Yet another Coalition education screw up

[bb21]

Can someone tell me why the new Education Secretary thinks the ability to perform long multiplication and division is a key skill these days, and at the age of 11? What does she think the ability to perform long division demonstrates?

Has she never heard of calculators?

Has she never heard of other methods to multiply and divide?

If she were so clever, perhaps she could demonstrate how to square root 1343853453478151 using long division by hand. (Yes, before anyone asks, hand square rooting is also a form of long division.) Clueless woman. :roll:

 

[GatwickDepress]

It's almost like there's an election coming!

 

[bb21]

It's almost like there's an election coming!

Cynical you.

That may be the reason. We shall see.

It's just that gibberish and incoherence coming from an Education Secretary always makes me angry.

 

[ExRes]

Politicians will never put things over properly or without a (self serving) reason, I do agree though that children need to learn the basics and be able to use their brains, it seems that for the past few years we've bred far too many school leavers with no idea whatsoever of basic mathematical or grammatical ability, take away the iphone or whatever and you have an educational vacuum of frightening proportions

 

[Bletchleyite]

Can someone tell me why the new Education Secretary thinks the ability to perform long multiplication and division is a key skill these days, and at the age of 11? What does she think the ability to perform long division demonstrates?

While being in IT I tend to have a calculator to hand on the PC and one on my phone as well, it isn't unknown for me to use basic forms of these to work stuff out quickly. Though it's more likely to be an estimating approach rather than an exact one, and it's less likely to be on paper.

On a slightly different front I've sort-of lost count of the number of times I've seen someone on the till in a shop baffled at me handing over something like £12.01 for something costing £7.01 where I haven't got £7 in coins nor a fiver (that is so I can have a fiver change rather than a load of coins, easier for both me and them), then they key it in the till and get a Eureka moment as they work it out, so maybe mental arithmetic does need more weight. That said, cash is becoming ever less important...

Actually, do they even teach the additive method of giving change (where the shop assistant counts up as they do)? I haven't heard that in a while. I guess mostly they don't need it in a shop, but it is a very quick and efficient method of checking your change.

Neil

 

[Oswyntail]

....
Has she never heard of calculators?

Have you never heard of machine failure?

....Has she never heard of other methods to multiply and divide?.....

Probably, but emphasised the tried and trusted.
These are basic skills that are used every day (shopping, cooking), and having to rely on a calculator is counter-productive. Once learned, the techniques can be applied anywhere, at any time.

 

[Busaholic]

For my exceedingly short-lived spell as a croupier on the roulette table I had to learn 13 and 17 times tables up to the power of 20 to enable prompt pay-out of the correct number of gaming chips. I am happy to say I have now completely forgotten these except in nightmares!

 

[bb21]

Have you never heard of machine failure?

Probably, but emphasised the tried and trusted.
These are basic skills that are used every day (shopping, cooking), and having to rely on a calculator is counter-productive. Once learned, the techniques can be applied anywhere, at any time.

Calculators are just one example. There are plenty of tools out there these days - mobile phones (which all have calculators installed these days), computers, tablets, etc.

Everyday arithmetic does not require long multiplication and long division. How many people perform such operations on a day-to-day basis?

Times tables are important, in addition to that, estimation skills.

What does learning long multiplication/division at the age of 11 achieve, when most of the pupils will not understand why it works?

 

[Bletchleyite]

Times tables are important, in addition to that, estimation skills.

Agreed. Actually on that one, remembering back to school, we were taught estimation, but not in a way that makes sense - we were told to round the numbers off and estimate longhand! It was only several years later I realised what the point was (and indeed use it all the time).

What does learning long multiplication/division at the age of 11 achieve, when most of the pupils will not understand why it works?

I can see your point. I don't learn effectively by rote - I have to understand why.

Neil

 

[Oswyntail]

Calculators are just one example. There are plenty of tools out there these days - mobile phones (which all have calculators installed these days), computers, tablets, etc.

