
Just finished Pigeons on the Grass by Wolfgang Koeppen(1951) a recommendation by Mach a few years back and a excellent, thought provoking study of troubled times. Munich in the late 1940s, a city emerging from the straitjacket of the Nazi's into a more uncertain future for the defeated....
My next classic novel takes me back to the Langton Quartet of Martin Boyd, set in Melboune, Australia and the second novel in the series A Difficult Young Man(1955), from Text Classics.
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If I were to advise on this panel that they are trying to set up I should say loudly concentrate first on Primary Maths and make sure that every Primary teacher is more mathematically able...."
My main memory of primary school maths is of moving mid-year in the second to last year and finding that I was way behind the others. Every day started with a problem written on the blackboard and I sat and stared at it panic-stricken with no idea how to solve it. I was so terrified of the teacher that I was no longer able even to do the things I theoretically was able to!
Yes it happened to many people. It wasn’t your fault. That’s what I was trying to say. I have seen and heard Primary teachers doing this with quite difficult concepts mainly because they don’t understand the subject and are scared of it although never admit that.Talked to many adults who have similar stories - and they were all quite capable once you could find when/where this block happened making them believe something which was not true.
CCCubbon wrote: "Morning all.You will not be surprised to read that I am interested in the maths talk today."
Like your good self, I also taught maths to pupils from around 9-10 years old up to A and S level candidates, so have quite a wide experience. I agree with many of your points, but not all.
The opinion that it is socially acceptable to be bad at Maths is widespread. How often we hear people on the television and radio boast about this failing.
This is shameful and pathetic. A few years ago, I remember some journos on the 'Today' programme laughing about how bad they were at Maths. It's fine to lack ability in a subject - there are plenty of things most of us can't do - but it seems distinctly peculiar to boast about it.
I should say loudly concentrate first on Primary Maths and make sure that every Primary teacher is more mathematically able.
Quite so... many primary teachers are not confident in maths (or science, which is now part of the National Curriculum in the UK). When I trained primary teachers in science, I made a point of being sure they understood the science themselves, as well as showing ways to teach it. Teacher trainers in maths need to also assume zero competence and understanding; doing a GCSE a minimum of 5 years earlier does not mean the trainee teacher has a sound grasp of the subject. So - check knowledge, and develop interesting ways to teach the subject effectively.
... people often equate Math with arithmetic and disregard all the other areas of the subject. It’s that breadth and the logical reasoning involved in the subject which make it so important.
I'm not so sure about this, because it seems to me that to prepare most people for life after school, what they need to be able to do mainly involves arithmetic - being able to check their tax codes; deciding on if a loan is affordable and the interest rate competitive; deciding on how best to invest any funds they have left over... etc. These are life skills which everyone needs, but which can be left out in an overly academic and theoretical approach to the subject. A personal example - my wife - no idiot - began her teaching career unable to be able to calculate percentages scored by her pupils in tests marked out of 20. Why? Because in France at that time, the maths curriculum was exceptionally abstract, dealing with functions and the like - but no percentages.
For those who might have a future in science or engineering (for example) those more abstract branches are crucial. So - teach everyone the basics in primary; in the 'middle period' from 11-15 (say) make sure all get some grounding in other areas such as algebra and geometry, and see if it's relevant to their future interests and careers; finally, make maths 16-18 relevant to school leavers who are not going into STEM subjects by being sure they know about pay slips, tax returns, interest rates and the rest. You can't force kids to learn anything they aren't interested in. (Of course, the teacher can make it more or less interesting, depending on their skill, but even so...)
Finally, bear in mind that some pupils have specific learning difficulties: one of my daughters is dyslexic and als had a major problem with tables - she was never able to learn them. In spite of that, she found 'work-arounds' and to my delight (and surprise) was able to pass her maths GCSE. She coped better, in fact, with algebra and geometry than with arithmetic. We're all different.
(As for Sunak - not read what he said, but I suspect that he's simply playing to the Daily Mail readership as opposed to proposing anything practical and useful wrt maths teaching or maths teachers.)
