Evens Puzzles

You may have come across these puzzles before, but I certainly haven’t.  There’s lots of good arithmetic and oodles of potential for making harder or easier versions, and pupils can devise their own.

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Evens

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I’ve only found them in a newspaper I loathe and despise – and then only once a month – but I’ve got several ideas in the pipeline for variations.

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Tim Gowers and a Great Test Match Victory

I’ve no idea how many of us – but I’ll guess it’s a very substantial number – know for a sure and certain fact that if we don’t comport ourselves appropriately during an important sporting fixture it will be our fault should our team lose.   Non-believers will see this as ridiculous superstition, or even immense arrogance, to think that our own behaviour can affect the performance of 22 sportsmen a couple of hundred miles away – but sports fans know it’s foolhardy in the extreme to tamper with the universe.

I’m greatly comforted to know that Tim Gowers is one of us. Sir W T Gowers is a mathematician of such quality that he has a Fields medal to his name. Yet he too knows how he should behave when his country needs him – I spotted a succession of excited tweets at the climactic afternoon of what has been described as one of the greatest Test Matches of all time.

Tim Gowers

(Mind you Tim Gowers is probably not quite as severely afflicted as I am. Frequently I’ll record sporting events so I can watch them as live later that evening. Even then I still have to make sure I behave myself correctly in case my carelessness affects the result of a game that finished eight hours previously.)

Incidentally I can claim to have met Tim Gowers on one occasion. My wife and made the two-hour drive to Cambridge to hear him talk and demonstrate his considerable skills as a jazz pianist.   We left marvelling not only at his versatility and the clarity of exposition but also his ingenuity – I’ve never before come across a musician or writer who told us about “scrunchy” chords. Thanks, Tim.

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Prostate Cancer

Here’s the background to a health issue I alluded to in a recent post. It won’t apply directly to many readers, but it will clue you up on my own situation. There’s a distinct gender aspect to it, but I don’t see any way round that.

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Short version: at the very start of the year we were told I’ve developed prostate cancer. After lots and lots of reading and talking and thinking I’ve opted for a course of twenty sessions of radiotherapy later this year. This is expected not just to control the cancer but eliminate it completely.

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Much longer version:  to be honest it wasn’t really much of a surprise at the very start of the year to be told that I have prostate cancer. My PSA reading had been going up for eighteen months or so; its traditional level was around 3 and soon readings were coming in at 6, 8, 9, and eventually 12, so clearly something was going on. There were plenty of reassurances (“we don’t worry too much if it’s below 50”) but it was pretty obvious the hospital at Stoke Mandeville was sure there was something there and they weren’t going to stop until they found it. So I had an MRI scan, which was an unusual way of starting Sunday morning but at least meant there wasn’t a parking problem. The scan didn’t find anything but the PSA continued to rise and the next step was a biopsy (I’d been led to expect this would be painful but in practice it was no more than rather uncomfortable).

The whole investigation took nine months or so, sometimes slow (“see you in three months”), sometimes quick (for the MRI I saw the Head of Urology on the Tuesday, had a phone call the next day, fixing the scan for the weekend). There were various messages that looked encouraging: “did not reveal any significant abnormality”, “has not shown any clinically significant tumour”, “I feel his prostate is clinically benign but …”.   Nevertheless, however positively you read them there always seemed a little wiggle room. There was never any suggestion that they were satisfied and were going to stop looking; it was always a case of “we’ll see you again in three months”, or “next …”.

It was the biopsy that finally located the problem, and on January 2nd we had a session with the Macmillan nurse who broke the news. Not all the information sank in, but what I did take from the session was his enormous positivity. The approach was very much “You get ill, you get treatment, you get better”. One of the better questions I asked was “On a scale of 1 (dreadful) to 10 (excellent) how should I feel about this news?” “A definite 9” he said. That sent me away feeling much better than I might have done – even when my phone rang the instant we got out of the door and with exquisite timing the plumber said “Happy New Year, Alan, how are you?”

I left the hospital with an armful of booklets, and soon had plenty more, courtesy of the charities and a friend or two. From this point, things went downhill a bit. I was acquiring more and more information, but I couldn’t evaluate it and get it all into focus. This hit the low point when I had my first session with the oncologist. He presented me with three strategies for dealing with things, and scrupulously avoided offering advice (I think now that perhaps I should have asked him for a recommendation, but I didn’t, and spent the next two or three months in a total whirl, deciding first on one option, then another, and then back again).

Fortunately, prostate cancers tend to be very slow growing so there’s little urgency to commit yourself quickly to a treatment plan. Indeed, the first strategy option is simply to do nothing at all, keeping an eye on things and not intervening until it looks necessary.   This is the strategy of “watchful waiting” and for many men is perfectly viable not just long-term, but permanently.