Yes, and the more complex they are, the more likely to fail. I would also guess that, in an everyday activity like shopping, you are unlikely to be carrying around the full arsenal

Everyday arithmetic does not require long multiplication and long division. How many people perform such operations on a day-to-day basis?

How does the unit price of a pack of 30 tesco value eggs @ £3.75 stack up against Morrissons 2 dozen at £3.20?

Times tables are important, in addition to that, estimation skills.

And what do estimation skills rely on?

What does learning long multiplication/division at the age of 11 achieve, when most of the pupils will not understand why it works?

Unless you are delving into deep philosophy, the "why" is the clearest part of how these techniques are taught (traditionally, of course)

 

[bb21]

Yes, and the more complex they are, the more likely to fail. I would also guess that, in an everyday activity like shopping, you are unlikely to be carrying around the full arsenal

A phone? How often does a phone fail?

Are you seriously telling me that anyone would be taking out a pen and paper and do long mults/divisions in the street? Or are you telling me that they would be performing it in their head?

How does the unit price of a pack of 30 tesco value eggs @ £3.75 stack up against Morrissons 2 dozen at £3.20?

And you are going to take out your pen and paper in the supermarket to work out unit prices?

Look at the price label is what most people will do.

Otherwise use estimates:

Tesco: 30 for £3.75, 3 for 37p, so about 12p each (and under 13p each for those more advanced).

Morrisons: 2 dozen for £3.20, 1 dozen for £1.60. If you know your times table, 12 x 12 is 144, a fair way short of £1.60 (add another 12 and it will still be under £1.60, so over 13p each, for those more at ease with numbers).

Morrisons therefore more expensive. In fact, with the difference so minute per egg, I'd wager that most people would not care. 30 for £3.75 and 24 for £3.20 are about similar ratios.

Alternatively,

Tesco: 30 for £3.75, so 3 for 37p. 30 less two lots of 3 is 24, so 24 would be about 80p less, therefore £2.95.

Again, Morrisons more expensive.

If you care about the price difference to the last penny or tenth of a penny, you would bring calculation aids with you.

And what do estimation skills rely on?

Times tables.

How many significant figures do you think estimates rely on?

Unless you are delving into deep philosophy, the "why" is the clearest part of how these techniques are taught (traditionally, of course)

At age 11, and most likely before then if the requirements set out by the Education Secretary were to be met?

How many kids at 11 will understand why? There is no point teaching them why if they cannot understand it.

 

[deltic]

Can someone tell me why the new Education Secretary thinks the ability to perform long multiplication and division is a key skill these days, and at the age of 11? What does she think the ability to perform long division demonstrates?

Has she never heard of calculators?

Has she never heard of other methods to multiply and divide?

If she were so clever, perhaps she could demonstrate how to square root 1343853453478151 using long division by hand. (Yes, before anyone asks, hand square rooting is also a form of long division.) Clueless woman. :roll:

I deal with numbers all the time at work and the ability to understand and estimate likely answers is vital. All too often junior staff will come and tell you the answer is x and you tell them it cant be and they say that's what their spreadsheet or calculator says it is. When you get them to go back and check they find they entered a number wrong etc.

Mental arithmetic is in many areas of life a very useful skill.

 

[bb21]

Mental arithmetic is in many areas of life a very useful skill.

Absolutely, and I fully support that.

That is why estimate skills are vital.

This is very different to the requirement that every pupil be able to perform long multiplication and long division.

 

[Oswyntail]

... Or are you telling me that they would be performing it in their head?....
How many kids at 11 will understand why? There is no point teaching them why if they cannot understand it.

Well yes, actually!
At my small village primary school (many years ago!) we were all taught LM and LD in the traditional way, understanding as much as was needed (based on the THTU structure of decimal numbers). The technique was instilled, and like so many techniques learned at an early age, became second nature. No, I cannot work out square roots in my head, because I was taught that technique later, but there again I rarely have to calculate the square root of anything.
As it happens, I struggled with LM at first, so I was certainly no maths prodigy. In later years, however, when sitting Accountancy in the AIB, I was not completely sunk when the calculator I was using began giving random answers because of low battery. If you have never had a phone that has failed, you are one in a million.

