Complex Numbers, Pythagoras, and Protractors

Honestly, you could hardly make it up. In the last week or ten days you may have spotted some or all of these:

***   Simon Jenkins in The Guardian pontificates about maths teaching.   Among his assertions is that a primary school complains that a child he knows hasn’t mastered complex numbers.   It’s not clear how much Jenkins knows about complex numbers but it doesn’t seem to extend to knowing the difference between complex numbers and fractions, or possibly decimals.

***   Then there’s a YouTube clip of Piers Morgan smugly telling us that he understands Pythagoras Theorem and can recite it as 3.147….

***   And yesterday I read that a golfer is being investigated for using his protractor – creatively, he’s apparently invented a way of using his protractor to measure distances rather than the usual angles. We then get a helpful clue that his protractor is also called a “compass” – we also learn that sailors have been using them a long time. And in further clarification we learn that the device has a third manifestation as a pair of “split dividers”.   Actually, it was pretty obvious to all of us that the protractor / compass was in fact a pair of dividers all along – but not a single member in the newspaper’s editorial and production team knows what a protractor looks like, let alone what one does.

………

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A Year Of Non-French

At the middle school I taught in, the top year (Y8) timetable had a unique subject called non-French.  Pupils were selected for this elite group using the sole criterion that the French department didn’t want to be bothered with them.  As you’ll imagine, this didn’t exactly enhance the children’s self-image; things were made worse still by the fact that nobody had the faintest idea of what the lessons should involve and that the group was taken reluctantly by whichever teacher had a free slot on their timetable that year.

I have to confess that the French department and the Head weren’t far-sighted educational thinkers, and neither of them saw anything wrong with putting a subject on the timetable for which the only guidance was that it wasn’t French.  So one year I decided I’d have a go with the group, and I must say we had a lot of fun.

Rule 1 was no text-books, and above all no worksheets.  Rule 2 was that we’d actually do something positively rather than because it would fill up a lesson or two.  So we read and performed comedy scripts such as the classic Tony Hancock Blood Donor.  Then we spent a month of lessons exploring some number magic tricks, leading up to a nerve-wracking and rather brilliant performance by the group in which they stunned the audience (i.e. the non-non-French remainder of the year group) by a variety of magical effects and amazing predictions.

I thought of them when I spotted a tweet forwarded by Simon Gregg about measurement using a trundle wheel.  One fine morning in early summer we decided to help the groundsman by measuring out the 100-metre track.  They organised themselves in half a dozen groups and remarkably, every group chose a different method.  One group used strides, one pigeon steps, one a metre stick, another made themselves a 10-metre length of string, ….  Even more remarkably, I was flabbergasted that the various methods all agreed within two or three metres – and were in close agreement with the official measurement determined by the school’s trundle wheel.

(Which is why the tweet intrigued me.  Simon’s correspondent reported that his trundle wheel measured differently from A to B than from B to A – and that their groundsman says that’s invariably the case!)

Another big topic we did was to make a simulation game of the development of railways across our local Chilterns area.  The pupils worked in teams, building routes which avoided hills and rivers to connect revenue-generating towns.  We looked at costs, and scheduling, and created a wonderful map of hexagons; the map filled the entire wall of the classroom.  One day a visitor came and was a little snooty that we’d played a game to model the process.  “Wouldn’t it be better to study what really happened?”, she said.  Which was what we’d done the very day before, so the non-Frenchers proudly demonstrated how one of their routes had followed the GWR track out to Reading and the West, while another had followed the Great Central route to Aylesbury and beyond, and another had taken the route out through Luton and Stevenage.  I did enjoy that moment!

As the climax of the year the group created and published a comic magazine called Creeps!, sales of which (enhanced by the donation of a huge box of Monster Munch by Walkers Crisps) were large enough to necessitate a reprint.

There was one spin-off that was nicely gratifying.  Upsetting the French department was always fun, and they were quite aggrieved by the whole business.  They’d been quite happy to slough off their discards, but didn’t much enjoy it when they faced a queue of their students asking if they could drop French and do non-French instead.