The second strategy option is hormone therapy, administered as injections effective for three months at a time. One consultant said this stops the cancer “in its tracks”. He was right; my PSA reading had gone as high as 12 and the first treatment of hormone therapy brought it down to 0.33, lower than it’s ever been.

However, there are disadvantages to hormone therapy. To stop the cancer growing it blocks your testosterone and obviously for any male there are potentially going to be side-effects. It also only works for a limited period; the Head of Urology suggested perhaps three to four years; the oncologist thought this was pessimistic.   Actually, I found the father of one our friends has been on hormone therapy for best part of twenty years.   But perhaps most significant of all is that while hormone therapy may stop the cancer growing it will not shrink it or destroy it, and sooner or later it’s likely to start growing again.

The third option is to tackle the cancer head on and destroy it. Now this is where information overload really hit me. Prostate cancer is a high profile illness and there are many techniques and oodles of research projects. Cryotherapy, ultra-sound, brachytherapy, surgery, radiotherapy, ….   Of these, radiotherapy was the only one offered to me, but in that first visit the oncologist was so determined that I should make up my own mind that he emphasised the downside (including potentially awkward side-effects involving the bladder and bowels) and indeed the negative aspects of the other strategies as well. (Actually, in more recent meetings he’s been much less wary of side-effects than he was back in February.)

So as spring progressed I had a growing mountain of information – but information on its own wasn’t much use if I had little ability to assess and evaluate it all. Should I opt for the waiting, for the hormone therapy, or something more aggressive – and if so, should I take the radiotherapy or look into other methods, possibly involving private funding? The charity helplines were warmly supportive, but for what I wanted were completely useless; understandably they couldn’t advise on individual cases. I now know, but didn’t then, that my local surgery has a dedicated prostate nurse I could have talked to. My own GP was very hostile to the use of radiotherapy, but then he was clearly influenced by a patient he’d seen the previous day for whom radiotherapy had proved unsatisfactory.

What I desperately wanted, and with the wealth of information there must be it’s surprising this doesn’t exist, is an app of some kind into which I could plug all my details – PSA, age, cancer rating, etc – to give me an idea of the choices other men in my situation were making.   I wasn’t necessarily looking for how effective the treatments were, simply to get a feeling for how many people did what. Better still, of course, would be an indication of life-expectancies – though the overall survival rates were so good that I comforted myself with the fact that actually it looked rather difficult to make a really poor choice.

It took until the middle of May, but eventually there were two light-bulb moments. It suddenly hit me one evening during a jazz club concert that rather than attempting to compare and evaluate the three strategies I should be asking a different question – what was my fundamental goal? The answer was obvious – in recent years my wife has suffered vary considerably from arthritis which has greatly limited her mobility.   Once I focused on this it was obvious that my strategy can only be to make sure that I am around for as long as possible to make life easier for her. I put things in these terms to the oncologist and his reply was instant – it had to be radiotherapy.

But he did suggest I visit a colleague in Oxford who’s an expert in the alternative strategy of ultrasound. I’ve never previously used a private consultation, but this turned out to be a brilliant way of spending £250. In effect he was giving a second opinion and his views were identical to the Stoke Mandeville oncologist. Though we were discussing ultrasound he gave me the second light-bulb moment by volunteering his opinion that in practice radiotherapy was much the better option.

From the very start the survival figures had looked hugely encouraging. Even the most pessimistic figures suggest that around 80% of all prostate cancer sufferers survive at least ten years. Given that 78-year olds have plenty more things to die of, 10+ years survival looks pretty good. The Oxford specialist put things dramatically – “If you have radiotherapy then your chance of dying from prostate cancer in the next fifteen years is less than 1%”.

My Stoke Mandeville oncologist agreed with everything the Oxford expert had said, so though it’s taken a heck of a long time at least I’m now in no doubt about how I should go ahead, and we signed the forms a few days ago. I’m expecting a twenty-day course of radiotherapy at the Churchill Hospital in Oxford, perhaps in November. I’d have rather liked to have got things out of the way before October 31st, but the timescale makes this unlikely. Still, with luck I won’t be having to drive the 35 miles to Oxford (and both of the experts have said I’ll be able to drive myself) throughout January or February.