 

[underbank]

I think some of the comments in this thread demonstrate the sheer amount of mistakes I see in spreadsheets and invoices created by my clients of my accountancy practice.

Things which would be glaringly obvious if the person doing it used their brain rather than their keyboard.

Like it's bleedingly obvious that 20% VAT on a £100 invoice isn't £2.

Or that a small column of 5 figures, each of which is tens of pounds can't possible add up to less than £50.

So hilarious to see how the staff in our local Spar shop managed in a power cut. They hadn't a clue and couldn't add up more than a couple of items in their heads, and failed miserably in working out change. However it was business as normal in the pie shop next door who had older staff who managed to add up several items in their heads and had no problem with change.

 

[Bayum]

Can someone tell me why the new Education Secretary thinks the ability to perform long multiplication and division is a key skill these days, and at the age of 11? What does she think the ability to perform long division demonstrates?

Has she never heard of calculators?

Has she never heard of other methods to multiply and divide?

If she were so clever, perhaps she could demonstrate how to square root 1343853453478151 using long division by hand. (Yes, before anyone asks, hand square rooting is also a form of long division.) Clueless woman. :roll:

As with any other skill that isn't taught for long periods, the skill would die out.

I don't agree with it being made compulsory that long division and multiplication are the only ways that children should be taught to multiply and divide, but I do agree that it should be taught alongside a range of other methods and children should be allowed to use the method they prefer.
--- old post above --- --- new post below ---

While being in IT I tend to have a calculator to hand on the PC and one on my phone as well, it isn't unknown for me to use basic forms of these to work stuff out quickly. Though it's more likely to be an estimating approach rather than an exact one, and it's less likely to be on paper.

On a slightly different front I've sort-of lost count of the number of times I've seen someone on the till in a shop baffled at me handing over something like £12.01 for something costing £7.01 where I haven't got £7 in coins nor a fiver (that is so I can have a fiver change rather than a load of coins, easier for both me and them), then they key it in the till and get a Eureka moment as they work it out, so maybe mental arithmetic does need more weight. That said, cash is becoming ever less important...

Actually, do they even teach the additive method of giving change (where the shop assistant counts up as they do)? I haven't heard that in a while. I guess mostly they don't need it in a shop, but it is a very quick and efficient method of checking your change.

Neil

It depends on where you come from, your education and inhouse training I guess. We still teach the 'count on up' method with money and change, but I also recognise that some of my class prefer to take away and find the amount of change that way.

 

[theblackwatch]

When I worked at Safeway (which was in 1987-89, scary...), we were expected to 'count up' people's change. I can't remember the last time I heard a staff member in a shop count my change back to me, or anyone else for that matter. Admittedly, a lot more people pay by card now than what they did years back though.

I don't think I could remember how to do long division now - but I can still remember my 12x tables off the top of my head!

 

[fowler9]

In the end if you want to learn, you will. The biggest problem in this country is kids who don't want to learn.

Neil

I don't agree with that at all. Why would kids just not want to learn unless someone had taught them not to bother?
--- old post above --- --- new post below ---

I would honestly say it was easier back then. Looking at science exam papers today, I would certainly say I would have gotten one or two grades below the original grade if I had attempted it back then.

I am of opinion that the grade inflation "problem" is mainly attributed to students becoming even more educated than before and there are even more resources on the internet to go over the bits you don't understand.

Medicine school is becoming even more competitive. Few years back then, you could get in if you worked hard. Nowadays, having ability not to procrastinate until last minute and is willing to work hard isn't enough to get you in.

You need also to be one of those kids who simply breezes through secondary school with good grades without having to work hard and works hard through A-Levels and medicine school exams with a cut-off set at much higher level than before.

I wouldn't say this is true at all. When I took A Level maths we used O level maths past papers to practice with. When I started studying A level Chemistry we were told that all the stuff we got taught at GCSE was bobbins. And I went to a "good" school.

