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Think your school teaches maths well? Please tell me....

Discussion in 'Mathematics' started by ballamory, Oct 6, 2012.

  1. Just another anecdote from the trenches, in case you still don't believe me...

    A colleague, by coincidence, mentioned today that he currently has a first year undergraduate student studying maths for science, that is unable to solve quadratic equations. No formula, no completing the square, no factorization, nothing. Apparently this student is even unable to solve a simple equation that reads x^2 = a^2.

    Just for your benefit, I'm making enquiries as to the exact make up of this student's A levels, although it is almost inevitable that they will be straight As, just by virtue of where this student is studying. Whether this includes maths or further maths specifically, though, is still to be established. I'll report back when I know more.
     
  2. Yes, it strikes me as absolutely imperative that you make further enquiries in to his/her qualifications. Report back as soon as possible and we'll get back to you, you know, when we're not actually teaching.
     
  3. Yes, the important work of teaching... And a bit of reading the TES forum, perhaps?

    Goodness me, some of you are a bit touchy, aren't you?

    Make sure you include some quadratic equations in that teaching, won't you? Wouldn't want people to get to university and still not, you know, know how to solve them?
     
  4. PaulDG

    PaulDG Occasional commenter

    It seems highly unlikely this could have included maths (though people do forget stuff or fail to recognise it in unfamiliar contexts).

    It would be extremely hard to get a decent grade in the first Core module without being able to solve quadratics and most of the trig in the later core modules would be impossible too.

    (It is, of course, possible to get a B at GCSE without having a clue about quadratics - not a real chance of getting an A though.)
     
  5. Guish

    Guish New commenter

    I don't know what's going on here. I teach CIE A levels as I work overseas. A student of mine got A in Maths A levels and he is doing Computer Science at Kent right now. The Maths/Stat he is doing is easy. He told me that the way he was taught was excellent and he got the right insights for uni when he at school with me. Being unable to solve quadfratic equations is alarming.Are UK A levels that different?
     
  6. PaulDG

    PaulDG Occasional commenter

    But almost certainly indicates the individual didn't do well in GCSE maths, let alone taking A level.

    I don't know. The specifications and past papers are available on the exam board websites, so it would be easy for you to check. I can't see how anyone who couldn't solve a quadratic would stand much of a chance of completing A level maths, let alone get a decent grade in it - most of even the simplest A level module would be a mystery to such a person.
     
  7. PaulDG

    PaulDG Occasional commenter

    Actually, maybe that is a little tricky..

    As it stands, it doesn't have a numerical solution, does it? just x = +/- a.

    When students are expecting to have to produce an actual answer, but all that's in front of them is a result like that, they tend to freeze up unless they're quite certain their "isn't that just +/- a?" will not be ridiculed.
     
  8. Here's another anecdote, then. A few years ago, I set an exam for students in a university department where most students have grade A at A level maths (or equivalent), and nobody has less than B. I accidentally set an exam question that required students, along the way, to calculate 60% of 10. Of course, I had had no intention of testing whether they could do percentages - it was just a task that came up in the course of doing what I was testing them on, and it didn't occur to me or to anyone else in the paper checking process that this might be a problem. They were not allowed calculators in the exam :) I'm not going to paste in the question, but trust me, there was no tricky wording: it was completely clear what they were being asked to do, and there was no sign from the papers that students were misinterpreting the question; they just couldn't do the sum. Here's a paste from the notes I took at the time with the papers in front of me.
    45 students attempted the question and got far enough with it that I could tell what they thought 60% of 10 was. Of these:
    27 students thought it was 6 (in some cases, after some crossing out, but they got there!)
    3
    students silently changed the sum to something easier (10% of 100 in
    two cases, 50% of 50 in a third - though is that really easier?!
    Possibly there was some other explanation for that...)
    4 students thought it was 600
    6 students thought it was 0.6
    1 student thought it was 0.06
    2
    students though it was 0
    1 student thought it was 100/6
    1 student thought it was 35 - I'd love to know what the reasoning there was.
    Now, I am not blaming teachers; I am completely mystified as to what's going on between school and university that makes so many apparently qualified students appear incompetent by the time we see them. But this anecdote, although particularly impressive, is not an isolated incident. We are not making it up. Somehow, what they learn in maths classes at school either doesn't stick, or doesn't make it outside maths classes, or both.
     
  9. DM

    DM New commenter

    I once set a fractions test for a group of leading academics (all Nobel Prize or Fields Medal winners). Seven out of ten of them thought one half of fifteen was nine. Blah blah. More nonsense. It's all your fault for being lazy no-good lefties.
     
  10. Guish

    Guish New commenter

    Kids forget easy stuff. Some of my IGCSE students forgot long division.
     
  11. Guish

    Guish New commenter

    Haha.[​IMG]
     
  12. PaulDG

    PaulDG Occasional commenter

    Why not?

    Did what ever it was you were teaching meant they'd not have access to calculators once graduating?

    What was that? Extreme desert survival techniques? Why did they need to know how to work out a percentage in those circumstances?

    There are now (apparently) 6 billion registered mobile phones on networks globally - almost everyone on the planet carries one all the time and they all have calculators. What possible higher study would mean they were prevented from accessing them?

    DId you allow them pens or did they have to make their own out of what they could cannibalise from the room and use their own blood for ink?
     
  13. You are aware that AS Level C1 exams are non-calculator exams, and have been for over 6 months now? It is important to keep on top of the latest developments, and not tell your students that they will always have a calculator in an exam.
     
  14. Guish

    Guish New commenter

    Paul was talking about the use of calculators after graduating from secondary school.
     
  15. So how do they pass C1 if we remind them to use their mobile phone, if they want to calculate 12 times 12?
     
  16. Same reason they aren't allowed calculators in history exams: because there was nothing in the exam that would require the use of a calculator, and allowing them calculators they wouldn't need would be making unnecessary work for the invigilators, and putting unnecessary work and perhaps expense on students (who would reasonably assume, if told that they could use calculators, that they should have calculators; since as you say every phone and computer has a calculator, not all students will possess stand-alone calculators by this point).
     
  17. Guish

    Guish New commenter

    You are right when you say that they need to be prepared to do workings manually for their external examinations. However, at university level, a student can go in any exam with a calculator. You don't test such skills over there. The whole discussion was on students not having access to calculators in a university test.
     
  18. Guish

    Guish New commenter

    One tends to forget easy Maths when one does complex things. It never happened to you that you tried to solve an easy question using advanced calculus or something like that while you could use something very simple instead. Maybe, something like that happened to these students.

     
  19. This is not true. An examination (at university, and surely at school too, unless more has changed since I was at school than I think) is done in a deliberately restricted environment. For good integrity reasons, students are only allowed to take in things that they may reasonably be thought to require.
    So to summarise:
    - PaulDG thinks it's unsurprising that a student with a good grade at A level maths can't solve x^2 = a^2, because that's tricky;
    - Guish thinks it's unsurprising that more than a third of such students can't work out 60% of 10, because that's easy.
    Does anyone think there's any sort of maths problem that someone with a high grade at A level maths could reasonably be expected to be able to solve? Anything in the happy medium of being neither too easy nor too tricky? Anything so easy that they shouldn't forget it? Do I need to be prepared for students who aren't sure what natural number comes after 3? If not, why not?
    I sound tetchy now and I feel it. I was prepared for teachers to say that they weren't sure why these students couldn't do 60% of 10 or what they could do about it. I was not prepared to be told that it was unreasonable to expect them to be able to do it.
     
  20. So, something in between simple percentages and quadratics....
    How about linear number sequences? I've heard they should be good at those by age 19.
     

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