I’m a little bit bemused that it took me so long and very grateful I was able to take so much time to make my choice. As a cancer sufferer I’ve really felt a considerable fraud; others have ghastly versions of the disease while I have no symptoms, no suffering, and the expectation of a complete cure. And though I’d rather not be in this position, people are already treating me as an expert and beginning to ask me for advice.   Given the demographic profile of my friends and contacts it seems pretty likely that others will eventually find themselves in the same boat. For what it’s worth, here are some suggestions – some of these are things I did OK, others I should have done better:

[a] take wife / partner / relative to important sessions, not only for support, but to have a second pair of ears, (and take a notebook as well – I have a rather full A4 ringbinder),

[b] work with both the hospital and your local GP / surgery, and not only with doctors but with their specialist nurses,

[c] don’t simply accept information, but ask for opinions and recommendations – you may not get them, but ask anyway,

[d] you may want to consider a variety of treatments – there’s so much work going on in the field that things are changing all the time,

[e] the charities and support organisations are full of help – https://prostatecanceruk.org , https://www.macmillan.org.uk , https://www.cancerresearchuk.org

[f] welcome experiences from friends, relations, colleagues,

[g] don’t lose sight of how amazingly good the survival rates are – I’ve even seen it suggested that those with prostate cancer actually have longer life-expectancies than men without!

[h] and when you’ve got all this information from dozens of sources, you’ll need to evaluate it all and come up with your own decision.

Good luck!

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The Last Lessons Of The Year

If you started teaching in 1962 there have been a lot of occasions when you’ve taught your last lessons of the school year. This time there’s a possibility – hopefully rather slight – that these might be the last lessons of all.

 I’m due to have a course of radiotherapy later this year, and while it’s expected to clear up the problem once and for all there is some possibility that the side effects might make me an unsuitable person to have around in the classroom. With luck that won’t be the case – I’ll know more in the next month or two.

 All the same, the possibility did mean that this year’s last lessons had a slightly more sombre context, so I indulged myself and used some of my favourite activities.

 

****** First I used a couple of challenges from ATMs “We Can Work It Out!” booklet. (www.atm.org.uk ) Each of these presents children with a dozen or so statements on individual cards. I find these infinitely fascinating; children who usually have a fit of the vapours when presented with any question with words in it respond just as positively as anyone else. Typically, at first glance the information is totally confusing. There is no obvious way through the problem; perhaps even the starting point and the target have to be identified. There may be irrelevant information to be ignored, and the remaining statements need to be interpreted and assessed.

For example in The Great Race from the “We Can Work It Out” booklet they have to evaluate a whole series of statements such as ’the green car finished before the yellow car’.

I wrote a little more a couple of weeks back, and this included information about two activities of my own, Martian Kings and Queens and the Properties Of 2D Shapes, and you can find this at

https://established1962.wordpress.com/2019/08/06/collaborative-problem-solving-we-can-work-it-out-martians-and-shapes/

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****** I also returned to the Stephen Von Worley’s animated display of numbers by that you can find at http://www.datapointed.net/visualizations/math/factorization/animated-diagrams/   So for example 3 and multiples of 3 have a display built around a triangle of three circles. 4 and multiples of 4 have a square array of four circles – so what do you do with 12?

I’ve written about this before (November 2016) at https://established1962.wordpress.com/2016/11/04/animated-factorisation/

One of the richest aspects of this is that you never know the path you’re going to follow. On one occasion we got into prime numbers, another looked at powers of 2, and this time we spent half an hour on estimation.

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****** Then there was Marilyn Burns’ lovely playing card challenge where a suit of cards is arranged so that when you deal them out in a particular fashion the cards arrive in sequence Ace, 2, 3, 4, …. The challenge for the pupil is to figure out just how the cards must be stacked to ensure this sequence happens for them. Everything you need, from introduction to months of extension and follow-up, is at http://www.marilynburnsmathblog.com/the-1-10-card-investigation/

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****** And I also included the simple simplest dice game of all, Pig. When it’s your turn you are allowed how to roll the die as many times as you like, keeping track of your total score. You can choose to stop rolling, and your score becomes safely banked. However, should you throw a 1 not only does your turn end, but your score for that turn is 0.

It’s wonderful fun, but Pig is not just fun, and it’s not just excellent mental arithmetic practice – every turn, and every throw, you need to make decisions, and the decisions change all of the time depending on the state of the game.

I wrote about Pig a few years back, but I never got around to publishing it until a few days ago.   It’s worth a look, because a couple of children taught me a version of their own that I’d never come across.

https://established1962.wordpress.com/2019/07/29/pig-or-bust/

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Collaborative Problem-Solving – We Can Work It Out!, Martians, and Shapes

I doubt they need any recommendation from me, but the “We Can Work It Out!” booklet is one of my favourite resources from the Association of Teachers of Mathematics ( www.atm.org.uk ). There are two collections, with lots of activities described as Collaborative Problem-Solving For The Mathematics Classroom, and they’re suitable for pupils in the upper primary and lower secondary age-range.