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A Place In The Sun

Here’s something I’ve never noticed before.  We live at number 6, and our kitchen caddy was emptied this morning.  It was a cool night, but by the time I collected the caddy the sun had warmed things up a bit.  Not quite enough, however, to complete the job – the light-coloured 6 had reflected the warmth back again rather than absorbing it, and the underside of the lid still had the condensation visible.

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Littlehampton Boys’ School, 1871-1911, part 2

This is the second half of the piece about Littlehampton Boys’ School and its Head, Thomas Slatford.   It’s particularly interesting about how the school and its curriculum developed, and also about how he was confident enough to challenge the judgement of Her Majesty’s Inspector.

A Man Secure in His Own Worth

When Slatford took up his post in 1871 being a head-teacher was an uncertain and not particularly attractive business. The majority of schools were village-based, under the effective control of the Rector, and there was no doubt who was the more important. When the Head called upon the Rector s/he’d be expected to use the tradesmen’s entrance and be sneered at by the Rector’s servants. One rural teacher complained in 1879 that he was regarded as “the parson’s fag, squire’s doormat, church scraper, professional singer, sub-curate, land surveyor, drill master, parish clerk, letter writer, librarian, washerwoman’s target, organist, choir master, and youth’s instructor”.

Just as important in a Head’s life would be Her Majesty’s Inspector, and the report on his annual visit to assess both the pupils and the teaching. Many HMI saw themselves as socially and intellectually superior to a mere teacher, and weren’t slow to make this clear.

I’ve not come across any other Head who felt so secure that he didn’t need to worry about either Rector or Inspector. He was acquainted with the Rector since his days as a pupil-teacher, and they’d stayed in contact both while Slatford trained at Culham College and during his first job at Falmouth. It was at the Rev. Rumball’s direct invitation that he came to Littlehampton.

In 1883 at least one Head was so intimidated by the inspection process that she committed suicide, but Slatford’s relations with the Rector, and with the School Board, were so solid that he was prepared to challenge HMI head on. HMI reports had always been good until an unfortunate and, I suspect, unique incident in early 1884. At the end of the visit the inspector’s assistant is hit by a missile from a catapult! Slatford desperately records how agreeable the inspectors are, but the damage is done, and the report says – not surprisingly, that better discipline should be maintained.

Moreover, the inspector has a long memory, and in the next several years discipline is criticised time and again. Eventually, Slatford snaps and he writes some 200 words where the fury still shines through today: “We all feel the sting of having a sore continually probed and we work on through the year like hounds fearing the lash.”

At his prompting, the Board very politely asks the Inspector to indicate “particulars you consider the discipline is defective … if you would make any suggestions for its improvement, for the School Board, as well as the Head Master, are most desirous that all cause of complaint should be removed and the school restored to a thoroughly good state of discipline.”

The Inspector’s reply is lost but the effect is explosive, and he resigns later in the year.   Subsequent inspectors are much more positive, and point out that with four classes in a single undivided room with appalling sonic characteristics the “resonance and din were almost unbearable”. Indeed, before long, HMI are demanding that more suitable premises are found. The demand is repeated, and a later report says tersely “School visited – I hope for the last time in these premises.”

And though he’s always receptive to constructive requests from parents, he gives no ground in more confrontational situations. To a father who criticises his arithmetic teaching he replies that Slatford doesn’t tell the man how to lay bricks and he’s not prepared to accept “impertinent interference”. Another critical father threatens to hit him, saying he’s quite prepared to pay the fine. Slatford doesn’t give an inch and the parent ends up “asking me to be as kind as I could as he had been delicate lately”!

Teachers and Curriculum

For any teacher following the changes in school and curriculum is immensely fascinating. At the start of Slatford’s career teaching focuses totally upon the narrow demands of the Revised Code’s insistence upon reading, writing, and arithmetic – and nothing more. By the time of his death, the range of subjects has been expanded, the leaving age has been raised, and the introduction of a more advanced Standard VII in 1882 meant schools offered a curriculum similar to that in lower secondary years today.