Gpfr wrote: "My main memory of primary school maths is of moving mid-year in the second to last year and finding that I was way behind the others. Every day started with a problem written on the blackboard and I sat and stared at it panic-stricken with no idea how to solve it. I was so terrified of the teacher that I was no longer able even to do the things I theoretically was able to!"Very poor planning by the school (who should have ensured that you'd be supported appropriately in the new setting), and probably poor teaching - the teacher, even without prompting, should have guessed what was wrong and given you extra assistance.
Reminds me of my experience of taking maths 'O' level a year early at grammar school, along with 5 others; we were then dumped at the back of the O level class (presumably timetabling meant we could not actually be 'taught' with the A level maths set), given books and told to get on with it. I coped OK with coordinate geometry, algebra and the like, but calculus was a closed book without some support and explanation (the text book was very poor). I don't believe I understood it properly until I had to teach it myself!
Have to disagree a little about logical reasoning. It’s not just arithmetic, it’s applying probability even without knowing that it’s probability, the ability to make decisions, judging whether something is true or not, spacial awareness, logic…..these are just part of what better maths education can give to people , there may not be a number in sight.
CCCubbon wrote: "Have to disagree a little about logical reasoning. It’s not just arithmetic, it’s applying probability even without knowing that it’s probability, the ability to make decisions, judging whether som..."never been that good at Maths but used it a lot through my work and my own passion for statistics and research. certainly i enjoy the maths of the sporting seasons, whether league tables, averages and all the other stuff.
interestingly, as i strongly support vocational pathways for less academic children than me and my friends, i have heard quite a few tales of kids failing to get apprenticeships in last 12 mths , due to lacking GCSE maths, which shows a toughening of the system. One of the the parents of a child denied a mechanics apprenticeship didnt need maths when he did it in the late 80s.
While GCSE maths is a basic level, i think making it a prequisite for vocational courses is damaging, as it excludes less academic children. I dont know what the GCSE maths pass % is nowadays, maybe its got worse and that is a reason for the basic Maths and English requirement creeping into vocational training, not just the graduate jobs where it always has been needed.
CCCubbon wrote: "Morning all.You will not be surprised to read that I am interested in the maths talk today. In this instance he is right to hold this ambition. The opinion that it is socially acceptable to be bad..."
I agree absolutely. Without a comprehensive understanding of mathematics, there are fundamental issues down the line that become harder to master. Whether that be science, engineering, money management or trying to count out musical parts written in alternating time signatures. None of them strictly require a preference for mathematics, but they all become easier with one.
My oldest is dyslexic, and it was quite obvious from an early age. Likewise, his grasp of mathematical concepts above his reach was also clear, which was heartening. He may need more time to read, but he can still visualize complex shapes and organize formulas. Fortunately, he didn't develop the dyscalculia that often runs hand-in-hand with dyslexia. My brother had both, and he had a much harder time adjusting to the paces in a time and place less accommodating to his difficulties., although he was able to adapt and flourish at a later age.
The fetishization of ignorance will only have auto-incendiary effects at some point in the future.
AB76 wrote: "CCCubbon wrote: "Have to disagree a little about logical reasoning. It’s not just arithmetic, it’s applying probability even without knowing that it’s probability, the ability to make decisions, ju..."Fgor my sins I set the special papers for a while - the pass mark was/is far lower than you would expect.
Since mathematics seems the topic du jour, here is a gift link to a NY Times op-ed piece from last week, "The Wondrous Connections Between Mathematics and Literature":https://www.nytimes.com/2023/04/07/op...
“Moby-Dick” was, for me, one of those books that languished in the guilt-inducing category of “things you should have read a long time ago,” and I just never got around to it. Plus, I am a mathematician. And despite my interest in literature, my intellectual priorities did not include 400-page novels about whales — or so I thought.The most prominent mathematician in the work of Conan Doyle is, of course, the estimable Professor James Moriarty, author of "The Dynamics of an Asteroid".