For each activity children are presented with a dozen or more cards, about the size of visiting cards.   Between them, the cards carry all the information about a situation – arranging a school trip, or the prices of a range of cakes.

These are four of the eleven cards in the first activity, The Great Race:

The Great Race

Children aren’t simply challenged to find the answer, they have to identify the path though the problem.  Indeed since they receive a pile of cards rather than a printed sheet they even have to locate the starting point for themselves. As the title and sub-title both suggest, these activities are particularly valuable for generating discussion and co-operative working with small groups of pupils.

Challenges like these can produce a positive response, even from children who are usually intimidated as soon as a couple of words creep into a question, and observing a group work through a problem gives you a vast amount of insight into their understanding, vocabulary, and every problem-solving skill you can think of.

As you’ll gather, I recommend “We Can Work It Out!” highly. The list price of each is £22, considerably cheaper for members; the books are spiral-bound to make photo-copying easier.  And if you opt for the e-book – which is sensible, because you need to print out activities – it’s cheaper still, at just over £8 for members.

You can find the current ATM catalogue, which includes both collections and is full to the brim with other great resources at http://bit.ly/ATM19cat

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A similar challenge of my own is called Martian Kings and Queens. I wrote about this in August 2015 (https://established1962.wordpress.com/2015/08/12/martian-kings-and-queens/ ) Have a go – you’ll find it works fine, though it’s a bit tough for my pupils and I really need to add an extra clue or two to soften things a bit.

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And here’s another one of mine, about two-dimensional shapes.  You need to find which shape goes in the central cell of a 3×3 square grid.

Here are the shapes:

Shapes 1

And here are the clues (which are deliberately in a not-very-helpful order):

Shapes 2

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Pig – Or Bust!

I fondly recall the time we took a group of children on a residential trip, and one evening after the children had gone to bed I introduced the adults to Pig.  Anyone who’s ever been away with a group of children knows that sooner or later you have to read the riot act after lights out to get them to stop talking and settle down.  This occasion reversed the natural order of things – it’s the only time in my life when I’ve been faced by a deputation of sleepy children demanding that the teachers behave themselves and stop making so much noise.

So let’s tell you about Pig.  It’s always been just about my favourite game.  You can play it in the classroom or at the pub, it needs nothing more than a single die and paper to keep score.  You can learn the rules in a minute and anyone – any age or any number – can play, and yet it’s so rich that a class of university maths students couldn’t agree whether it’s a game of luck or skill.

When it’s your turn to play you roll the die.  Indeed, you can roll it as many times as you like, keeping the total score as you go.  When you decide to stop throwing your total score is recorded.  So if I roll 3, 4, 2, 3, 6 I can stop throwing and bank the score of 18.  Alternatively I could make a couple more throws – 2 and 5, say –  in which case I bank 25 rather than 18.

There’s just one restriction to this – if I throw a 1, then my turn ends immediately.  All my score for that round is lost, and I score 0.

The advantage of banking your score is that banked scores cannot be lost.  If, therefore, I’ve banked 25 and next time I roll 6, 6, 6, 6, 6, 1 – then I’ll curse bitterly at the thought that I could have banked a further 30 points, but at least I’ll start my next turn with the 25 still in the bank.

The winner is of course the person with the highest score, or perhaps the first person to reach 100.

Alternatively, you can play to a time limit – and you get a whole new set of factors to take into account.

But when I started to tell Issa and Milly about the game they instantly recognised a game they play.  It’s called Bust.  It needs a pair of dice, and each player has a scoresheet.  Your scoresheet in divided into four columns, headed B, U, S, T.

Both dice are rolled and their score is totalled.  Each player scores the total and the dice are scored again, and again, just like Pig.  However, there are three differences; firstly, every player – not just the person who rolls – gets the score.  Secondly, each player makes their own decision when to stop scoring and bank the accrued total; the others keep scoring till they choose to stop (or of course Bust out).  Thirdly, the trigger that ends the round and (if you haven’t already opted to bank your score) gives you a score of zero is when both dice show the same number.  (Alternatively, the round must end when everyone has banked their score.)

In Bust play lasts for four rounds – your first score goes in column B, next round in column U, and then in columns S and T.  As you’ll guess, you win when the total of your four scores is higher than anyone else.

The arithmetic’s more challenging; everyone’s involved all the time, and with every roll of the dice you have a decision to make.

This was five years or more ago, and I’ve not till now got around to publishing it – and I’ve never come across anyone else who knows the game.

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Any Ideas?

I’d never seen one of these before.

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Here it is again, with a coin giving you an idea of the actual size:

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It certainly reminds you of the net for a cube, or possibly an open box.