In science alone we learn of an explosion when making hydrogen in 1901, while another teacher suffers burns when experimenting with phosphorus. (I did the same experiment on teaching practice, with much the same result. I recall saying “Please excuse me a moment, my hand seems to be on fire”). Incidentally, by 1910 the inspectors are recommending that there should be fewer demonstrations, with the pupils performing more experiments for themselves.

Slatford was no stick-in-the-mud. He was a member – and I imagine this was rather unusual – of the National Union of Elementary Teachers (the forerunner of the NUT). He welcomes opportunities for outdoor lessons – gardening, drill, and sending the young pupils of Standard I “to go out and map some of the streets around ….

In 1896 he tells a pupil-teacher that his lesson was “too much an ‘instruction’. …. I have asked him to let the children work out more for themselves.” (More than a hundred years later, most of our recent Education ministers have believed there should be a lot more instruction, and that there are far too many children working things out for themselves.)

When the Education Department recommends the application of kindergarten methods with younger children he quickly arranges for his wife to give some lessons to boys in Standard I.   (She was a Head herself and she was far more forthright than him, describing the national curriculum of the time as ‘ridiculous’.)

Subsequently we read of the smallest children having a dolls’ house and other toys, and before long he is convinced of the value of women teachers with his younger pupils – by the time of his death there are three long-term women on the staff and he regards them very highly.

In his first years Slatford at Littlehampton was the sole qualified teacher, and insisted that lessons were conducted according to his thinking and his alone. He is highly critical that his pupil-teacher Raymond Gibbs shows too light a touch with his class, and is furious when another, Horace Boswell, suggests that Standard I boys cannot yet use a ruler accurately. “This, I of course said, was not his business he was here to carry out my wishes not to criticise or express opinions on them. He works hard with the class but is a little too opinionated perhaps.

In fact, both Gibbs and Boswell proved to be outstandingly successful pupil-teachers, the very best in the whole county. Slatford’s record with pupil-teachers is exceptional; they often come back to see him and their pupils are pleased to see them – “their faces so brightened …”.

This isn’t the only entry to show Slatford wanted schooling to be more than the imposition of curriculum tuition upon reluctant pupils. For many of those at school in the second half of the nineteenth century school was something forced upon them, and which they disliked intensely. I was hugely interested to pick up little fragments showing that Slatford tried for something more. He mentions teaching boys to play draughts in the lunch period, and that a pupil-teacher plays with his boys after school.

After 21 years at the school he muses that he tries to make “… a place where the paths of learning are paths of pleasantness too.” One Christmas he goes round school and is impressed by the number of Christmas cards pupils have given their teachers, as “evidence of kindly feeling between them”.

In 1911, the final year of his life, he goes further. A mother says her son is worried about Science “though he is fond of it and very fond of his teacher.” Slatford speaks to the teacher and reports back to the mother “he must make a friend of his teacher and that we want children to ask questions.”

I was reminded of what the educationalist H C Dent, wrote – and it was teachers like Slatford he was talking about – “Some teachers even dared to think that they and their pupils should be friends, not foes, should work with, not against, each other; and they initiated the most profoundly important transformation of the English elementary school, from a place of hatred to one of happiness.”

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Littlehampton Boys’ School, 1871-1911, part 1

Here’s the latest in my Schools History research. I’ve spent much of the summer immersed in a 400-page volume of the Logbooks of Littlehampton Elementary Boys’ School from 1871-1911. There’s lots to say, so I’ve put it into two parts. They’re still longer than I’d like, but I hope you’ll find them interesting.

Setting the Scene

School logbooks all date from a government requirement of the 1860s. In fact, they’re by no means rare, and in many cases it’s possible to study them without access to the originals. Several are available as CD-ROMs, and many more in digitised archives; this is one of a small number which have been transcribed and put into book form.