 

[Tom B]

When I worked at Safeway (which was in 1987-89, scary...), we were expected to 'count up' people's change. I can't remember the last time I heard a staff member in a shop count my change back to me, or anyone else for that matter. Admittedly, a lot more people pay by card now than what they did years back though.

I don't think I could remember how to do long division now - but I can still remember my 12x tables off the top of my head!

Yes, I've also noticed that it's quite rare for shop staff to count change back to you now - and I was born when you left Safeway!

 

[TheKnightWho]

not what I have been told , but then this was by someone who handles admissions for a course where they receive up to 8 applicants for every place so obviously they have to use numerous criteria to sift down to a manageable number of candidates before final offers are decided upon .

I've specifically had experience with Oxford applications, which have the large assumption that most candidates are more than capable of coping with the actual course itself. They just want to ensure they have the best.
--- old post above --- --- new post below ---

And you are going to take out your pen and paper in the supermarket to work out unit prices?

Look at the price label is what most people will do.

Otherwise use estimates:

Tesco: 30 for £3.75, 3 for 37p, so about 12p each (and under 13p each for those more advanced).

Morrisons: 2 dozen for £3.20, 1 dozen for £1.60. If you know your times table, 12 x 12 is 144, a fair way short of £1.60 (add another 12 and it will still be under £1.60, so over 13p each, for those more at ease with numbers).

Morrisons therefore more expensive. In fact, with the difference so minute per egg, I'd wager that most people would not care. 30 for £3.75 and 24 for £3.20 are about similar ratios.

Alternatively,

Tesco: 30 for £3.75, so 3 for 37p. 30 less two lots of 3 is 24, so 24 would be about 80p less, therefore £2.95.

Again, Morrisons more expensive.

If you care about the price difference to the last penny or tenth of a penny, you would bring calculation aids with you.

There's a more efficient way than either of those:

Tesco's are 65p extra for an extra 6 eggs. That would be ~11p extra per egg. Morrison's are clearly more than 11p per egg, and so Tesco's must be cheaper.

(This is similar to your second method, but you don't have to add/subtract so many awkward numbers.)

 

[Abpj17]

Can someone tell me why the new Education Secretary thinks the ability to perform long multiplication and division is a key skill these days, and at the age of 11? What does she think the ability to perform long division demonstrates?

Has she never heard of calculators?

Has she never heard of other methods to multiply and divide?

If she were so clever, perhaps she could demonstrate how to square root 1343853453478151 using long division by hand. (Yes, before anyone asks, hand square rooting is also a form of long division.) Clueless woman. :roll:

Maths isn't actually all about the numbers/answers as I suspect you know Over reliance on calculators doesn't make you numerically literate - which is really important for, for example, understanding statistics (probability, polls etc.) and finances (savings, loans, discounts etc.).

And the ability to solve complex puzzles and analyse problems is a pretty vital skill for most knowledge workers.

There is a reason that maths is one of the degrees with the highest employability rates.

(On the shopping stuff, tbf, I just shop online at ocado where the price per unit is conveniently displayed

...and what my dad did in the early 70s at O-level is what I did in the mid-90s at A-levels - I had copies of his text books so it was pretty obvious)

 

[Metrailway]

I think some of the comments in this thread demonstrate the sheer amount of mistakes I see in spreadsheets and invoices created by my clients of my accountancy practice.

Things which would be glaringly obvious if the person doing it used their brain rather than their keyboard.

Like it's bleedingly obvious that 20% VAT on a £100 invoice isn't £2.

Or that a small column of 5 figures, each of which is tens of pounds can't possible add up to less than £50.

So hilarious to see how the staff in our local Spar shop managed in a power cut. They hadn't a clue and couldn't add up more than a couple of items in their heads, and failed miserably in working out change. However it was business as normal in the pie shop next door who had older staff who managed to add up several items in their heads and had no problem with change.

I completely concur with your comments. I work with clients (and sometimes their accountants) and do find the number of basic numerical mistakes I see staggering.

I find that the older the person, the maths tends to be better. I say this as a mere 'twentysomething'.

