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"In my day" - has the country got better at maths?

Discussion in 'Mathematics' started by PaulDG, Jul 10, 2011.

  1. PaulDG

    PaulDG Occasional commenter

    The thread on percentages had me musing back to my first job.

    One of the purchasing assistants there just didn't understand reverse percentages either. With her desk top calculator, she simply deducted 12.5% to find the pre-VAT (which was 12.5% at the time) price of items.

    But thinking about it, she almost certainly didn't have an O level in maths.

    These days, she'd have that GCSE A*-C, but she still wouldn't be able to do reverse percentages.
     
  2. Its not even up for debate. The suggestion of standards of maths at any level in the mainstream being equal to that of decades before is not IMO something up for discussion.

     
  3. DeborahCarol

    DeborahCarol New commenter

    Anecdotal.
    I remember my 80 year-old grandmother (don't know about her maths qualifications, but she became a maid at 14) totting up for a restaurant bill in her head faster than any of the rest of us could do it.
    A A Milne - Christopher Robin at age six was reciting a poem to help him learn his tables. Included upper tables!
     
  4. googolplex

    googolplex Occasional commenter

    Top end standards lower. There's no question about this - as Betamale says, not even open for debate. There's no way the current GCSE and A-level push kids as far as they used to, which is how they've become more inclusive qualifications.
    Far less emphasis on numeracy for the masses, together with an encouragement to fiddle with understanding giving students a flimsy choice of strategies rather than learn a rock solid routine; this has led to a whole generation of kids who just don't have an efficient strategy for performing basic numerical routines.
    However, it's not all doom and gloom. I would argue that a more inclusive A-level is good for being more accessible to all - there's certainly a much bigger uptake now than at any stage in the last 10 years - that's got to be good. But there's still a hell of a way to go.
    Also, at GCSE a far greater proportion of kids get access to higher tier topics than was the case in the 1990s and, given the exclusivity of the previous O-level, I would guess in previous decades as well.
     
  5. David Getling

    David Getling Lead commenter

    Many years ago there was less job choice for highly numerate graduates. Therefore it's possible that more of them ended up as maths teachers.

    While I'm not claiming it as fact, one might certainly hypothesise that the fall in maths standards might show a correlation to the ability of those teaching it.
     
  6. Anonymous

    Anonymous New commenter

    I understand GCSEs have got easier.What I am more interested is the maths ability of the whole population. How would a cohort of 16 year olds in the 1950s compare to a cohort today? How many in the 50s would take exams? What about those who didn't take exams - what was their ability like?
    I'm not so much interested in the exams - more the country's overall maths ability. Were things better- granted anyone who can do pounds, shillings and pence must have some ability!
     
  7. googolplex

    googolplex Occasional commenter

    You imply there was a halcyon era when maths teaching was so much better.... When exactly?!
    I was at a grammar school in the 1970s. Top "whatever percent" (as we were constantly told). Three maths teachers. One superb - an absolute inspiration for me. One who was a total swine and had no distinction to make between teaching and bullying. The last had absolutely no control whatsoever. Standards of teaching now by comparison? Far in excess of then if my current school is anything to go by...
     
  8. Tandy

    Tandy New commenter

    Really interesting question, Robyn. I think that the main issue to look at is what you are defining to be "maths ability"... this is at the heart of the problem, and at the heart of much of what is about to go wrong with mathematics education.
    For me, mathematics ability is the ability to take a real world problem, synthesise the information, turn it in to a mathematical model (with assumptions, approximations, etc), try to fit it to a desired outcome, then convert back in to a real world solution. In otherwords, mathematics is about being able to overcome challenges that you are faced with.
    The mathematics curriculum should, therefore, always be forward looking. We should always be trying to best guess what will be the challenges that our students (and thier children) will face in the next 50, 100, 150... years.
    The world has changed at a faster pace in the 200 years since the industrial revolution than ever before. What a child in 1600 had to know, was pretty much the same as one in 1700 (dependent on social class). But what the child of 1800 needed was vastly different to the child of 1900. And compare the child of 1900 to one of today, well they are worlds apart in the challenges they face.
    The troubld we have is that mass education systems were designed around 150 years ago, and have not changed a jot since then. Sure there are silly little reforms, playing at the periphery, but it is essentially the same system.
    Mathematics curriculum has evolved a little in those years, but not by a great deal. So we have students learning (often rote) how to undertake longwinded calculations etc, when these are now irrelvant (I do of course understand the benefits of understanding how things work, but this can be dealt with in other ways).
    We now have a really unhealthy situation (league tables have helped to create this) where people are obsessed with looking backwards in education.
    The current secretary of state (hopefully won't be around too long) is trying to force upon the nation the education that he had as a child - the narrow (rather stupid) notion that if it worked for him then it must be right. The arrogance of "well I went to a school, so I must understand schooling".
    Nick Gibb, the schools minister, upon getting his post immediately insisted that every child should be able to do long division. Really!? Why on earth would anyone want to be able to do long division? At what point in their lives will this be relevant? What use will it be in the future world? I would say none at all.
    Now, there will be folk who hurrumph over this and say "ah, but it is a good foundation for algebraic long division". Well, yes. But why on earth are we teaching that?! Why are we so insistent on holding back innovation - there are technological packages that will handle any algebraic long division you care to throw at it. And calculus, etc. The skills we should be teaching is understanding the solutions, knowing when they make sense and when they don't, being able to interpret them, and being able to apply the solutions to given situations.
    This will really hack some folk off. But it is no different to those who were really hacked off about using a calculator instead of log tables etc.