Most of the logbooks I’ve seen come from village schools, the vast majority being under the close supervision of the Rector. Littlehampton Elementary Boys’ School is very different; after the first few years it’s administered by an elected Board. Littlehampton is a town of streets and alleys, with sports clubs and organisations like the boys’ brigade. In country schools boys bring mice from the fields and celebrate May Day with dancing; in Littlehampton there’s a train service to London, and shop-keepers sell nine-year-olds cigarettes or lead shot for their catapults.

Perhaps uniquely, this forty-year logbook is kept by a single person, Thomas Slatford, from the time of his arrival at the age of 23 until his death forty years later. This gives us a consistent narrative and an in-depth picture of the growth of a school over a period of enormous change.

Best of all, Slatford breaks the rules on almost every page. The instructions require that he make “the briefest entry which will suffice” to record routine matters, and that “No reflections or opinions of a general character are to be entered in the Log Book”.   In practice plenty of Heads found it beneficial to use the log to vent frustrations, but few went as far as complaining that too many mothers spend their time reading “cheap literature if it deserves such a name”, or recording imputations that boys are being bribed with drink and tobacco – by the church authorities no less – to miss school to sing in the church choir.

Slatford lived in a time of dramatic change. At the start of the nineteenth century Littlehampton was a was a fishing village with a population of just a few hundred, but with the coming of the railway it rapidly grew into a popular seaside resort; indeed, access was so convenient that one of the pupil-teachers at the school could cycle the 65 miles to London. By 1911 the population had grown to some 8000.

Holidaymakers brought great economic benefits to the town, but these came at a cost. Many children ceased attending school in the season to assist parents and employers catering for vast numbers of visitors.   Attendance was further hit as visiting attractions – circuses, waxworks, fairs – arrived in town on an almost weekly basis. And there was also considerable deprivation, and unemployment in the winter months, contributing a regular outflow as families emigrated to Canada, the USA, and Australia.

The school perfectly reflected this era of change. In 1871 Slatford was the sole teacher of some 70 boys and his only assistants were older pupils. By 1911 he had moved the school into new and purpose-built premises and he could call upon half a dozen qualified assistant staff to teach more than 300 boys.

Head teachers had a daunting workload. In smaller schools like Littlehampton in 1871 – s/he would be the only teacher, assisted by one or two pupil-teachers – older pupils who were undergoing an apprenticeship. However committed they were, they were still teenagers learning on the job – and that learning included 90 minutes training and tuition every day, which of course added hugely to the Head’s load.

Even with pupil-teacher help the Head still taught full-time, often taking double or triple classes, and examining every class several times a year to check on their progress. On top of all that, s/he was the only point of contact for every administrative matter – ordering stock, building maintenance, bookkeeping, liaising with parents and visitors, checking on absence and illness….

Here’s a single entry from 1893 (notice the final sting in the tail!): “George James Smart’s sister brought him up and said he had truanted yesterday afternoon. Carpenter (St. I) has been stealing figs from the Manor House garden. Punished him. The Vicar came to tell me that Ellis’s mother could not attend to them. Walter’s father (St. I) has deserted them and so they have gone to a relative at Brighton. Mr Matthews away Tuesday and Friday at Sheffield Park. Collard’s family has small pox. Sent Alfred Muschin (St. I) home, he has a ring worm the sister in the Infant School has been home some time for the same reason. Strudwick (St. II) has gone to Arundel where his father is at work on the Castle. Received notice that Inspection is June 20.

A Humane Man?

There are many indications of Slatford’s fundamentally humane nature. There is a wealth of feeling behind “it is sad to see some of the little faces so pinched. There is so much want and distress.”

Frequently he promises anxious parents he’ll keep an eye on their son, and he tries to help those who are particularly deprived. “I suppose he has the worst man in the place for a father, an utterly immoral man and a wife-beater. So I have tried to make it as pleasant as I can for the boy but I am afraid he is an incorrigible truant.”

Most obviously, he often prefers to avoid using corporal punishment in favour of talking to the pupil in depth, giving them a second chance, or requiring children to stay behind to catch up on incomplete work. Moreover, he insists that no-one else on his staff may strike a pupil and reprimands those who do – indeed, such teachers often leave soon afterwards.

