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Dublin: 9 °C Thursday 20 June, 2013

Leaving Cert maths problems ‘must be addressed’, says TD

Plus, the mixed reaction from Sixth Years on Twitter.

Image: Sasko Lazarov/Photocall Ireland

THERE HAVE BEEN calls made for the State Examinations Commission and Education Minister to assess the fairness of this year’s Leaving Certificate higher level maths exam after paper two was deemed ‘a disgrace’ by a textbook author.

Commenting a day after Paper Two upset a number of students and teachers, Sinn Féin’s spokesperson for education Seán Crowe said changes to the exam had presented “significant difficulties”.

“There has been a good deal of criticism of the exam with one teacher, Brendan Gildea, saying that the majority of candidates he spoke to were devastated after sitting the test. This is a very worrying situation,” said Crowe.

The State Examinations Commission and Education Minister Ruairí Quinn must seriously assess the criticism levelled at the exam and take steps to improve its content and fairness.

This year’s paper examined students as part of the new Project Maths syllabus but some teachers had issues with question seven on statistics, stating it did not assess what the candidates had actually learned.

Gildea, a co-author of the New Concise Maths project maths textbook, labelled the exam ‘a disgrace’ while being interviewed on RTÉ’s Drivetime.

However, there was a mixed reaction to the paper among students on Twitter:

Leaving Cert maths problems ‘must be addressed’, says TD
1 / 13
  • @Kate_180494

  • @Kaylataylorf

  • @Alyssaa41

  • @MuireannNiSh

    Muireann here may have gone a bit far?
  • @SophieVarian_

    Sophie fell into the 'not-so-happy' camp, we think.
  • @so0wmeagoodtime

    Some people were OK after yesterday's paper.
  • @Hollie_Melia

    Fair play!
  • @Siobhan_od93

    A pragmatic approach from Siobhan.
  • @SiobhealNicEoch

    The Dublin Rose empathised with the Sixth Year students
  • @AdrianKavanagh

    And this is coming from a University lecturer.
  • @Queefballs

    There was no sympathy from 'The Beef'. Plus, won't someone think of the Fifth Years?
  • @VasHapeninKaty

    Won't someone think of the Third Years?
  • @RyanHargadon

    Won't someone think of us too?

Students have had to dust themselves off from yesterday’s difficulties to face into Irish and biology papers today.

‘Worst day ever’: Leaving Cert students react to English Paper Two>

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Comments (47 Comments)

  • This is the first year that students en masse sat the project maths paper 2, with the paper 1 being left the way it was. Paper 1 will be changed next year, but there were 24 pilot schools who were a year ahead of everyone else, they sat project maths paper 2 last year, and paper 1&2 this year, and I know in one school the paper 1 on Friday was considered an absolute disaster. RTE conveniently never visited or mentioned the existence of pilot schools in its report that Friday.

    These project maths papers, both sample papers, Department of Education samples, and past papers from the pilot schools, have been full of vague and ambigious questions, clearly not written by anybody with a comprehensive understanding of mathematics, and although I don’t think the syllabus is half bad, the papers are awfully written across the board, this paper 2 from yesterday wasn’t an exception.

    Reply
    • Can you give us some examples?

      Reply
    • Unmarked scatter plot graphs, with questions asking for an estimate of the correlation co-efficient. I understand the premise of the question, but when I might look at a graph with an obvious strong correlation I might say .8, someone else might say .6 or .95.

      Statistics questions where the mean and standard deviation of a distribution is given, without the explicit statement that the distribution is Gaussian. Again I understand that Gaussian is the only continuous distribution at Leaving Cert level but the Binomial distribution, a discrete distribution, is also studied, and it has an independent mean and variance. It’s clearly not something a capable mathematical mind would overlook.

      A question giving you the height of a plant over a certain number of days, and asking you to find the height of the plant on day 17, assuming an arithmetic sequence. that was fine, until the paper decided you were a biology student and asked you for reasons why the plant might not be that height on day 17. An easy question admittedly, but not on topic by any means, when the student is expecting all their answers to have a mathematical basis.

      Not to mention spelling mistakes, revamping of the syllabus while the students were learning material (you’ll notice that vectors and cyclis quadrilaterals are still on sample papers, despite being removed from syllabus), and I won’t mention anything I was told about Project Maths Paper 1, as I didn’t see the paper yet myself and therefore can’t confirm anything I was told.

      Reply
    • Thanks for posting the details. This is not the way to improve the standard of maths education.

      Reply
    • No problem

      Reply
    • Statistics questions where the mean and standard deviation of a distribution is given, without the explicit statement that the distribution is Gaussian. Again I understand that Gaussian is the only continuous distribution at Leaving Cert level but the Binomial distribution, a discrete distribution, is also studied, and it has an independent mean and variance. It’s clearly not something a capable mathematical mind would overlook.

      Er, yes it is. It’s like being given a hammer and a power screwdriver and being asked to drive a nail without being told explicitly to use the hammer.

      You *might* have an argument if you said that n was very high and therefore you were using the Binomial as an approximation to the Poisson distribution, but honestly, that’s past the syllabus for the LC and not justifiable from the information contained in the question.