    So, what I am saying, in repsonse to your original question, is that you can't compare the "maths ability" because maths ability now means something entirely differrent.
    Kids of the 50s could do long division. Kids today can cope with multiple streams of information at the same time. Kids of the 50s could use a slide rule. Kids of today can model simple harmonic motion using computer software and video equipment. Kids of the 50s could regurgitate their tables. Kids of today can programme a spreadsheet to undertake millions of calculations in seconds.
    I know which I would rather have.
    But by bogging down the mathematics curriculum with all the tosh of the 50s child (as Gove would love to do), we are restricting the space in the curriculum that should be filled with the mathematics that the future will need. The protectionism around the mathematics curriculum is harming the life chances of our students now and in the future, as well as harming the ability of this country to compete and flourish.
    It is time to transform the mathematics curriculum not simply reform the same old one over and over and over and over...
     
  9. PaulDG

    PaulDG Occasional commenter

    No we don't.

    I happen to believe we'd be in a much better place if we did have students rote learning how to undertake longwinded calculations, but we certainly don't have that going on now!

    (BTW, I was once in the camp of "we don't need any pen and paper arithmetic now that calculators are universally available". I know better now!)
     
  10. googolplex

    googolplex Occasional commenter

    Tandy, I'm not sure I agree with you.
    Many of us who stayed awake for long enough during the labour party's costly and totally pointless trumpeting of diplomas, would have remembered them pointing to the need for a 21st century education system, where we compete with eastern economies which have more G&T students than we have students altogether, and all of that... Yet, if you examine the systems which these countries have adopted for their education, theirs' seem to be based on the very same traditional rote learning system you seem to criticise.
    I don't think required basic mathematical skills have changed much at all. ICT/Computers/Calculators have been with us for many years now but we are still trying to come to terms with them. The ability to compute without a calculator is as important now as it ever was. Having strategies for dealing with particular situations is a key part of forming building blocks upon which the rest of learning can take off. My feeling is that ICT has let us take our eye off the things that really matter, and kids in the last 20 years or so have been building their learning upon very insecure foundations.
    It isn't just numeracy, though. Algebra. In the UK, we teach equations in a couple of lessons and expect them to remain known. Our school regularly takes on students from Macau who have shown me some of their learning from home. They are streets ahead of our students in terms of their ability to manipulate algebra. Their learning was by rote, extended, over many months of lessons, and taken to a far greater depth than any of our students could ever cope with. It reminded me very much of my own experiences. Algebraic fractions, etc, are no issue for these students. How do we teach these things if we haven't already given kids a thorough grounding in fractions in the first place? And, as you mention it, I happen to think division is a key skill, as important as any other aspect of number work - and the fact that we shy away from it, on the back of technological advances, is a huge mistake.
    Our system is obsessed with equipping students with a variety of means of tackling problems, emphasising understanding and choice over methodology, repetition and confidence. They don't even end up being jacks of all trades, leave alone the master of one... I wish we could provide them with more coherent and strategies for dealing with basic mathematics - teach a few things well; by all means investigate other things afterwards. Our curriculum is far too wide, particularly at KS2-4. We also let students finish with their maths far too early. I was talking to someone from US who said that many universities in the states have kids learning a core curriculum in the first year of University - a curriculum which includes things like calculus. We need to keep all kids moving towards this outcome, and we need them to have a core of basic skills, which, yes, includes solid strategies for dealing with number - not because Gove et all have jumped on the bandwagon, but because these things are important.
    There's a place for a transformed education system, but not one that throws the baby out with the bathwater. Fundemantal skills are as important now as they ever were, whether or not we have machines capable of automating such processes.
     
