# “… Tables Not Well Known”

*This is another posting from my history of schools findings.*

*For more than 150 years there’s been one yardstick that’s been used to give a quick judgment by all and sundry about mathematics learning – “Do they know their tables?” And you’ve only got to look at school logbooks or HMI reports to realise that in spite of 150 years of teachers’ efforts the answer has invariably been “No”.*

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Long after many countries had universal elementary education England was known for having perhaps the worst schools in Europe. No-one had much interest in schooling; there had been too many revolutions in Europe for the landed gentry to want the population to become educated, and parents and employers were keen to have children – even those as young as six or seven – working for a living.

Consequently, it wasn’t until 1832 that the Government made the first tentative grant, putting £20 000 towards the building of elementary schools. Of course, the £20 000 covered the country as a whole, but a new school might cost only £60 or so, so it was a useful start. A few years later a system allowing promising pupils to train in their schools was developed, followed by the emergence of training colleges. At last elementary education in England had taken off, and growth and momentum were rapid – I found a reference as soon as 1850 to a teachers’ magazine which encouraged teachers “to make the learning of tables interesting, instead of mere mechanical routine”.

But within a few years the Government found to its horror that the £20 000 grant had grown to nearly a million pounds every year. As governments invariably do in such cases, it set up a committee, and in 1862 the draconian Revised Code was introduced. The Code soon became known as Payment By Results, for schools would only receive a grant for those children who met nationally decreed standards of attainment and attendance.

Anyone who’s been involved in education in recent times will have little difficulty in believing what happened next. Children were tested annually the “Three Rs”, Reading, Writing, and Arithmetic. Children worked in one of six levels of attainment, known as Standards. Not surprisingly, the examination became the focal point of the school year. The Head’s job security depended upon the results, so the curriculum narrowed down to the three Rs and little else, with children spending the preceding weeks or even months doing nothing but practise for the examination. I found that one school even postponed the Christmas and New Year holidays until after the Inspector’s visit!

In the run-up to the tests even Scripture lessons might be abandoned, a serious matter given how important the church, and in particular the Rector, was to most schools. For example, a week before the inspection in 1865 one Head recorded in her logbook “*Instead of having Scripture Lessons children questioned on the Multiplication Table*”.

The examination was carried out via a visit from one of Her Majesty’s Inspectors. Most HMI were appointed for their Church connections, usually with a university background; they’d see themselves having considerably higher social standing than a mere teacher and often they might have little understanding of children. So both teacher and children might dread the annual visit; at least one Head was so terrified by a coming inspection that she drowned herself.

The actual arithmetic syllabus could hardly have been more narrow. In Standard I, for the youngest children, the requirement was “Form on blackboard or slate, from dictation, figures up to 20. Name at sight figures up to 20. Add and subtract figures up to 10, orally, from examples on blackboard”.

Standard II required “A sum in simple addition or subtraction and the multiplication table”, and Standard III “A sum in any simple rule as far as short division (inclusive)”. For most, schooling would finish well before they reached higher Standards.

School logbooks make it clear that such a limited syllabus and so much at stake meant teachers gave the highest priority to the learning of tables. We see teachers devising the same techniques we use today – “*Find the plan of getting St II to learn their Multiplication Tables at home answers well*.” And “*Encouraged children to get table books of their own, bring them to school and say tables from them*.” Those who like to use rock or rap versions of tables are following the example of the Devon teacher of 150 years ago who encouraged her children to sing their tables from 2.30 to 3pm.

Teachers recognised the benefits of a little and often approach: “*Find the II St know much of their Multiplication Table, as I devote a short time on Tuesdays and Fridays to hearing it having been learnt at home*”. They seized every opportunity for a little practice, even when lining up: “*Examined the children in the Multiplication Table while at the line*”. I even found a Head who devised the Buddy approach used in my own school, observing, as we too find, its value to both parties: “*On Thursday adopted a fresh plan for teaching Arithmetic. For about twenty minutes gave everyone on the three upper classes a child from the lower classes to teach …. Found it beneficial to both the elder and the younger ones.*”

It’s frequently asserted that children used to know their tables perfectly, but it’s clear that this common belief simply isn’t true. Virtually every logbook finds Heads bemoaning their pupils’ inadequate knowledge. One Head writes in three successive months he finds it necessary to keep one class in for not learning their tables. Next year’s equivalent class is just as unsuccessful, and the year after that he finds himself keeping them behind not occasionally but every day for a week. (Declining standards, no doubt!) And this is no ogre, but a Head who joins the children at play, and enjoys snowball fights and playing cricket with them. Children bring him flowers, and worry when he’s ill. He’s constantly looking to find better ways to teach; he’s ambivalent about using the cane, but is forced to admit that other punishments don’t always work – “*Find that threatening children with an extra ½ hr at school is no punishment for some say they would like staying*.”