Nevertheless, keeping discipline was a central feature of Slatford’s work, and he was perfectly prepared to use the cane when he felt it necessary, even when on occasion he recognised it might do no good. As the school expanded, both in pupil numbers and their age (the leaving age was raised twice in the 1890s) the accounts of misbehaviour increase.   Truancy (often encouraged by parents and employers), pilfering, stone-throwing and bullying occurred throughout his time, but smoking (“It is disgraceful that children so young should be served with such things. Three for a halfpenny!”), obscenity in the toilets, and the writing of “horrid filth” on paper occur more and more. Even in the last year of his life, however, he is prepared to give a second chance: “The boy turned so ghastly that I did not punish him.”

But his humanity is not the same as ours, and much is horrifying to us. He doesn’t just cane pupils, but records it as ‘flogging’ or ‘whipping’. He doesn’t hesitate to involve the police, and on one occasion ties a boy to a desk until the policeman arrives. On another, he locks two brothers in the cellar.

Illness and even death occur time and time again. It was rather rare for a year not to be marked by the death of pupils, and on one awful occasion he is called to the infants’ school to find their teacher dying.   On two occasions – the deaths of his wife and young son – his own family suffers, but his grief is mentioned only briefly, and we never hear anything of his domestic and family life.

He’s more forthcoming about one or two bees in his bonnet – he had a prejudice against cross-eyed boys (“dishonest and untruthful”), and tended to see the railway in a bleakly negative light. He also complained about women being obsessed with soap-opera reading (though this is an indication of a dramatic improvement in literacy, given that in the middle of the century 50% of the population needed to sign with their mark),

(continued in part 2)

Give A Dog A Bad Name – Johann Georg Büttner

There’s a story I tell whenever I get the opportunity. You must know it too. It’s the story of how the young Carl Friedrich Gauss, who in 1785 or so was aged about eight, was set the task of adding the whole numbers from 1 to 100.   Rather than adding each number in turn, he promptly wrote the answer on his slate and placed it on the teacher’s desk.

It’s a great story, and it offers probably the only piece of genius mathematics which we can all grasp.   I’ll invite children – and indeed teachers – to consider how he might have been able to give the answer so quickly.   He never did explain his method, but presumably recognised that you can take the highest and lowest numbers, 1 and 100, and add them to make 101. Then the next highest and the next lowest, 99 and 2, making 101 again, and so on.   Then all he had to do was notice that there will be 50 pairs totalling 101, so giving a total of 101×50, equalling 5050.

One of the things I love about this is the immense power it gives us. We’re not restricted to adding the integers from 1 to 100; adding the whole numbers from 1 to 1000 is little more work. Your set of numbers doesn’t have to start with 1, and as long as they increase by the same amount each time they don’t have to be whole numbers either. Once you’ve understood the method you can find the total of sets which include fractions, decimals, and negatives – there’s a formula you can use for summing such series, but learning it becomes wholly redundant.

Another reason the story’s so popular is its great human interest and it’s been told time and time again; there’s a website with well over a hundred versions (http://bit-player.org/wp-content/extras/gaussfiles/gauss-snippets.html ). Many of them are very fanciful, but it’s easy to pull out the basis – the task itself, the little boy, and the school-master Johann Georg Büttner.

Many of the versions have incorporated details which are distinctly fanciful – that Büttner was idle, or a sadistic bully, who was scornful and disbelieving of his young pupil. Often there’s a David and Goliath slant – the ingenious pupil defeating the hulking teacher. Now in the last couple of years I’ve done a large amount of reading about mathematics teaching and I’d like to offer a different interpretation which I think is far more accurate.

It’s lucky Gauss was born in Germany. If he’d been English it’s likely the world would never have heard of him. It’s frequently said England was the worst educated country in Europe; in England it’s unlikely there would have been a school for him to go to, and there was no great desire from anyone to do much about it.   The church and the gentry didn’t want their peasants to be too well educated, and parents were happy to put their children out to work – most English eight-yearolds would already have been working and earning for a couple of years.