That all changed one day when I overheard a mathematician friend mention that “Moby-Dick” contains a reference to cycloids.
Cycloids are among the most beautiful mathematical curves in existence — the French mathematician Blaise Pascal found them so distractingly fascinating that he claimed merely thinking about them could relieve the pain of a bad toothache — but applications to whaling are not usually listed on their résumé.
Intrigued, I finally read “Moby-Dick,” and was delighted to find that it abounds with mathematical metaphors. I realized further it’s not just Herman Melville; Leo Tolstoy writes about calculus, James Joyce about geometry. Fractal structure underlies Michael Crichton’s “Jurassic Park” and algebraic principles govern various forms of poetry. We mathematicians even appear in work by authors as disparate as Arthur Conan Doyle and Chimamanda Ngozi Adichie.
CCCubbon wrote: "AB76 wrote: "CCCubbon wrote: "Have to disagree a little about logical reasoning. It’s not just arithmetic, it’s applying probability even without knowing that it’s probability, the ability to make ..."really? were the passes worse than in English? (I guess english language is the best GCSE to compare to Maths, as its the absolute basics)
my school days are almost 30 years gone but i never really enjoyed maths. having scientist or science trained grandparents on my maternal side did not come through for their grandchildren, all four(inc me), are humanities graduates in History.
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..."
Talking about mathematics and literature, some years ago I taught one of the then directors of the French gas company who loved mathematics and hence loved Lewis Carroll, for example, A Tangled Tale: 10 stories presenting mathematical problems published in a monthly magazine.
AB76 wrote: "CCCubbon wrote: "AB76 wrote: "CCCubbon wrote: "Have to disagree a little about logical reasoning. It’s not just arithmetic, it’s applying probability even without knowing that it’s probability, the..."Think I should be clearer. The score that a candidate needs to obtain in order to pass the exam is lower than you would expect
CCCubbon wrote: "AB76 wrote: "CCCubbon wrote: "AB76 wrote: "CCCubbon wrote: "Have to disagree a little about logical reasoning. It’s not just arithmetic, it’s applying probability even without knowing that it’s pro..."ok i see, thats probably all about government/politicians getting to boast that 22.6% of kids passed at maths compared to 22.5% the previous year(while not admitting the pass mark had lowered)
CCCubbon wrote: "Morning all.You will not be surprised to read that I am interested in the maths talk today. In this instance he is right to hold this ambition. The opinion that it is socially acceptable to be bad..."
Have a hug CCC. I have given up trying to post on the G because, if you don't follow the party line, you get vicious comments from folks who don't believe anyone should have an opinion that differs from their own, or the mods put you on pre-mod.
Gpfr wrote: "CCCubbon wrote: "You will not be surprised to read that I am interested in the maths talk today. In this instance he is right to hold this ambition...If I were to advise on this panel that they ar..."
A great example of bad teaching I would have thought. My neighbour, who is not academic and went to a secondary modern, had problems with Maths and was told by the teacher that she was stupid. Not a great help.
As you probably know, I am of a certain age. After taking early retirement from branch banking I worked for a little while for a motor accident repair company. I found that the folks there had a problem with working out a price less or plus VAT. So I wrote the formula out for them and stuck it on the wall in the office.I only got as far as O level Maths passed when I was 15. I tend to think that those doing sciences or economics will need to study Maths beyond O level. I can imagine that those doing other subjects in the sixth form might be in the Maths classes in body but not in mind.
In my simplistic view I think everyone need Arithmetic, but not everyone needs Maths,
I wait to be shot down in flames.
giveusaclue wrote: "As you probably know, I am of a certain age. After taking early retirement from branch banking I worked for a little while for a motor accident repair company. I found that the folks there had a pr..."Probably surprise you to know that I am not particularly good at arithmetic - i make mistakes like everyone else. not very good at Mechanics I struggled at times, struggle now trying to understand the physics in ‘ on the Origin of time ‘ by Kennedy the sequel to Hawkings Brief History . Suppose strength is scope, have a go at anything, love it, great when it works out. Numbers etc talk to me!