It’s the backing for an adhesive plaster, as needed by anyone foolish enough to attempt a do-it-yourself thumbectomy while gardening.

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And here it is in action.  It’s certainly a lot neater than my original bandage, which was about the size of a peach.  It doesn’t look much now, and it’s all cleared up quite considerably, but it didn’t half hurt, and there was a vast amount of blood – I needed some quick improvisation to avoid a carpet crisis.

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Teddy’s Farewell

 

Teddy

We finally said goodbye to our son’s teddy this week. Both Simon and teddy are now in their mid-forties and they haven’t seen much of each other for a good while, so we finally cut the knot – even though it made me feel like, in Arthur Mailey’s unforgettable words “a boy who had killed a dove”.

(You can find Mailey’s beautiful account of how he fared when as a very young player he bowled to the mighty Victor Trumper at   http://www.espncricinfo.com/australia/content/story/211734.html

Read the story even if you’ve no interest in cricket:

As he walked past me he smiled, patted the back of his bat and said, ‘It was too good for me.’

“There was no triumph in me as I watched the receding figure. I felt like a boy who had killed a dove.”)

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Simon’s teddy often accompanied me to courses I ran for teachers. He was very co-operative when we explored the handshake problem – if a group of people all shake hands with each other how many handshakes are needed? How many if another person (or indeed teddy) joins the group?

On one occasion a teacher was rather uncomplimentary about teddy’s clothing.   “I’m sure we’d be just as offended by your trousers if you hadn’t taken them off for 25 years”, I replied.

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Lilian Casselden

My most recent post looked at the logbook from Wendover School, and mentioned a young teacher called Lilian Casselden. 

 

It’s rare to pick up any sort of personal detail from school logbooks.  Even the Heads themselves tend to be shadowy figures, and others are little more than names, or frequently just “the Assistant”.  Lilian Casselden is the only exception I’ve come across and she’s certainly worth a post in her own right.

The 1881 census shows her being born into a family of teachers – both her parents, and two sisters as well.  They lived in Bromley, and not surprisingly, Lilian herself became a Pupil Teacher at 13, and then spent a couple of years working in a school in Penge just a few miles from home.

Lilian 1881

In 1893 she was appointed to the staff at Wendover, where the Head was by no means easy to please.  There had been a long run of unsatisfactory appointments, but clearly Lilian was a very good teacher indeed; she impressed him immediately as a “very energetic painstaking teacher”.

He reported she kept good order among her pupils, and the gloss didn’t wear off – she fitted in very well for more than two years until one Friday there was a dramatic entry in the log book “Through some irregularity in the life of Miss Casselden before she became an Assistant in this School she has been called upon to resign”.

On the following Monday her resignation was handed in and she left Wendover the very next day.

Plenty of teachers who were merely incompetent were allowed to work out a period of notice, and for Lilian to be kicked out of town immediately is unique. It was nothing to do with her work, and there was no suggestion anything criminal was involved, so the best guess may be that it was a case of “cherchez l’homme”.

Not only do we not know what the “irregularity” was, there’s also a further mystery – how was it that the information came to the attention of the authorities at Wendover more than 2½ years after the event.

Whatever the reason was for her enforced resignation she wasn’t going to get a character reference, but we do know that in 1896 Lilian went back to Bromley.  She was welcomed back to the school where she herself had been a pupil, and she remained at Bromley Common until 1909.   She was formally described as the sewing mistress, but it’s inconceivable that someone with her background wouldn’t have been given much greater responsibility in more than a dozen years at the school.

Lillian

She was clearly concerned that time was passing, and by the time of the 1901 census – thirty years after she was born – she declared herself to be 27.

Lilian 1901

A full ten years later in 1911 she was claiming to be just 30.   But by then she’d married Percy Gain at Croydon in 1909. Percy worked in the GPO Engineering Department and by 1911 they were living in Wales; later they moved to Devon, where Lilian died in 1954.

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Acknowledgement:  Lilan’s distinctive name meant I was able to find out much more about her via the fortuitous discovery of a fascinating website devoted to the elementary schools of Bromley.  Remarkably, the site actually has a section devoted to Lillian herself.   ( http://www.barnes113.karoo.net/History/pupil_teachers.htm )

The site is the work of Rob Barnes; I’d love to be able to contact him to share information, but frustratingly, I haven’t been able to find any way of doing so.

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Wendover School

This is another of my pieces about elementary schools and their teachers in the Victorian and post-Victorian era

 

Logbook entries needed to be brief and factual, avoiding personal comments; however, writers would naturally want to show themselves in the best light, so it’s very easy to read too much into entries. Nevertheless A G Fleming does, at least for me, come over as the best type of teacher. He develops several successful pupil teachers, he isn’t afraid of new ideas, he displays a considerable breadth of knowledge, and he is fair minded and uses punishment rarely and, by the standards of the day, humanely.