And where there was provision it was often scarcely deserving of being called a school, with the teacher someone looking to top up his main income, or an older person no longer able to earn a living in other ways. England was so slow developing an educational system that Gauss was middle-aged by the time the first tentative steps towards a national English system of schools were taken, and the first generation who’d studied and trained to be teachers didn’t emerge until he was an old man. Indeed, it’s scarcely believable, but when Gauss died in 1855 there were hundreds of English teachers who were illiterate and couldn’t sign their name to documents.

So Carl was indeed fortunate to have been born in one of the German states. Prussia, for example, had established teacher training programmes before 1750 (virtually a century before England), and had compulsory state education to 13 before 1800. In England attendance didn’t become compulsory until 1880 and it was only at the very end of the century that the leaving age was raised even to 11, and then 12. But even in 1898 attendance was still nowhere near 100% and there were still cases of 5 and 6-yearolds working 12 or 15 hours a week.

Far from being an ignorant oaf Büttner was a trained professional.   Rather than ridicule Carl’s achievement, he created an individual programme specially for him. His assistant Johann Martin Bartels lived on the same street as Carl, and Büttner arranged for him to give Gauss individual tuition. Bartels may well have been the most remarkable teaching assistant of all time – indeed, he became a university mathematics professor himself, numbering Lobachevsky among his students. His relationship with Gauss was so productive that they were still corresponding forty years later. What an amazing piece of good fortune that a tiny school should have such a tutor available!

The help Büttner and Bartels gave Carl didn’t end there. From his own purse Büttner bought Carl the best mathematics texts available, and he had the contacts to ensure that Carl’s education didn’t end at the elementary stage but continued into secondary school; from there he and Bartels arranged for the Duke of Brunswick to provide for a university fellowship which set him on the path to become the “Prince of mathematicians”.

Few of us will have the good fortune to number a genius among our pupils – the closest I’ve got is to have known Dick Tahta, who Stephen Hawking has always acknowledged as his inspiration. Johann Georg Büttner appreciated a pupil with exceptional ability, and deserves a far better reputation than he’s been given. He recognised and nurtured one of the greatest mathematical geniuses of all time and rather than traduce his memory all teachers should be proud of the example he set us nearly 250 years ago.

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Farewell, August

August is traditionally the silly season for newspapers, and there are a couple of educational stories they regularly treat us to. Firstly, there’s the grand announcement of the results, which gives columnists the perfect win-win situation. If the number of successful students goes down, then clearly educational standards are falling. And when the numbers go up – well, it’s obvious the exams are easier and hence standards must be falling.

It’s not just the writers who get busy; the photographers have an even better time. It’s truly remarkable just how many successful students are amazingly attractive young women.   Judging by the photographs, only about 1% of successful candidates are boys or less attractive females.

There’s another regular August story, and this one’s more complicated and more serious as well. Each year the boundary points at which levels are awarded are liable to change slightly. So a mark of 75 may receive a different level this year to what was awarded last year. This can cause immense pain to teachers and pupils, and is liable to be interpreted by columnists as political manipulation, and by teachers as “arbitrary” or “capricious”. Now at the Key Stage 2 / 11-year-old level this is an area I know something about, and I presume the same principles apply elsewhere.

The basic factor is that it’s relatively easy to set examinations that test the syllabus or programme of study in a valid way. However, it’s quite impossible to set two examinations on the same syllabus on which pupils will perform identically, and here’s why.   We’ll simplify our syllabus so that it consists of one element only, that children must master their multiplication facts; so that on a certain date in May every child will be tested and to make it fair they’ll all be tested on the same statement. Let’s say we ask them 6×9. Their papers are sent off for marking, the results are analysed, and in August the results become available and perhaps 85% of children are found to have been successful.