It was the Payment By Results code that required schools to keep a logbook, so logbooks aren’t actually all that rare. Some have been transcribed and others put onto CD ROM, so they can be both convenient and inexpensive to study. Much of what you read comes across as truly historical – children unable to attend because they have no boots, or absenting themselves at harvest time because they’re working in the fields. There are enormous class sizes – in one case 104 children in a room so small they had to take turns to sit down. Illness and epidemics are frequent and pupil funerals are tragically by no means unusual – one terrible story featured a family who lost each of their five children in a measles outbreak.

In other ways you find yourself thinking that things haven’t changed a bit – demanding pupils “*Oliver G cannot be left a minute without his getting into mischief …*”, daunting workloads and endless paperwork, publishers offering workcards and schemes promising to meet syllabus requirements, and – of course – the never-ending struggle to master the multiplication tables.

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# Plus Ça Change

*These extracts are taken from “A Social History of Education in England” by John Lawson and Harold Silver. The authors are writing about the “Payment By Results” system introduced in 1862. Grants to schools were determined by the proficiency of children from six years old as tested individually by the inspectors.*

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“…. As T H Huxley later put it: ‘the Revised Code did not compel any schoolmaster to leave off teaching anything; but, by the very simple process of refusing to pay for many kinds of teaching, it has practically put an end to them.’ Matthew Arnold, poet and HMI, was the inspector most responsive to the effects of the code. Under the old system a good inspector heard selected children read and questioned whole classes on all their subjects: ‘the whole life and power of a class, the fitness of its composition, its handling by the teacher, were well tested.’ Under the new system, however, he was unable to test any of these: ‘he hears every child in the group before him read, and so far his examination is more complete than the old inspection. But he does not question them; he does not … go beyond the three matters, reading, writing, and arithmetic.’

“The result was generally an increase in rote learning, and even inspectors not opposed to the principle of the revised code reported on its deadening and disheartening effects. The need to drill the children to meet the inspection requirements was reflected in the schools’ activities throughout the year. Frequent testing became common. Some of the improvements of the 1850s in curriculum and method in many schools were cut short. Even religious instruction was sometimes dropped as the inspection approached.

“…. The possibility of new thinking about educational methods and about the curriculum became paralysed by the operation of the code.

“…. Payment by results was a view of the nature of elementary education from which it took the system generations to recover. Edward Thring looked back at the experience of payment by results and the inspection of minds like ‘specimens on a board with a pin stuck through them like beetles’, and appealed to teachers to get rid of the vestiges of the system: ‘strive for liberty to teach, have mercy on the slow, the ignorant, the weak’. A former inspector looked back in 1911 at the thirty or more years of ‘Code despotism’ in which he had been involved, and thought the efforts were still being felt of ‘that deadly system … which seems to have been devised for the express purpose of arresting growth and strangling life, which bound all of us, myself included, with links of iron’.”

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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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# Snakes and Ladders Revisited

*Here’s an account of a hugely enjoyable school visit. By a happy coincidence, just two days later I was at a conference at London Olympia. A recent President of the Mathematical Association and I were both speaking about mathematical games. In his opening remarks he said Snakes and Ladders was of no interest as it offered no opportunity for decision-making. Fortunately I had some photographs of my visit with me, and I was able to tell him some of the things we’d done in school and encourage him to reconsider.*

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For a long time I’d had a large piece of cardboard about 120cm square in our garage. I knew it would come in useful one day, and when I got the opportunity to work with the Y4 class at Hawridge and Cholesbury School I knew just what I was going to do with it. I fetched it indoors and ruled it into six rows and six columns of 20cm squares and took it with me to the school’s “Numbers Day”.

Everyone knows Snakes and Ladders, so everyone was able to tell me that the square at the bottom left would be number 1, and the squares along the bottom row of the board would be numbered from 1 to 6, and in the next row up the numbers 7 to 12 would run from right to left, with the left to right / right to left pattern continuing.

This gave us plenty of chance to explore questions like “Where will 16 be?”, “What number is two squares above 18?”, and “What number is in the third square along in the top row?”

We discussed what similar questions might arise if I’d chosen to use a different number of squares in each row, but this was a brief digression. I’d also taken along some 20cm squares of coloured paper, and I invited the children to complete the board, which I found waiting for me when I returned an hour later. I’d also given some strips of various lengths for the children to make into snakes and ladders.