Few can have had such an appalling start as Fleming; in his very first week in 1868 he has to record that five boys – from a school of just fifty or so – are drowned when the ice they’re playing gives way. The tragedy was all the worse because the school was closed for a half holiday given to recognise the service of the vicar. At the time Wendover school was a smallish one, for boys only. Fleming is fortunate to be able to employ a pupil teacher, and the first is his son, Herbert. He’s not afraid to criticize him where necessary, but there is a quiet pride when Herbert completes his apprenticeship satisfactorily in 1874 (“The senior pupil-teacher left Wendover having completed his apprenticeship with great satisfaction and credit”).

Although the school had such low numbers it was always exceptionally generously staffed, with two or even three pupil teachers (a dozen miles away, at Cheddington, the head was responsible for more than a hundred children with a single pupil teacher).   Though Fleming always tries to find good things to say, some of his pupil teachers aren’t up to the task.   One decides he doesn’t actually like the work, and his replacement initially promises well, but within a year “received notice to leave on account of incapacity, idleness, and health”, which seems pretty comprehensive. Emma Beeby, on the other hand, passes nationally in the top dozen pupil teachers out of more than 1500, and others do well enough to become permanent additions to the staff.

Fleming’s no stick-in-the-mud. In his first week at the school he gives a talk on Electricity, and soon takes the boys to an industrial exhibition. He writes that when the Rector visits with a friend “they were pleased with the method I have lately adopted in teaching Subtraction” – as a maths teacher, I’d dearly love to know more, but simply recognising that different methods exist is more than some teachers I worked with have managed. He tries introducing “Home Lessons” and finds them successful enough that he employs them throughout the school. In 1877 – which seems remarkably early to me – there is a photograph taken of the children in the playground.

In 1875 the school amalgamates with the girls’ school, and Fleming embraces the opportunity to try out small-scale trials so the final process goes smoothly, and later that year the expanded school is able to present an evening performance of songs and recitations etc by the children which “surprised and pleased the parents.”

By this time the numbers have rocketed, from somewhere around 20 to 117 within six months, but the staffing continues to be remarkably generous – he has no fewer than four pupil teachers, and, on top of that, ladies from the village help with knitting and needlework.

It’s rare for Fleming to mention behaviour, and usually he deals with problems by keeping children behind, or sending them back home. But once or twice you realise how different things were 150 years ago. There’s no indication it was anything to do with school, but he records “A boy, Benjamin Terry, is now undergoing his term of imprisonment”, and in one of his very rare examples of using the cane he writes “I was obliged to administer corporal punishment to Eliza Fantham, who has been giving a very great deal of trouble lately. In consequence of her striking at me, she received a few more strokes than she otherwise would have done. The number of strokes did not exceed six or seven.”   (Later Heads were to repeatedly include Fanthams in the log – see footnote 1.)

A certificated teacher needed to have a tremendous breadth of knowledge. In mathematics alone Fleming refers, among many other topics, to Simple Proportion to Standard V, and Subtraction and Multiplication of Decimals to Standard VI.   The pupils in these higher standards also faced Compound Multiplication of Weights and Measures, Interest, “Circulating Decimals”, and “Double Rule of Three” (if like me you’ve never heard of this, you’ll want to know that ‘The Double Rule of Three, sometimes called Compound Proportion, teaches by having five numbers given to find a sixth which, if the proportion be direct, must bear the same proportion to the fourth and fifth, as the third does to the first and second. But if the proportion be inverse, the sixth number must bear the same proportion to the fourth and fifth, as the first does to the second and third’. He also goes beyond arithmetic and “Started a class in 1st Grade Geometry this week”.

Outside mathematics, in formal English, among others, he mentions parsing, pronouns, and prosody.   On just one double-page spread in the log, he records teaching lessons on Druids, Reindeer, Manufacturers of England, Gunpowder Plot, River System of England, The Cat, Copper, The Pig, The Tea Plant, Climate of England, The Elephant, while at different times he teaches about the geography of Russia and “the Geological Character and Soil of Buckinghamshire.”

In 1877 his wife’s ill-health compels him to resign. He’s spent nearly ten years at the school and received “a valuable testimonial from the Teachers and Scholars of the Day and Sunday Schools.” He’s clearly made an excellent job of overseeing the transition form a small boys’ school to a much larger mixed-school, and the current inspection report says “The school is a credit to all concerned with it … children answered … with great promptness and intelligence. The discipline very good”.