But what do you do next May? You could ask next year’s pupils 6×9 again, and perhaps 93% of children are successful.   But in the meantime you know parents have been practising their children on 6×9, publishers have been bringing out 6×9 games, worksheets, and practice cards; schools have been putting on 6×9 practice sessions, and a thousand Youtube channels show 6×9 rhymes and raps.

So next May you decide to ask 7×8 instead, and this time 87% pass. But we don’t have much idea why this is. Is it because all the extra practice has meant children know their tables better this year? Teachers will claim the higher pass rate is down to their skill and commitment, while the government will claim a triumph for their enlightened policies. But perhaps the whole cohort is of slightly different ability. And it’s certainly true that 7×8 won’t present exactly the same level of difficulty as 6×9 to every child – some may find it easier to remember, and others harder.

And of course in the real exam there’s not just one, but dozens of questions sampling dozens of syllabus skills, so while we can be pretty sure we’re setting an exam that is fair and valid we really can’t say that a mark of 60% indicates the same level of performance as it did last year.

So just how do we ensure that a grade from last year is comparable to the same grade this year? This is vitally important and it’s a hugely sensitive issue. It’s also fiendishly difficult, and the boards use every method they can think of; many aren’t particularly watertight in themselves, but they do offer pointers. There may be an Anchor test, taken by a random selection of the age-group; the Anchor test stays the same year after year, so that gives an indication how each cohort compares to the last. Another process is that some of last year’s candidates sat this year’s paper immediately before they sat their own test, so we can reason their performance on the two tests will be similar. Of course the statisticians will be at work as well. There are likely to be other processes involved I don’t know about, but one I have experienced is where a panel of the most expert authorities sit down and examine a selection of papers at this year’s borderlines and compare them with borderline papers from previous years.

All of these are partial indicators only, and they all have disadvantages, but when they’ve all been taken into account it may be necessary to take the decision that one or more of last year’s boundaries may need to be adjusted by a point or two.  I’m as sceptical about politicians as you are, but I’ve been given every assurance that this judgment is made on educational grounds and nothing else whatsoever.  You can at least be certain that no examination board ever adjusts boundaries without a huge amount of thought and effort, and you can be 100% sure this is never done in an “arbitrary” or “capricious” manner.

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The New Sink

We’ve recently had some kitchen improvements, so we now have a nice shiny stainless steel sink.   We’re rather proud of it, but what no-one told us is that even the top-range models are so sensitive that they take offence if you don’t speak nicely, or if you forget to wish them good morning in an agreeable manner.

Consequently, within five minutes the first scratch appeared. True it was invisible to all but high-powered lighting and advanced microscopy, but I was at the hardware store buying a sink mat moments later.   The sink mat worked very well but it really didn’t look state-of-the-art, and a couple of weeks later we were in a kitchen shop and found something rather more interesting.

We’d discovered a device called a SinkSaverTM. The basis of this is that the designer has said that the business area of your sink can be thought of as a 3×3 square. One of the nine cells will be the drain area, so there are eight cells which the Sinksaver needs to protect.

The problem for the designer is that different models of sink have the drain in different positions.   Sometimes the drain is at a corner, sometimes in the centre, and others – like ours – have the drain in the middle of one side. So the designer has produce a device which is made of two separate sections which can be clipped securely together to accommodate the drain in any one of the three possible positions.

You can find out more at  https://www.josephjoseph.com/en-gb/product/sink-saver/  – but before you do that, can you work out the shapes of the two sections?

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The Logbook

I first published this piece two years ago following a chance encounter with a school logbook.  By the end of the week the owners of the logbook had invited me to talk to their history group about the history of mathematics teaching in elementary schools.  Only after agreeing did it sink in that I actually didn’t know very much at all about the subject, and I’ve spent the last couple of years trying to find out.

It’s become a major interest; I’ve explored texts, archives, reports, lots more logbooks; I’ve picked the brains of everyone I can think of and I seem to have run out of people who know more than I do.  I’ve found out a lot of interesting things along the way, so I plan to make regular postings on the topic.  To start the ball rolling, this is my original piece.