Seriously though I find myself agreeing with giveusaclue.Perhaps arithmetic and maths should be separate subjects?
Greenfairy wrote: "https://images.app.goo.gl/RgdeVZyJ4b7...I couldn't resist this suggestion about reading in the bath"
Haha, I just put my ereader in a sealable plastic food bag. I have a friend who dropped a library book in the bath, had to confess, and pay for a replacement. She dropped a cup of coffee in the bath another time! I wouldn't say she is on the clumsy side......
Bill wrote: " The most prominent mathematician in the work of Conan Doyle is, of course, the estimable Professor James Moriarty, author of "The Dynamics of an Asteroid".."The connection never occurred to me before but now that you mention it, C. Auguste Dupin's nemesis, "D. ", is also a mathematician (and, equally significantly in Dupin's view, a poet).
Berkley wrote: "Bill wrote: " The most prominent mathematician in the work of Conan Doyle is, of course, the estimable Professor James Moriarty, author of "The Dynamics of an Asteroid".."The connection never occ..."
Paul mentioned that some mathematic is needed in music and the same is true for poetry . A different kind of music perhaps but in writing a poem it has to ‘sound’ right , the stresses and so on.
Maths creeps in everywhere. Home decorating - symmetry to please the eye? Doesthis belong with that group? Geometry, pattern… furniture ( no good having a table with legs of different levgths) , sports leagues, How do you aim to score a goal in netball or basketball- (without knowing you are using calculus), driving the car?
and I haven’t even mentioned mobile phones and how we are deluged by data these days
Maths is everywhere in life - it’s not just arithmetic.
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One day when my son was at collège (1st -4th years of secondary school), he came to me with his homework and asked, "Do you think I need to do a schéma cartésien? Of course, I had not the slightest notion what a schéma cartésien was, but I took his book, read the instructions very carefully and said, "No, I don't think so." Fortunately — and amazingly — I was right.
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I read another of these novelised biographies, Le Stradivarius de Goebbels by Yoann Iacono, the 1st novel of a high-level civil servant. He'd at first intended it to be non-fiction but then decided to make it a novel.Again around the 2nd world war, it's an intriguing story. A young Japanese violinist, Nejiko Suwa, came to Paris to continue studying, shortly before the war. She stayed there and in 1943, Goebbels presented her with what was said to be a stradivarius (confiscated from its previous owner who was Jewish). Nejiko performed all through the war with the Berlin Philharmonic orchestra.
As I said, the story seemed intriguing, but the book was disappointing, slight, insubstantial, and the characters didn't come to life. I read to the end (a quick read) because I wanted to know what happened to Nejiko and the violin, but I really don't recommend it.
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Now I'm reading S.G. MacLean's The Black Friar, the second of her Seeker series. Damian Seeker is an intelligence agent under Cromwell. Reading the first in the series was what prompted me to read the life of Cromwell, and I'm pleased now to have that background, although it's not necessary in order to enjoy the books, she makes it clear enough what the 5th Monarchists are, for example. (A Protestant sect with Millienalist beliefs, preparing for the 2nd coming.)
I've also just started another non-fiction book, Les Croisades vues par les Arabes by Amin Maalouf, a Franco-Lebanese writer.
For any non-scientists here I would like to draw attention again to the excellent Mathematician’s Delight by W.W. Sawyer, which CC recommended a while back. I found it interesting and manageable, despite having no math beyond O level. I like to use geometry to work out, e.g. carpentry problems, and I enjoy doing arithmetic and equations in my head, just for the feeling of staying agile.
I wouldn’t be too hard on Sunak. Any effort to improve basic mathematical understanding has got to be worth it, and higher math is useful in areas you might not expect. Years ago I had a colleague who left the law to become a merchant banker, as they were then called – he wanted to be more of a decision-maker than an adviser. Later he said that the thing that surprised him was the level of mathematics involved. He struggled to stay up with his new colleagues, who were really sharp at calculating rates of return in different scenarios and – CC is spot on – probabilities.