The new Master is Harry Bowles, and he serves for three years during which the school is broadly successful, though later HMI comments become a little more qualified, and some of the support teaching gives concerns – so that (even though the inspector makes a special point of praising pupil teacher Mary Louise Eldridge) the Vicar decides no further pupil teachers should be employed. For the next thirty years or so only monitors – cheaper, and often children and with no pretensions to becoming teachers themselves – are used to support the certificated teachers.

Bowles served from 1877 and in 1880 he leaves and is replaced by Samuel Vallis, whose tenure proved little short of disastrous. In 1882 the inspector wrote “A great blot; the children are restless and inattentive, and their work is careless & full of blunders. Speaking of them my assistant says ‘such careless papers were never sent out of Wendover before.” The report demands that next year HMI must look for excellence “from a school which is provided with everything that money can buy and at which the teaching power supplied (3 certificated teachers and two paid monitors for an average attendance of 113) may be called ‘enormous’”.

Vallis (below) had little chance of surviving such a report, and was quickly replaced in 1883.

vallis

The new Master by George Bushell (below). Bushell was in post for nearly a quarter of a century, until 1907, by which time the roll grew to more than 200. I found it difficult to warm to him, even though he suffered the awful tragedy of his wife’s sudden death in 1887, and losing his second wife in 1901. And he rarely mentions bad behaviour or the need to punish pupils, though on one occasion he reports “Was compelled to punish Fredk. Jordan rather severely for disobedience, which has had a good effect upon the whole school.”

bushell

However, he’s clearly no progressive, even in matters of language. I’m not too worried if he regularly calls children who come from a distance “foreigners”, but even in 1900 it must have sounded a little reactionary to talk of forming a “Dunces” class, and he makes his attitude to the children in this class plain by entrusting them to a monitor rather than a qualified teacher. He’s no friend to curriculum development either, and it has to be forced upon him for grudging implementation (“The new subjects render the work much more difficult and trying to teachers.”) Object Lessons are introduced reluctantly – or reintroduced, as they were first used back in Fleming’s time. He’s particularly negative about geography and never has anything good to say about it – the parents don’t want it, the teachers can’t handle it, the pupils find it too difficult, ….

In arithmetic he has – like some today – something of an obsession with long division, which gets mentioned on page after page. He emphasises repeated practice and says that incorrect sums “must be altered by their doing the rules over & over again”, to which the inspector comments “I hope to find … less mechanical practising in arithmetic.”

When staffing is stable school seems to proceed smoothly enough and to HMI satisfaction, but from time to time he finds it difficult to attract and keep suitable assistants, and some of the appointments last only a few days. One such drought is solved in 1893 with the arrival of a young woman called Lilian Casselden, who impresses as a “very energetic painstaking teacher” who keeps good order among her pupils. She fits in very well for two years until one Friday there is a dramatic entry in the log book – dramatic enough that I’ll make a separate posting about Lilian.

While staffing during the second half of the 1890s and the first years of the twentieth century seem to have been very settled, nevertheless HMI’s favourable comments are increasingly leavened with advice about teaching methods. Those of us who’ve written inspection reports will recognise that while the carefully chosen language may appear mild enough it may actually carry a strong message – “I hope to find some improvement in the method of teaching as time goes on, e.g. a more free and general use of the blackboard, … , and in the lower classes more careful supervision of the material used by the scholars.”

At best Bushell records the inspectors’ advice neutrally. However, he makes his feelings clear enough on one occasion, when a new HMI visits and stays all day “visiting all the Classes and criticised the teaching. He made various remarks & recommended what in his idea were improved methods of teaching some subjects.” By now Bushell is within three or four years of his retirement and possibly still recovering from the death of his second wife, and his own teaching doesn’t escape the inspector’s severe criticism “… the first class ought to be a stronger one than it is. I hope next year to find more self-reliance and honesty in their work, more smartness of discipline, and that out of turn and simultaneous answering no longer exist.”

A couple of years later similar and more extensive comments are made “The order & tone are not what one wants, and this affects the children’s attention and the evenness & soundness of their work. …. Next year, however, I shall look for improvement. I shall look for evidence of a stronger guiding hand: of more carefully thought schemes: of an organization framed with a more definite purpose: of an influence, a School influence, affecting and strengthening both intelligence and character.   Unless I find this it will be difficult for me to say that the efficiency of the school is of the kind which one has a right to expect.”

There were still a couple of years to go, but Bushell was fast approaching retirement and neither the Education Committee nor HMI wanted to rock the boat. The next couple of reports were milder, but still brought out the inspectors’ view that a new hand was needed on the tiller: “The oral work is not very strong; more should be obtained from the children, less should be told them.”

Bushell’s final term finished in June 1907; he’d been at the school since September 1883.