Recently I spent a quite fascinating afternoon looking at an old school logbook.  It wasn’t until the 1870 Education Act that education became universal, and it used to be mandatory for schools to keep a record of events.  The Headteacher would make an entry at least once a week; judging by this particular logbook, dating from the latter years of the nineteenth century, the Head would have a lot of discretion about how this requirement would be met.

Over a period of thirty years or so the job changed hands a few times, and some incumbents wrote just a single line – sometimes simply “Nothing important happened this week”.

Later Heads wrote more, and as the book filled up over the years they would regularly be writing a page or more.

The school was in a village  with a population of 500 or so near Banbury, around halfway between London and Birmingham, and the book covers the period from the mid-1880s to 1906.  Typically, roll numbers were around 75 with an infants class and another class for older children.

It was a rural community and children were often away from school helping with duties like potato-picking and harvesting, and others I’ve never heard of – “leasing”, and “birdminding”.   A consequence of the 1870 Act was that the authorities were pretty strict about attendance, with visits from the attendance officer and the attendance registers being audited frequently.  Later Heads would state the percentage attendance for both classes every week, but even so clearly had the authority to use some discretion (on one occasion the Head decided not to open school on the day Barnum and Bailey’s circus came to town).

It wasn’t just the attendance officer that the Head had to worry about.  He himself taught fulltime and needed to supervise other classes to check on progress; the Rector visited regularly, and the Government Inspector came as well, perhaps once a year.   I was a little surprised to note that often the reports of the Head and the Inspector would often give mathematics (more precisely, arithmetic) a low profile, being subsumed within “Basic” studies. Greater priority might be given, particularly in the Infants, to Handwriting, Singing, Needlework, or Recitation.

(“…. The knowledge of the elementary subjects is good on the whole, but Arithmetic is weak in the fifth and seventh standards.  Geography is good, History fair, and Needlework is well done.”

Ever since I began teaching we’ve been told that in the olden days every child knew their multiplication tables.   It’s not true!

(“Standard III want great attention in their arithmetic tables not well known.”)

There’s another widespread belief – that children in the past were impeccably behaved, and that today’s society, and teachers in particular, have allowed standards of behaviour to plummet. The 1890s Head had plenty of non-impeccable pupils. In a school of just 75 or so, half a dozen are named week after week and several others less frequently.  Not all of them were boys – Minnie W seems to have been a real problem, being excluded from class time after time.  Her brother? / cousin? Reginald is pretty well as bad, while Oliver G “can’t be left for a moment without getting into mischief”. One senses a grim smirk on the next page when Oliver falls off a prohibited wall and breaks his leg – but a year later he “is just as bad as before he broke his leg”.

John J was another regular offender, with a particular habit of “molesting the girls on their way to school”.

I was shocked by one incident, when I read that Ernest L and Clement W (another relation to Minnie and Reginald!) attacked their teacher on her way home. I’ve never heard of such an incident, and I hope the teacher was satisfied that sending offenders home and making them apologise dealt adequately with the matter.

(“Two boys, Ernest L and Clement W, waylaid their teacher on her way home and stoned her – troublesome boys but the first is an imbecile and dangerous.  The correspondent asked that he might be sent home and the other to apologise.”)

Indeed, and contrary to what one might have expected, corporal punishment seems to have been rare. In 300 pages I found only one direct mention, when John J “an excessively bad boy … at last had a stripe this Friday afternoon”.  From another source I find that boys in their early teens would routinely receive fierce punishment (birching, or hard labour) for stealing items worth just a few pence, so if physical punishment at the school was indeed as rare as it seems then that does indeed surprise me.

No doubt the teachers breathed sighs of relief when Oliver and John and Reginald left school for the last time, probably at the age of 13.  Little did anyone know that several of those happy, carefree, mischievous boys had fewer than fifteen years left to look forward to.  This tiny village of just a few hundred sent 86 men to fight in the Great War, and no fewer than 25 never returned.  Reginald and Clement died on the Somme within a few months of each other; to the unimaginable grief of their parents both lost an elder brother as well.

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