 

[Bletchleyite]

I don't agree with that at all. Why would kids just not want to learn unless someone had taught them not to bother?

You might have hit the nail on the head with the latter, it isn't seen as "cool" to be good at school, which is a perception that could do with changing. That said, perhaps technology and the fact that many (most?) young people like working with it will change that in some way.

Neil

 

[maniacmartin]

Someone I know has a calculator that has a percentage button and lets you type things like 100 + 20 %, which would yield 120. Rather confusing syntax if you ask me, but apparently its intuitive.

Cue her turning gross prices to net by typing 100 - 20%, and not being able to understand my explanation as to why this will subtract the wrong 20%.

 

[bb21]

Well yes, actually!
At my small village primary school (many years ago!) we were all taught LM and LD in the traditional way, understanding as much as was needed (based on the THTU structure of decimal numbers). The technique was instilled, and like so many techniques learned at an early age, became second nature. No, I cannot work out square roots in my head, because I was taught that technique later, but there again I rarely have to calculate the square root of anything.

Then you (and your classmates) must be one of the brighter ones at it. At all the schools I taught (which are by no means low achieving), plenty of 12 and 13-year-olds struggle with it.

But none of that is important.

The central issue remains the question I asked earlier. What skills are we teaching them through long multiplication and long division? What objectives (among the ones you gave above) cannot be achieved through a better understanding and application of estimate skills (which are far more important and useful)? Why should long multiplication / long division be made compulsory over other methods to perform manual calculation, many of which far more intuitive than these ones?

As it happens, I struggled with LM at first, so I was certainly no maths prodigy. In later years, however, when sitting Accountancy in the AIB, I was not completely sunk when the calculator I was using began giving random answers because of low battery. If you have never had a phone that has failed, you are one in a million.

That has no relevance to the world we live in today. Are we teaching them long multiplication / long division to perform better in exams, or to give them essential life skills which they can use?

How often do you find yourself in a work/life situation these days with all calculation aids died out and needing to perform high-precision calculation, with no access to any help whatsoever?

I would even go so far as to say that if one needs to perform long multiplication / long division on a regular basis in a work environment, not using a calculation aid is stupidity, as time wasted on doing it manually can be better spend improving productivity in other respects.

I don't agree with it being made compulsory that long division and multiplication are the only ways that children should be taught to multiply and divide, but I do agree that it should be taught alongside a range of other methods and children should be allowed to use the method they prefer.

That I absolutely agree with.

Children should be taught various skills - diagonal method, line method, point method, box method, etc. Some find certain ones easier and others find other ones easier. They all serve the same purpose, so why should it be compulsory that everyone be judged against the same prescribed method, which for all purposes can be argued to be something with very little practical use in today's world?

There's a more efficient way than either of those:

I knew some clever dick will find a better way, but you see my point. There are various approaches.

Maths isn't actually all about the numbers/answers as I suspect you know Over reliance on calculators doesn't make you numerically literate - which is really important for, for example, understanding statistics (probability, polls etc.) and finances (savings, loans, discounts etc.).

I agree, that is why estimate skills are so important. It gives you a sense of proportion, size, and helps make it possible to make quick and informed decisions.

I am not advocating complete reliance on calculators (indeed that would be completely wrong and counter-productive), nor am I saying that manual calculation methods should not be taught. I simply do not agree that one particular method which sees very little practical use in today's world be give such prominent status.

And the ability to solve complex puzzles and analyse problems is a pretty vital skill for most knowledge workers.

There, my friend, you have nailed one of the biggest failures of today's mathematics education in the secondary and further education sector, and has been for a great many years. Mathematics has very little to do with numbers, yet very little emphasis is placed on teaching students how to approach problems and analyse them, how to break a question down, how to construct the arguments they use in a logical and coherent manner, etc.