I’ve a nagging feeling I’ve probably been rather unfair to him, and allowed my reservations to outweigh his many qualities.  Nevertheless, he does feel like a much less sympathetic character than his predecessor A G Fleming, or the near-contemporary William Wotton Winsor less than a dozen miles away at Cheddington.  All the same, Bushell had done a job far harder than any I ever had to do, and done it for nearly 25 years. Once he’d located good people they tended to stay with him for many years, most notably Lizzie Cummings, who was a monitor for a possibly unprecedented seventeen years. He doesn’t seem to have had any difficulties with discipline, and his relations with parents were – with the possible exception of the Fanthams – excellent. However, he’d suffered grievous ill-fortune, he was the choir-master and organist at the church, and it seems clear that he was worn out and probably had little wish to take the school forward into the more expansive curriculum of the first years of the twentieth century.

Bushell’s replacement was A W Molineux (below), who was to serve virtually as long as he did, from 1907 until 1930. He immediately gave the school the new impetus the inspectors wanted. They were pleased to note a more satisfactory programme of work for younger children, and more practical work and experience – plasticene, clay, and cardboard modelling, and teachers were encouraged to take their classes out on Nature Study walks. He records talking with pupils following an appearance of a comet one evening.   Cookery was introduced; also Gardening, with both boys and girls winning prizes at local exhibitions and completing courses qualifying the school for grants.

molyneux

For the first time, teachers went on professional development courses, and the school also hosted the Aylesbury and Leighton Buzzard Teachers’ Association. Soon the school was held in such regard that the Education Authority made a point of appointing a promising pupil teacher it wanted to place – the first at Wendover for thirty years. Molineux introduced a more overtly caring aspect – there were none of Bushell’s references to “Dunces”, and he talks of “distant pupils” rather than “foreigners”.   He gives up most of his Whit holiday to teach boys to swim, and arranges for a visiting speaker to talk to the girls about caring for young children.

Relations with the wider community and with parents are excellent, and the inspectors are impressed when he introduces “the practice that obtains of sending a Report of each child’s progress to the parents at the end of each term”. Not surprisingly, the inspectors feel able to report: “The Mixed school is in good hands. Mr. Molineux has done much to improve the tone and discipline of the school & to raise the standard of the work, and his assistants are rendering him loyal and thoughtful service”

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Footnote 1 …… Fleming was merely the first Master to have problems with the Fantham family, and over twenty years from 1874 no fewer than ten Fantham children are mentioned in the log, sometimes for being of limited ability, more often for irregular attendance and bad behaviour. In 1885 when the school was used as a polling station in the General Election George Bushell ruled that the wearing of party colours and use of slogans should be banned, and he “also advised the children not to mix with the rough element in the street”. The family took exception to this, and the Fantham children, notably Alice, disobeyed the instructions and stayed away from school.   This became a long-running saga, the Attendance Officer proved unable to persuade them to return, and the matter came to the notice of the inspectors, who asked the local authority to take Mr Fantham to court. Even after conviction he continued to hold out and it wasn’t until the summer of 1888 – nearly three years later – that Alice eventually returned to school.

Clearly the Fanthams saw no reason to let a good grudge go to waste, and the feud continued for years.   In 1892 George Bushell records that for a January inspection “many who had been ill came and did well. All who were able to come were present, with one exception, Harry Fantham being kept away with no reason.”   Indeed, Fantham children were still being recorded as irregular attenders in 1896.

(I confess I myself taught a couple of Fanthams, though by this time they’d moved up in the world and were local solicitors.)

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Footnote 2 …… I was intrigued by the case of Lillian Casselden, and you’ll find out more about her in my next post.

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Footnote 3 …… It’s easy to think of the late Victorian and Edwardian period as being one of a leisurely pace; I recently studied one school in a isolated village where children seemed to be living very similar lives to those their grandparents had experienced.

In fact, the rate of change could be even greater than in our own day. For several years now, Wendover has been embroiled in controversy over proposals for HS2, with no apparent progress. The train came late to Wendover and work on building the line from London to Aylesbury wasn’t begun until 1890. However, within just four years the service was so established that on one Friday afternoon school was begun early, so giving the teachers the chance to catch the train to London for the start of the Whitsun holiday. By 1911 it was so bedded into local life that the start of term had to be delayed when a railway strike meant that many families were stranded and were unable to get back to Wendover as planned.

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Acknowledgements …… All the information from the log book comes from the CD-ROM version produced by the Buckinghamshire Family History Society in co-operation with the School. The Society produces several such CDs which are available very cheaply and make the information available in a very convenient and easy-to-use form. ( www.bucksfhs.org.uk )

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