So the next stage was to position the snakes and the ladders. I’d rather assumed that we might choose to use a short, a medium, and a long ladder, and similarly with snakes. However, the class were adamant they wanted to use all five of each. For each, they considered and discussed the best placing. Their familiarity with the game ensured that in each case the positioning could be discussed with insight, rather than just slapping the snake / ladder down more or less randomly. Naturally we used blutack to position the snakes and the ladders rather than gluing them into permanent positions.

So we were now pretty well ready to actually try our game out. We agreed we all wanted to use the same simple rules (that you start off the board at position 0, there’s no need to throw a Six to start, and the first to reach or pass square 36 would be the winner).

Their decision to use all the snakes and all the ladders that we’d made, and their positioning of them, was triumphantly vindicated. Their ladder on 16 led to a snake on 22, which in turn sent them to a further ladder at 12, which invariably caused great delight. And the fact that our board had just 36 squares meant that games didn’t drag on – a typical game lasted under five minutes.

But I had one more trick up my sleeve, and this was the one that ensured our game became a high-quality investigative experience. I rolled the die three times, getting throws of 4, 6, and 1. If I use these throws in order I end up on square 5. But what If I can choose the order in which I use these three throws – can I get to 20 or even beyond?

So we now have an activity of almost limitless flexibility. I might give you four throws (say, 2, 3, 5, 5) to explore. Or I can ask you how far you can reach if I let you choose your own set of three throws. And what’s the smallest set of throws that will let you win the game?

And of course, as soon as we reposition any of our snakes and ladders we’ve got a whole new set of situations to explore.

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# A Productive Conversation With Susie

I was helping out in the class of a friend, and she asked me to have a word with Susie, sitting at the back of the class. It’s a long time ago now, and I can’t begin to recall what the problem was, but I do know our conversation went pretty much like this:

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Susie: Can you help me please? I can’t do this one.

Alan: Let’s have a look at it. What’s the problem?

S: I can’t do any of it.

A: OK. Well, how do you think you might start?

S: (Pause, then) Well, I suppose I could ….

A: That seems a good idea.

S: But what do I do next?

A: What do you think you could try?

S: (Pause, then) Well, I might do ….

A: OK

S: But what then?

A: Well –

S (Pause, then huge, radiant, smile): Oh, I see! It’s OK! I’ve got it now! Thank you so much!

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Now I’d no wish to destroy Susie’s conviction that I’m the greatest maths teacher that ever lived, but I’d not said one insightful word about the problem. I’d not even needed to look at it – all I’d needed to do was lend an ear and a little encouragement. Any teacher, or any parent, could have done the same.

And the message? Well, an obvious one is that Susie got far more satisfaction from solving the problem herself than if I’d said “First you do this, then you do that, …”. But the bigger one for teachers and pupils is that seeing maths as a subject that has to be done at a hundred miles an hour does nobody any favours. The biggest factor in Susie’s success was being able to think her own way through the question without pressure and in her own time.

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It was Denise Gaskins in her blog Let’s Play Math ( http://letsplaymath.net/about/ ) who reminded me about Susie. Denise posted a famous clip of a couple of primary pupils tackling a problem about fractions, and if you’ve got 6½ minutes to spare you can see the video at https://www.youtube.com/watch?v=Q-yichde66s

It’s a very similar message – that by giving the girl and boy the time to tackle the problem (and the resources to do so practically) followed by the opportunity to talk about it at their own pace you get a depth of learning that goes far beyond giving them a batch of mechanical rules.

Here’s what Denise had to say: http://letsplaymath.net/2014/08/13/fractions-15-110-180-1/

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# A School Visit

I’ve always been heavily involved with the Key Stage 2 Tests. I’m a senior member of the marking team, I’ve been involved in pre-testing and post-testing, I’ve been a member of the question-writing team, and I think I’m the only civilian ever to lead the evaluation of national pupil performance. I’m often asked to take trial papers into schools so the authorities can try out questions and whole papers.

At the end of the summer term in 2013 I made one such trial visit to a school which was happy to be involved in the pre-testing. It was an unforgettable experience and I couldn’t stop thinking about it and talking about the school for days afterwards. The intake and area seemed unremarkable but everything else was little short of amazing. The school invariably has terrific results in the Tests, but there was every indication these were gained through high expectations, excellent relationships between and among staff and pupils, and exceptional teaching.

I spent a morning with the Year 6 class. This was a mixed-ability group – though only in the sense that half the class were at level 5 and the other half at level 6 (if you’re not used to English levels, level 5 corresponds to the highest-rated standard – and level 6 goes beyond that, i.e. exceptional).