  11. Tandy

    Tandy New commenter

    It is heartening to hear that you don't, but my comment was about the system as a whole. From the hundreds of schools that I have worked with and inspected, my experience is different. Inspection lessons might be all singing all dancing, but a quick chat to the kids and looking through thousands of exercise books tells me that for the majority of students in schools in England, mathematics lessons are typified by lesson after lesson of page after page of regurgitation - the same type of equation solved 50 times, the same type of percentage question over and over, pages of useless notes, and mindnumbing repetition.

    This is not to say that I don't understand the place for practice and mastery - but it should only be one ingredient.
    Better in what way? What do you see as the benefits?

    I hear time and again secondary school teachers telling me thateverything would be ok if they arrived from primary knowing the basic. But what is meant by this "ok"? I suspect that they mean the students would be able to do better at the curriculum as it stands and pass more exams.

    But what if these are the problem? The qualifications that we have presently are, by all intents and purposes, entirely useless to the vast majority of the population in terms of their future needs. If the curriculum was different, if mathematics went back to being about what it should be about instead of this horrendous "numeracy" garbage that assumes mathematics is just about the mastery of number skills, then perhaps these "basics" might become things like the ability to understand and interpret problems; the acceptance that getting an answer isn't an easy thing and takes much time, thought and dedication; the ability to think for oneself; the ability to critically analyse a situation; the ability to draw on multiple areas of learning and combine together to overcome a situation; etc etc
    I'm not saying we don't need any. I'm saying that a system that rejects where we actually are, is one that sets us up to fail as individuals and as a nation. We can't ignore the fact that the world has moved on at great pace. We are sending students out in to the marketplace with GCSEs, A Levels and Mathematics Degrees that are irrelevant and useless in the world of modern industry, commerce and even academia, so that we now have the ridiculous situation where, upon hiring someone new, most businesses just assume that they have to teach them how to do everything.

     
  12. googolplex

    googolplex Occasional commenter

    My contacts in modern industry bemoan the fact that kids leave universities with degrees in maths and engineering, but unable to cope with the most basic maths relevant to the job - basic stuff like numeracy, as well as trigonometry, complex numbers etc. There is nothing new about such skills. The old curriculum taught these things well enough. The current one waters things down so much, that kids really don't know these things in sufficient depth. They would be horrified by an ofsted inspector proposing we get shot of things like long division...
     
  13. Sounds typical of all the notebooks and workbooks I see



    What is maths education for? is a good question. I wish I had a good answer.



    Talk about giving people problem solving skills is all well and good, and should be done. But problem solving skills are rarely transferable from one field to the next, and not always from one problem to a different problem in the same field.




    I don't see why anybody needs more than Foundation C grade in every day life. If they do need more, they will be in jobs where they will get training in whatever is missing.
     
  14. Tandy

    Tandy New commenter

    This is turning into an interesting conversation - one that Gove should be flipping having

    My point is: So what? Why is this seen as useful? What are we actually trying to achieve with our students?
    Indeed! Maybe we are trying to promote too many trades. Personally, I think the protectionist view of subjects standing alone is a damaging one too. When on earth, in any meaningful job, do you only apply a single subject?
    I hear this all the time, but nobody is saying why they need these skills. I sometimes wonder if those of us who do perfectly well from the type of system that we have at the moment (I'm one, Gove is another), bother to understand what the experiences of the vast majority of the population actually look like. For most people, the mathematics curriculum as it stands is useless, and for many it is even worse than that, it is counterproductive.
    I know. And I'm playing Devil's Advocate a little here, because I think asking these questions is important. I have had these discussions with many folk, and still no-one can give me a good reason for the current system and how it will shape the future lives of the majority. When I talk to colleagues in industry, the mathematics curriculum and qualifications are simply mocked as being redundant.
    (I actually have fundamental disagreements with the notion of "General Education" but that's another story altogether...)
     
  15. Tandy

    Tandy New commenter

    I'm not sure about this, Steve. I'm talking about an approach to working.
    Problem solving is the opposite to what I see being taught at the moment.
    Problem solving is about an attitude to work that says, yeah it's ok not to get an answer immediately. It's ok to fail and make mistakes. It's ok to redesign problems or make assumptions. It's ok for a solution to take ages to arrive at. It's ok for the solution to involve number, algebra, statistics, mechanics, geometry all in one.
    The current system is breading students who just want to be spoonfed. Transmit information at me, then I will repeat it. Oh, and if I don't get an answer straightaway, then I'm giving up!