The standards of some of the freshers are truly shocking (but obviously standard vary with some who are very good), even those who got A's at A-Level. Plenty of them cannot string together a couple of coherent arguments, and plenty cannot recognise a question if worded or presented slightly differently. Every year we end up spending the first few weeks re-teaching them the most basic things they should have learned and remembered, and should be rolling off the top of their head. Did their colleges train them to answer exam questions (which they would inevitably forget once the exams were done), or did they teach them how to dissect a problem and understand it?

Someone I know has a calculator that has a percentage button and lets you type things like 100 + 20 %, which would yield 120. Rather confusing syntax if you ask me, but apparently its intuitive.

Cue her turning gross prices to net by typing 100 - 20%, and not being able to understand my explanation as to why this will subtract the wrong 20%.

You'd be surprised how many people don't realise that adding 20% then subtracting 20% will not give you the same number you started with.

 

[Bayum]

Just read Cameron's latest proposal for schools. Unfortunately the prime minister seems to think that teachers are trying their hardest to get as little progress out of their students as possible. But instead of offering support, which schools are in desperate need of, he wants to palm them off to academy chains to save 'the public purse' no doubt.

I fail to see how standards are expected to be moved when there seems little support from government and a media rhetoric that galvanises schools as the bad ones.

 

[bb21]

I refuse to comment on general government policies on education these days, only specific items, as I can feel my blood boil just thinking about them. Whenever I discuss these matters with close friends, I end up using expletives on a more and more frequent basis, which are not suitable for general viewing on the forum.

Suffice to say that since Ruth Kelly, the government has been getting very little right imo, with very few policies genuinely intended for raising standards rather than being populist, headline-grabbing and ideology reinforcement, be it Labour or the Tories. (I am not surprised. You don't see the full impact of education policies until at least a decade down the line, mostly probably longer, by which time the incumbent will be long gone.)

 

[tony_mac]

Why should long multiplication / long division be made compulsory over other methods to perform manual calculation, many of which far more intuitive than these ones?

I wouldn't take the details too seriously, it's just another populist soundbite

plenty cannot recognise a question if worded or presented slightly differently.

That's what I thought about the Sheffield 'impossible' economics exam -

http://www.independent.co.uk/student/news/university-of-sheffield-students-demand-investigation-over-highly-unfair-exam-10014553.html
There doesn't seem to be anything difficult, just terms that the students didn't recognise.

Did their colleges train them to answer exam questions (which they would inevitably forget once the exams were done), or did they teach them how to dissect a problem and understand it?

That's a problem with the current regime of results, inspections, and change of management forced upon 'failing' schools - there is so much incentive to improve results at the cost of any real education.

Schools also seem to be held weirdly accountable for the results and behaviour of their students, as if they should have some mind-control ability.
http://www.theargus.co.uk/education/11750616.Governors_condemn_Ofsted_inspectors_for_marking_school_down_for__gay__slur/

 

[GatwickDepress]

I remember our maths was taught from great big 1980s textbooks. Not an issue, but this was in 2008/9! Problems involving cricket scores or billiards weren't understood by most...

Cynical you.

That may be the reason. We shall see.

It's just that gibberish and incoherence coming from an Education Secretary always makes me angry.

Do I get a prize if I'm right?

Being from a teaching family, I can sympathise and agree with that. The political posturing, ideologues, and general nonsense an Education Secretary spouts can spout does make one reach for the sugar pills!

 

[Oswyntail]

Then you (and your classmates) must be one of the brighter ones at it. At all the schools I taught (which are by no means low achieving), plenty of 12 and 13-year-olds struggle with it....

As I said, small village school, with a full range of ability and achievements. My wife, similar vintage, had the same experience in her school in Borehamwood, with the same mix of children. So it worked with small and large groups across the ability spectrum. Could it be down to a better teacher, with faith in her methods and understanding?

Children should be taught various skills - diagonal method, line method, point method, box method, etc. Some find certain ones easier and others find other ones easier.

Except that the visual methods such as you describe do require pencil and paper, and so are unsuitable for many contexts. To my mind the more graphic approaches are more confusing to children who are capable at a very early age of grasping procedures and implementing them. It is patronising, IMHO, to think that you have to explain everything graphically.