I wouldn’t be too hard on Sunak. Any effort to improve basic mathematical understanding has got to be worth it, and higher math is useful in areas you might not expect. Years ago I had a colleague who left the law to become a merchant banker, as they were then called – he wanted to be more of a decision-maker than an adviser. Later he said that the thing that surprised him was the level of mathematics involved. He struggled to stay up with his new colleagues, who were really sharp at calculating rates of return in different scenarios and – CC is spot on – probabilities.
Another ex-maths teacher here, though for much of my teaching career I didn’t volunteer that information.. I taught a couple of years of maths in my early twenties, then moved to sport. And a couple of years at the end. I used to get many phone calls and emails asking me to work again in maths after I retired at 56, but never was in the slightest bit interested.
I had some memorable years teaching, and was lucky enough to work all over the world, but didn’t enjoy it in the last year or two.
Whale by Cheon Myeong-Kwan translated from the Korean by Jae Won Chung and on the International Booker Longlist.
This is a dreamlike fantasy of a novel quite different to anything I have read before.
It is the story of a mother and a daughter. The mother, Geumbok, is from a remote mountain village, and throughout the first part of the book her fortunes rise, then fall, and ultimately rise again, until eventually she builds her own movie theatre in the shape of a whale.
The real entertainment though is in the interactions that involve her daughter, Chunhui, phenomenally large and immensely strong, a mute bricklayer, who can speak only with an elephant named Jumbo, who she befriends.
Both protagonists encounter more than their share of violence, but there is humour and magic in equal amounts also.
There is a vast amount of characters in the periphery with deep and complicated backstories. For much of the book the chapters are in effect, a series of short stories that recount Geumbok and Chunhui’s surreal adventures with these bizarre folk.
Whilst the writing is often comedic, the tone is a philosophical one, with a twist of nostalgia and melancholy. The book is a classic in Korean literature, and this translation, though making the Booker Longlist, is not the first into English.
It certainly kept my attention, though it isn’t really my sort of thing.
The Little Buddhist Monk by César Aira translated from the Spanish (Argentina) by Nick Caistor.
There’s a quote from a review on the cover of this book, something I dislike, though in this case I must admit that it is accurate, ‘reading Aira is dizzying’ it says.
He is an expert at subverting expectations, and once again I was fooled. It begins with no fuss..
A little Buddhist monk was anxious to emigrate from his native land, which was none other than Korea. He wanted to go to Europe or America. The project had been incubating in his brain from his early years, almost since infancy, and had coloured his entire life.
So the tiny monk studies language and culture, and chooses his right moment to interrupt a French photographer and his wife, to help them with sightseeing and to get around the city.
He takes them to places that the French photographer begins to question. He and his wife wonder what they have agreed to. Before they (and of course the reader) realise it they are they are caught up in irrationality.
They had been very rash in allowing themselves to be taken so far, but before that they had been even more rash in trusting everything they were seeing and hearing uncritically, without thinking..
Though grounded in reality we are into the realm of the absurd, to the point of surreality.
It’s perhaps not the best Aira to start with, but nonetheless a charming short read.
Interestingly the New Directions edition is paired with The Proof, which would be a good place to start. Though it is worth noting that Aira cannot be predicted, no two novels bear any resemblance to anything else he has written, which is just one of the reasons that he is such a pleasure to read.
Here Be Icebergs by Katya Adaui translated from the Spanish (Peru) by
Rosalind Harvey
.
Though Adaui does delve into complex themes in these stories, gun ownership, a family whose young son has died, a politician under house arrest, child abuse, the element of shock is minimal.
With the exception of the first offering, The Hunger Angel, the stories are very short, so the characters are left under-developed and the atmosphere around potentially horrific subject matter is too light.