After the children had sat the trial test the teacher insisted (unlike the school I visited the following day, where the teacher couldn’t have been less obliging and couldn’t get me out of the door quickly enough) that I spend the rest of the morning talking with them and giving them feedback and further ideas. They were brilliant, full of enthusiasm and suggestions of their own, mutually supportive, and highly articulate even though most came from families who’d only arrived in the country in the last generation or two. When was the last time a primary school pupil said “That’s an example of litotes, isn’t it?” when you were speaking to pupils, and then kindly explained it for you?

It was as near magical an experience as I ever wish to have. The Head asked me to sign the visitors’ book, and I noticed that a few days before Her Majesty’s Chief Inspector of Schools had visited and enjoyed himself just as much as I had. I don’t blame him for pointing out that here was a school which you might have expected to be unremarkable yet was producing the very highest standards, and doing so not by rote learning and teaching to the test but by a culture of high expectations and mutual support.

It was a wonderful visit and I felt a little guilty I’d been paid for the experience.

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A few weeks later I opened the paper and saw the school’s name mentioned. I assumed I was going to read of its usual performance at the very top of the national rankings. No, it wasn’t that at all. The school, or someone within it, had been found guilty of Maladministration – in other words, fiddling the answers (and since I’m usually involved in the reviews and appeals panel I know we do find a few examples of some very dubious behaviour every year).

So the school’s results were cancelled and the school has been removed from the most recent performance tables. The reputation of the whole school is tarnished and careers are ruined. Of course, I don’t know what the misdemeanours were. But what I do know is that I was invited into that school and made welcome by the Head and the Year 6 teacher and class. Every moment of the morning made it clear that those pupils had been magnificently prepared for secondary school by the school and their teacher. And I also know that the most exciting and joyous school visit I’ve ever made turned out to be the saddest.

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# It’s Official: England’s Performance Is Among The Best In The World

That’s a headline you didn’t read this week, which is a great shame, not least because it’s actually true.

Given their normal degree of accuracy and fairness I suppose it’s no surprise to see newspaper headlines like “Britain’s Stagnating Schools”, and “Anxious UK Pupils Lag Behind In Maths”. Most of our newspapers don’t need much excuse to beat up teachers, and they used the PISA reports to blast away at everything in sight.

No-one seemed to try very hard to make it clear that the information wasn’t gleaned across the whole school system, but related to tests given to 15-yearolds. Now in actual fact, pupils in primary schools in England really score rather highly in tests, regularly featuring in the top ten or better. I’ll say that again, in case any reporters are listening – primary pupil performance in England is “Very good”. I know that, because those are the words Stefano Pozzi – who’s the senior official at the DfE most responsible for leading the development of the new National Curriculum – used when he talked to a dozen of us earlier this year. The official NFER report states that “England’s performance at year 5 is amongst the best in the world and continues to improve”.

One of the countries we’re often enjoined to imitate is South Korea. There are lots of reasons why the Pacific Rim countries have such success rates, but I’m pretty certain one of the biggest is the culture that means that a quite astonishing 1.7% of the national GDP is spent on out-of-school additional tuition. That’s a cost equivalent to 80% of the total government expenditure on primary and secondary education. I suppose that as a One-To-One tutor I’m programmed to be particularly interested in this, but nearly three-quarters of South Korean children receive an average of seven hours a week of extra tuition; the government has recently been forced to pass a law that requires tutoring institutions to close by 10pm – otherwise students might still be studying in them at 1am.

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# Chess In Schools and Communities

Recently I was invited by Chess In Schools and Communities to talk to them about National Curriculum mathematics and I spent a delightful day with an inspiring group of people. CSC have a project in which a chess tutor works alongside the Y5 teacher for a lesson a week; their task is to teach the children chess and the project will be evaluated to see if there is an effect on the children’s mathematics learning. A separate project at Manchester Metropolitan University has already found some very positive suggestions that Y3 chess-players did substantially better when given a test involving non-verbal reasoning, maths, and problem-solving questions.

There are some areas of the Y5 programme of study where mathematics can clearly draw benefits from chess – co-ordinates, symmetry, translation. Even more obvious are the links with the problem-solving thinking we’re accustomed to call Using And Applying Mathematics, where the current Y5 curriculum requires children to “Solve problems …, Explore puzzles, find / confirm solutions …, Plan and pursue an enquiry …, Explore patterns and relationships, …, Explain reasoning, …”.

