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Have We Made Maths Too Hard? 12:00 to 13:00 29 October 2017

Discussion in 'Mathematics' started by tonygilland, Oct 11, 2017.

  1. tonygilland

    tonygilland New commenter

    Have We Made Maths Too Hard? 12:00 to 13:00 29 October 2017

    Battle of Ideas Festival, Sat 28 to Sun 29 October 2017, Barbican Centre, London, EC2Y
    In a rush towards greater rigour and mathematical fluency for all, have we over-estimated the capacity of schools and colleges to deliver? Should we pay more attention to the differing needs and abilities of students? Or should we celebrate greater ambition and keep pushing teachers and students to scale ever-greater heights?

    Speakers include:
    · Kristopher Boulton, director of education, Up Learn
    · David Perks, founder and principal, East London Science School
    · Charlie Stripp, director, National Centre for Excellence in the Teaching of Mathematics; chief executive, Mathematics in Education and Industry
    · Helen Ward, journalist, TES

    Other education debates include:
    sbkrobson likes this.
  2. David Getling

    David Getling Lead commenter

    I always laugh when I hear the nonsense about maths being too hard. Am I the only one with books on spherical geometry that remind us how, at one time, this was part of the school maths syllabus? Just to give one example.

    The trouble is that people today, and not just the kids, expect rich rewards without having to put in the hard yards. Rather than dumbing down, kids need to be reminded that anything worthwhile takes considerable effort. And, when the going gets tough, the tough get going. For decades now, parents and schools have been raising quitters.
    gravell likes this.
  3. PFCDaz

    PFCDaz New commenter

    “The children now love luxury. They have bad manners, contempt for authority; they show disrespect for elders and love chatter in place of exercise.” Socrates 469-399BC ;)
    sazad99 and sbkrobson like this.
  4. BillyBobJoe

    BillyBobJoe Established commenter

    I think maths is probably too difficult relative to other subjects. Whether that means maths is too hard or other subjects are too easy is open to discussion. Certainly the disparity between English and maths results is there for all to see.
    gravell likes this.
  5. JaquesJaquesLiverot

    JaquesJaquesLiverot Established commenter

    This debate is raging in Computing forums, with (presumably younger) teachers saying that the new GCSE is too hard, and the A level is more like undergraduate level.

    Well, no - I was surprised how easy the GCSE was, and many elements of the A level (e.g. normalised floating point binary and manipulating logical expressions, e.g. with De Morgan's Duals) were actually in CSE Computer Studies in the 80s. The A level is nothing like my degree course.

    That then got me wondering whether degree standards have declined as much as A levels and level 2 qualifications, and having spoken to neighbours and friends who have tried to recruit graduate engineers and computer scientists recently, I can only conclude that they have.
  6. JaquesJaquesLiverot

    JaquesJaquesLiverot Established commenter

    We did differentiation, integration and matrices for O level Maths, as well as things like number bases and modular arithmetic. Matrices in particular are useful these days for things like machine learning, and modular arithmetic is a programming staple - why were they removed from the curriculum?
  7. Karvol

    Karvol Occasional commenter

    A girl, who was schooled in an independent school in the UK, has started on Maths HL (IB) at our school (not in the UK). She did GCSEs and achieved top grades in all of them.

    She clearly has the ability to cope with Maths HL but her background knowledge is woefully lacking. It is lacking to the extent that a serious amount of additional work has to be done so that she is at the level of our existing students.

    The level of GCSE mathematics in the UK is far too low for those students who wish to go on to study mathematics at a decent level, based upon my (admittedly limited) experience of students who have done them.
  8. David Getling

    David Getling Lead commenter

    Karvol your comment about knowledge reminds me of the reaction I get when I recommend the OUP I.B. physics or chemistry I.B. texts to my A-level students. Eyes glaze over with a But it's so big!
    I recommend them because there is a very substantial overlap, and in that overlap things are almost always explained far better and in a bit more detail, and there are far fewer mistakes. They really do put the rather terse A-level texts to shame.

    Obviously, I can't comment on most subjects, but it's not just at GCSE, or just in maths that the UK puts in a poor show.

    It's said that the new linear maths A-level is meant to put more emphasis on problem solving but here's just one of the things I've noticed. The complex number material that was previously spread across FP1 and FP2 has now been lumped together, BUT some of harder loci stuff seems to have disappeared.

    Jaques, I don't know how close you are to my shade under 60 years, but I too remember doing all the things you mention at O-level.
  9. primenumbers

    primenumbers New commenter

    It feels hard for students because of only 2 tiers of exam. Many students have a false sense of achievement when their grade 6 or even 7 turns out to be inadequate to study A Level Maths.

    There are also too many topics to study. Trying to teach some topics like graph transformation or proof to students who don't have solid algebra skill is worse than trying to pull your own teeth out.