     
  16. Tandy

    Tandy New commenter

    I agree that the current system is not the way to go. But I don't think that going back to the system of the 50s is the right course either. Surely taking the best from what we know and mixing this with some real thought about what people might need to know in the future is a better option?
     
  17. PaulDG

    PaulDG Occasional commenter

    Sure, we all agree with that.

    Except there seems little consensus about what this "best from both" would actually mean.

    As I wrote earlier, I used to subscribe to the idea that pen and paper arithmetic was useless; that calculators meant that no one needed to learn times tables & do long multiplication and division, but then I found it near-impossible to teach "area" to a class where even the simplest examples of length x breadth mean nothing to them because they just didn't connect "finding how many squares are in the boundary" with "multiplication" as multiplication itself meant nothing!

    So now, I'd strongly favour a "back to basics" approach in primary. Send them to us in Secondary drilled in column addition & subtraction, long multiplication & division, decimals and fractions.

    The we can teach them the rest.

    (And if someone else wants to define what that "rest" should be, that's fine by me. IMHO, it needs to have a lot more "measure" in it and a lot more algebra. And while I think statistics is a delight, I believe we waste too much time teaching too much of it. Very few really gain a "feel" for statistics from doing GCSE maths and as even government ministers clearly don't understand what "average" means, we're on a hiding to nothing trying to teach it as mainstream.)
     
  18. Maths_Mike

    Maths_Mike New commenter

    I totally agree with this - and yet on the other hand I very much see Tandy's point and I am a big fan of applied maths - the using of maths to solve problems and if ICT be it a computer or calculator facilitate this then fine.
     
  19. Maths_Mike

    Maths_Mike New commenter

    I general I feel the following - basics are important and they need to be learnt and practiced and for the majority these skills - i.e. arithmetic should be taught at primary level. I think we have definitely regressed in terms of numeracy skills and thats a shame - for one thing depsite calculators and computers lack of these skills knocks a childs confidence.
    I actually think we need more statistics and probability - it is an important and widely used topic and it provides many opportunities for excellent maths.
    fundamentally however NOTHING will chnage until the exams are updated. While we persist in skills based test with question like 36 x 24 etc etc testing simple skills totally out of context and with no problem solving elements what so ever then we are not likley to pursuade convince anyone that maths needs to be taught differently.
     
  20. I've said it before, and I'll say it again ... from my limited time in teaching (2 years) my views on what maths "is" has changed drastically. I used to think it was (and should be) about learning processes so that you can "put stuff in" and get the right answer out becuase you've learnt the process.
    I very quickly came to realise that maths, in schools, needs a degree of that, but it should be about helping kids develop inquisitive minds and an ability to break down a problem - ANY problem, not even anything related to maths per se - and come up with a good solution.
    To do this, however, we need to get the foundations laid down first. They NEED to learn basic number bonds, operations, fractions/decimals/percentages, simple algebra and some angle/shape work at a young age - and learn it well! Most of this should, IMO, be done through vast amounts of repitions and, yes, learning times table and the likes by rote.
    Once these skills have been secured, then we can start taking things further. Too many times, pupils will hit brick walls because they can't add simple fractions, or don't understand why £90 + 10% doesn't equal £100, when £100 - 10% = £90. It is almost impossible to address anything vaguely "real" with the majority of pupils because it has to be so hugely controlled to avoid any tricky topics and only teach/test one or two very narrow skills.
    I view it like a master-tradesman. My Dad has a fair-sized toolbox with a good number of tools in it. He knows exactly what to he can do with those tools and rarely needs to buy the latest gadgets. Some of his younger colleagues lug around 4 or 5 times as much as him. They know the name and intended purpose of each of their tools and scoff at my dad for his archaic choices. However, my dad can turn his hand to pretty much anything because he has learned his basics to perfection and has then developed the art/skill/intuition of problem solving. His colleagues, however, when hit with a new problem will ask "right, which ONE tool has been designed to do this ONE job?".
    So ... get the basics taught and learned properly. Narrow and deep to start off, remembering that understanding can come after knowledge, and then we can broaden once we know we won't have to stop every two seconds to tell Johnny that 1/2 x 1/2 is not 1, 8 squared is not 16 and 32.5 x 10 does not equal 32.50 because you "stick a zero" on it.
     

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