It’s hard for me to think of any other two star books I have read from Charco, and I have got through quite a few. I usually praise everything they publish. It’s nice to read a Peruvian writer, and there is certainly some potential here, but I can’t help but feel that at just under £10 for just over 100 pages they are asking too much; a more competitive price, or more content please…
and Widdershins by Oliver Onions
Oliver Onions was a prolific writer of tales of the supernatural in the first half of the 20th century. Despite what one might think initially, he did write under his given name, though omitted the George. He is recognised as a master of the genre, though he did write quite a lot of other stuff.
The highlight of this book is without doubt, the novella, The Beckoning Fair One.
In this, an unsuccessful writer moves into rooms in an empty mansion, hoping that the isolation will help his failing creativity. The reverse happens. His sensitivity and imagination are enhanced by his seclusion, but his sanity is gradually destroyed in the process.
The other seven stories are of the short format. Bear in mind that this was his first published collection of stories, in 1911, so the consistency of their quality is understandably varied.
I would select two as being the best of the bunch.
The Cigarette Case in which a man comes to terms with a ghostly incident from his younger years, and Rooum in which an engineer is pursued by a mysterious and terrifying being.
Though his first collection, this is the one he is perhaps best known for.
I am keen to seek out some of his later work though, The Painted Face from 1929, and The Hand of Kornelius Voyt from 1939.
Valancourt have reissued the latter in 2011, but the former looks difficult to get hold of (hint to any publisher keen to discover a lost work..).
CCCubbon wrote: "Berkley wrote: "Bill wrote: " The most prominent mathematician in the work of Conan Doyle is, of course, the estimable Professor James Moriarty, author of "The Dynamics of an Asteroid".."The conn..."
Talk about confused! What are Maths? Are we talking Algebra on up?
I can't ever remember anyone here (USA) using the word - Maths.
I do love numbers - and was good at them until Trigonometry and never was able to see hidden lines in Mechanical Drawing - no surprise for me.
A friend of mine was at the library this weekend as were a number of 'last minute filers' as today is Income Tax day in the States. (Note that local libraries host free tax services during the season (for those who qualify) which runs from sometime in February until today.) He was kvetching about people who put off doing their taxes until it cannot be put off any longer. I wonder if this is because some feel all this is above their heads?
Anyway mine were done in March, and Uncle has already extracted his due from my checking account.
Andy wrote: "and Widdershins by Oliver Onions Oliver Onions was a prolific writer of tales of the supernatural in the first half of the 20th centur..."
how is the Green Spain trip going Andy, has it lived up to your expectations? Getting warmer now?
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Just in case anyone here thinks I have forgotten about yellow cars, I have posted a photo I clipped today.I'm finding that I cannot count the ones I see parked, because they always seem to be there. I'm focusing on those in motion which have been more difficult to find lately.
AB76 wrote: "Andy wrote: "and Widdershins by Oliver Onions Oliver Onions was a prolific writer of tales of the supernatural in the first half of th..."
More than expectations AB thanks.
Though the mountain areas have depopulation problems, for me, that is perfect, very few people around at all.
I’m just south of Oviedo, so into the Picos at the weekend, and no doubt they will be busier.
20C or so in the afternoons, 2 or 3C minimums at night. Lots of sun. Great for the solar panels, and the outdoors.
Dog is loving it also.
Gpfr wrote: "Beautiful views in your latest photos, Andy."Absolutely. Best time of year I think.
Andy wrote: "AB76 wrote: "Andy wrote: "and Widdershins by Oliver Onions Oliver Onions was a prolific writer of tales of the supernatural in the fir..."
Picos are amazing...you will love that area and if you get a chance, pop into Oviedo. a literary reference is La Regenta by Alas, set in Oviedo(with a Hardyesque name change), its a brilliant novel and a key one of Green Spain, alongside The House of Ulloa by Parda-Bazan. both are 19th century
good to see your four legged friend his loving it too...
my first trip into the Picos was in summer 2002, we drove in via Leon, so into the tunnel that leads north. we left straw coloured fields in blazing 34c sun and came out at the other end into cool, fresh english weather, sort of 21c with mist and low cloud. one of my mates wanted to put the heating on in the car!