    Was the last GCSE Maths paper hard? No it wasn't but to test such a wide range of ability, from grade 4 to 9 then it was much harder for the majority of candidates.
  10. Maths_Shed

    Maths_Shed Occasional commenter

    It's not fair to compare what we did for O Levels with what they are asked to do today, we had a narrower range but a greater depth, it's like the question "list all the rectangles with an area of 24cm^2", you are criticising 4 x 6 because you did 3 x 8.
  11. hs9981

    hs9981 Established commenter

    I showed an old GCSE paper to a korean elementary school teacher. They laughed!
    primenumbers likes this.
  12. googolplex

    googolplex Occasional commenter

    Those who quote from topics which used to appear in old O level papers seem to forget that the O level exam was accessed by a relatively small proportion of students, mostly from Grammar/independent Schools.
    The current GCSE isn't too hard. In fact it isn't hard enough for the most able. But then, I remember sitting in my grammar school class, receiving back our mock O-level maths papers in the 1970s and most of the top half of the class getting percentages in the high 90s. Clearly that exam wasn't challenging us either.
    But then, at the bottom end of the class, there were lads, intelligent lads too who have gone on to prosper in careers in industry, who just didn't get it, who were languishing with very low percentages.
    Tough papers are divisive, they polarise confidence in students and do not necessarily bring out the best in everyone.
    The problem, as always, with this maths GCSE is the lack of effective tiering. I recall teaching GCSE maths in the 90s when there were (can't remember exactly) something like 7 papers, graded in difficulty. Students were entered for two consecutive papers. That worked. This current two tier system is the problem and has created a middle ground of students who are lost - they either do Foundation and spend too much time on silly questions, or they do higher and languish in their abject failure, going though life knowing that they can't do maths and passing on that feeling of failure to their children.
    At the top end, we should make it tough - even tougher than now, to really challenge those most able students.
  13. phlogiston

    phlogiston Star commenter

    Maths is a complex subject, and I think we need pragmatic expectations. Some of the kids I work with give us cause for celebration when they get entry level 3 maths. They have massive difficulties and should not be subjected to the same expectations as the kids in other schools who have joyfully soared through A level maths and further maths.
    Perhaps having harder GCSE will inspire a few more, but we need realism about what the middle level kids want to achieve and can achieve - and what we expect them to achieve.
  14. BillyBobJoe

    BillyBobJoe Established commenter

    I see, David Getling, that you're making comments about the UK based on your experience of England again. You might like to compare with the SQA Advanced Highers as well as the A-Level (and the National 5 as well as the GCSE) if you wish to be able to comment on the whole of the UK.
    thekizzaa likes this.
  15. gainly

    gainly Lead commenter

    Certainly O level and A level exams used to be harder, but they were taken by a minority of students. Now everyone is required to take maths up to GCSE and repeat it if they don't achieve a grade 4. The real misconception is that somehow, by just making the exams harder, standards will be raised. The only actual result seems to have been to lower the grade boundaries so that for Edexcel only 17% was required for a grade 4 on the higher paper.
  16. JaquesJaquesLiverot

    JaquesJaquesLiverot Established commenter

    I occasionally meet primary students (and until August had a primary-age child myself), and the thing that strikes me is how good they are at Maths. We like to compare GCSEs with what we did in school, but a more telling comparison is to compare them with KS2 SATs papers - with the old Foundation papers it struck me that a lot of students hadn't made any progress since year 6.
  17. andrewchambers

    andrewchambers New commenter

    I would agree with this - (though I don't know how the new GCSE maths stacks up) - the old GCSE was nowhere near good enough to prepare students for HL Mathematics. My recommendation is for students wanting to do IB HL to have done Cambridge Additional Maths in Y11 (as a large number of the students they are competing against already have). Students who have come from just GCSE find the jump immense.
  18. gainly

    gainly Lead commenter

    The new GCSE maths is clearly too hard for some students. What is the point of trying to teach them exact values of trigonometric ratios when to do 9x12 they would write out 12 nine times and add them up. On the other hand even the new GCSE is too easy for the most able students. What is needed is a greater range of qualifications, or at least more tiers, but I don't think there is any chance of our wise political leaders agreeing to that.
    phlogiston likes this.
  19. armandine2

    armandine2 Established commenter

    I was doing some hard maths last night - following my late professor's derivation of the force on a submerged plate. Part of which proved an equation by using the weight of liquid above the plate. I was happy to get to the end knowing the mathematical 'narrative/manipulation'. Unfortunately my physics textbook has a section on the hydrostatic paradox, and now I'm less assured with his methodology.
  20. andrewchambers

    andrewchambers New commenter

    I agree - the most workable solution I think would be: (apologies I'm going to stick with letters rather than numbers)

    1) a Numeracy GCSE - with a top grade of C. This could strip out topics like geometry and focus on numerical (and simple algebraic) applications. Lots of finance, budgeting and data analysis. An expectation that this would be offered to students weak at maths (bottom sets)

    2) Maths Core - with a top grade of A. This would be like the usual GCSE (tweaked to exclude the hardest content) and suitable for middle sets

    3) Maths Extended - with a top grade above A* which is designed for students who potentially can take maths at A level. More rigour, more algebraic manipulation, more topics. This would be the usual GCSE for top sets.

    Every other way of dividing up the syllabus ends up shortchanging some students - either those at the bottom, or those at the top.
    PFCDaz likes this.

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