I’ve spent a lifetime using games in the classroom, and I suggested that using games offers four main benefits. A game like chess contributes to all four, and the maths classroom will draw particular benefits from the third and the fourth:

…… Games have a socialising value – children need to take turns, win and lose with grace, abide by the rules and the etiquette,

……Games are part of our cultural heritage (chess, cards, dominoes, backgammon, …); and from outside the UK chess itself, and Go, mancala, …. ,

……Games give enjoyment, and an environment in which children can accept high levels of challenge,

……Playing a game requires skills of observation, analysing, forming a plan, asking “What happens if?” These have a very high correlation with the skills used in Using and Applying Mathematics.

You can find out about CSC at http://www.chessinschools.co.uk/

http://educationendowmentfoundation.org.uk/projects will give you information about the research project.

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# Calculators

*** In a Y4 classroom I asked children to put 8 into their calculator and add on the number which would make it display 20. I then asked them to work in pairs and use their own numbers. Every pair was able to choose the target that suited them – within 15 minutes one pair was playing to 1000, with the rule that their numbers must have at least three places of decimals!

*** If all the number keys except the 3 and 4 have fallen off your calculator how can you make it display numbers like 10?

*** Paul, aged 6, and not of exceptional ability, told me “I do experiments with my calculator; I see what happens when I multiply numbers by 99”. I set him the challenge of finding two two-digit numbers whose product is 7326, and he refused to go out to break until he’d found them.

*** I have a special calculator that the manufacturers call the “Wrongulator”. If you ask it the answer to 4×4 it shows 11. For 22-8 it shows 9. What do you think it displays for 27+19?

The obvious thing that calculators do is give the answer to sums. From there it’s a very short step to say that they impede mental and written arithmetic. But in each of the cases above, ask yourself where the arithmetic is actually being done, and then you get a different perspective. All the arithmetic is being done by the children, and being done mentally; the calculator’s rôle is providing feedback on the work already done in the head. In the Y4 classroom no teacher can possibly give instant feedback to fifteen pairs of children each working at a different problem (and what teacher has ever dared ask children to do six- or seven-digit mental arithmetic?). Similarly, without the stimulus of the calculator could I ever have expected a 6-yearold to be able to handle multiplication by 99? The “Broken Calculator” activity is so well-established that a Google search locates more than 47 000 000 hits. And my Wrongulator turns the conventional situation around so that you have to think what the answer should be, rather than what answer it actually displays.

Each of these activities makes it clear that the calculator has the potential to stimulate and enhance children’s mental arithmetic rather than stunt it. It’s now approaching thirty years since since Hilary Shuard’s CAN project demonstrated that when primary children had unrestricted use of a calculator their arithmetical understanding and fluency were not handicapped but greatly improved. In an allied project in Hertfordshire we found this was true not just for junior school children, but for all ages from Early Years through secondary.

Policy-makers are happy to encourage schools to spend thousands and thousands on computers and allied equipment, but ignore the proven benefits of the simplest piece of IT, which every child has in their pocket on their mobile phone. We have a quasi-religious attachment to traditional algorithms for long division, etc. Why stop there? After all, at school I had to learn an algorithm for extracting square roots, and even once encountered the corresponding method for cube roots!

I often read superficial arguments that calculators necessarily reduce mental exercise (not true – see the examples above) and that mental exercise is analogous to physical exercise. Maybe it is, but anyone who advances that view to me is liable to be asked whether they do their washing by taking it down to the river bank. Everybody knows that the traditional way of washing is by banging it with stones, but having a washing machine makes it possible to wash more things more efficiently, and make more time to do other things.

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# Education Endowment Foundation

You may not have come across the Education Endowment Foundation. I’m pretty sure the Secretary of State hasn’t, because otherwise I rather doubt he’d continue to fund it – many of its findings are likely to be unpalatable to him and his colleagues.

In its Toolkit the EEF looks at all the research relating to a number of teaching initiatives and quantifies their effects. The results are given in the form of the amount of the additional months of progress pupils are likely to make in a year as a result of the approach being used in school.

**Feedback**, and **Meta-Cognition and Self-Regulation** (“Learning To Learn”), are both capable of adding as much as eight months of progress. **One-To-One Tuition** is one of a further half-dozen strategies which can produce at least five months’ extra progress in a year.

On the other hand, **Extending the School Day**, and giving **Homework in Primary Schools** are among those policies which generate only small benefits, while **School Uniform** results in no added progress.

Some initiatives actually have negative effects. Using **Ability Grouping** may result in progress on average being *reduced* by a month, while requiring students to **Repeat A Year** has the worst results of all the 30+ strategies surveyed; not only is it an expensive initiative, but after one year, students who are required to repeat are four months behind those who move on.

http://educationendowmentfoundation.org.uk/toolkit

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