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Love the pic of the dog with the signpost, "Which way should we go?" 😃
MKWhen yuoung I used to think that some magician had come up with all those trig tables - in fact it was all rather a wonder but useful.
When it came that I had to teach trigonometry I didn’t want the student to think there was anything magical so we started with a circle of known easy radius. I would get them to draw a line from the centre to circumference then measure an angle of say 30⁰ at the centre, Another radius then draw a perpendicular line from the point on the circumference where the second radius met down to theier original line. Yes of course rt angled triangle in a circle.
Then I would get them to measure the line they just drew and divide by the radius (didn’t say hypotenuse at first)
Their answer should be about a half of course.
Then they were asked to experiment with other angles and make notes of their findings. Then using other radius lengths and always the answer for 30 degrees the same………….There is an enormous amount of work buried in this. Some catch on very quickly and they can forge ahead.
Lo trigonometry! Make your own tables.
Got them eventually to compare their figure with the tables ……
Lots and lots of experimenting and cosine tangents etc …. But the thing was that they knew it wasn’t magic just relationships that held true
Think that without this practical lesson it is all a mystery to many.
Thought you might be interested
AB76 wrote: "Andy wrote: "AB76 wrote: "Andy wrote: "and Widdershins by Oliver Onions Oliver Onions was a prolific writer of tales of the supernatur..."
I’ve been in Picos twice before, but both times on the north side, so this time the south. No doubt there will be more people.
Thanks for the recommendation of Oviedo, but we don’t do cities unless it’s absolutely necessary, various reasons, including Roja not a fan, security of van, too many people…
Gpfr wrote: "Andy wrote: "Gpfr wrote: "Beautiful views in your latest photos, Andy."Love the pic of the dog with the signpost, "Which way should we go?" 😃"
He always does that at junctions, with or without signpost.
Often at home I just let him choose, but almost always end up at the river… that’s labs..
We went walking in Picos de Europa a few years ago and went up on the cable car at Fuente De which is quite terrifying. As it nears the top it almost looks as if it’s going to crash. It’s very very steep ascent. We walked down once and it was almost too much for me - I was shattered and there were several miles back to the hotel where we had left the car. MrC tried to cadge a lift but no luck and he had to do those last few miles to get it and come back and collect exhauted me. Oh dear.
Andy wrote: "AB76 wrote: "Andy wrote: "AB76 wrote: "Andy wrote: "and Widdershins by Oliver Onions Oliver Onions was a prolific writer of tales of t..."
Roja is very wise like his master, stick to the big wide open!
Its so lush up there and will be even more so in early to mid spring, i remember one part of the trip looking down into a valley completely covered in cloud, azure sky above and white cloud below me, we were very high up (this was in August and it was still as green as the UK)
I never, ever thought that this would happen, but I find myself agreeing with Jacob Rees Mogg...You see, it's about erasing the"n" word from the books of my beloved P.G Wodehouse, I agree they it should be taken out but the minstrel bands should remain as it's historically correct that minstrel bands were a "thing" in that era.
Correction : "that" it should be taken out, my cat wants treats and decided that I should cease to type and fetch her some.
Greenfairy wrote: "I never, ever thought that this would happen, but I find myself agreeing with Jacob Rees Mogg...You see, it's about erasing the"n" word from the books of my beloved P.G Wodehouse, I agree they it ..."
i really should read some Wodehouse..still havent done so and i'm 47! any recommendation of which novel to start with>?
Carry on Jeeves, or any of the Blandings stories, you will be an addict in no time! :)
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Ersatz TLS
Books mentioned in this topic
Poison Romance and Poison Mysteries (other topics)The Russian Interpreter (other topics)
The Postman Always Rings Twice (other topics)
Double Indemnity (other topics)
Mildred Pierce (other topics)
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Authors mentioned in this topic
Michael Connelly (other topics)Andrew Lycett (other topics)
Ai Jiang (other topics)
Natascha Bruce (other topics)
Dorothy Tse (other topics)
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As always, happy reading!