      When the Gaussian distribution is taught, you’re taught it applies to manufacturing tolerances (amongst other examples, but that’s the classic one). It’s the default distribution you use when you’re considering *anything* that is described as random, until you find something about the process that says it is better represented by another distribution. So if you’re not explicitly told by the question that it’s *not* gaussian (as you were in a previous question on basketball), you use gaussian. That’s not just exam technique, that’s how it’s used in the “real world”.

      Reply
    • In fact, scratch that, it actually states “normally distributed” in the question as well. So they do tell you explicitly to use the Gaussian distribution, even though they didn’t have to for you to know you should.

      (“Normal distribution” is the actual name for what we usually call the “Gaussian distribution”)

      Reply
    • “It’s like being given a hammer and a power screwdriver and being asked to drive a nail without being told explicitly to use the hammer.”

      Distributions aren’t tools to be used when attacking a problem, you can’t make a judgement call on what distribution you reckon a random variable follows. Iif I was given a situation complete with mean and variance, I’d expect to be given the information that it’s Gaussian. In fact that question I was referring to was a questin on tyre durability, and I would argue that tyre duration follows an Exponential, not a Gaussian distribution. So clarity would have been nice and I repeat my assertion that it’s not something a capable mathematician would overlook.

      “So if you’re not explicitly told by the question that it’s *not* gaussian (as you were in a previous question on basketball), you use gaussian.”
      Again, teaching someone just to slap a Gaussian distribution on something because they don’t know how it acts isn’t good mathematical practice either. It reeks of implied assumptions and a satisficing method that shouldn’t be encountered when students are being taught a subject whose value is placed almost entirely on it’s rigorous foundations.

      Reply
    • Distributions aren’t tools to be used when attacking a problem, you can’t make a judgement call on what distribution you reckon a random variable follows

      No, you can’t. So you *always* use Gaussian *until* you can show something else is more appropriate.

      Iif I was given a situation complete with mean and variance, I’d expect to be given the information that it’s Gaussian. In fact that question I was referring to was a questin on tyre durability, and I would argue that tyre duration follows an Exponential, not a Gaussian distribution.

      Okay, I think we’re looking at different papers; I was talking about the question where they’re talking about manufacturing batteries.

      [quote]Again, teaching someone just to slap a Gaussian distribution on something because they don’t know how it acts isn’t good mathematical practice either.[/quote]
      No, it really is good practice, even if it doesn’t sound like it.

      The reason the Gaussian distribution is the first one you learn despite how long it’s been since it was formulated, is that it can be applied, with reasonable accuracy, to damn near everything. Half the world you live in depends on this. Your ABS brakes, your car’s engine computer, your fridge, your microwave, your TV, the computer you’re reading this on, all the machines that make all of those machines, and a million other things besides, just wouldn’t work if that wasn’t true.

      Reply
    • I can see this discussion getting side-tracked into how much more common the Normal distribution is in comparison to other distributions, so I won’t get into it, the point I was making was that it’s unmathematical to phrase questions as they did, thereby implying that the Normal distribution is the only major distribution in existence. And that this phrasing, combined with worse mistakes, is widespread through sample papers.

      It was rushed out prematurely, to on top of that rushed out to Leaving Cert students instead of Junior Cert, and the above is just some evidence of this.

      Another one for you, f(x)=2e^-x. find where f crosses the x and y axes. Don’t think I need to point out to you the problems with that one.

      Reply
  • Be curious to see the paper. Tbh I’m sure that this is a mix of genuine concern about the difficulty combined with outcry from students who have been tutored for two years by teachers who have attempted to approach this syllabus like the last, i.e. learn it all off. Our education system is a disgrace, learning by rote is endemic, teachers who cannot teach without the crutch of by rote are not given the support and re-training they need and the in-service components of project maths are being taught by people who do not understand the material and hence are incapable of passing anything onto teachers. A total mess, only likely to get worse as funding is slashed over the next few years.

    Hypocrisy of the government: calling for a knowledge economy with one hand, taking away funding with the other.

    Reply
  • Begrudgy I sat the exam, an exam that neither student nor teacher had any definitive method in how to study or teach it bar the sample papers set by the state exam commission and when it turned out the exam was nothing like the sample papers, there was stuff asked that wasn’t covered properly in the text books and the stuff that was well covered in the text books weren’t even mentioned. If this government want to entice international companies to ireland they wud want to bang their heads together to come up with a plan on how to teach and examine maths the new course rather than just examine and hope students wing it on the day

    Reply
  • Peter 12/06/12 #

    Does anyone have a link to the paper, just for my curiosity

    Reply
    • That’s not that outrageous – though Q7 was funny (as in funny ha-ha). Do we really have any LC students who aren’t aware of the concept of mortgages?
      Actually, is that the paper being decried? It looks far too simple to be higher level maths?

      Reply
    • If so many had issues with it, then teachers syllabus knowledge needs to be addressed immediately so that these sections are properly covered and thought. I did my leaving in 2000 and thought that paper was hard, this seems to have gotten easier, saying that I spent 5 years doing engineering maths after so looking back at this, I can’t judge.
      Teachers though need to be fully understanding of the material they are teaching, by rote or half ass grasp will not suffice when dealing with a new syllabus or structure.
      Like Einstein said, if you can’t explain it in the most simple terms then you don’t understand what your talking about.

      Reply
  • As someone who did the old higher paper I would like to see this new one is it on boards or anywhere? Maths always throws up a few curve balls, even on the old paper, and if it was contained in one question then thats not too bad, if it was part c of six questions it should be uproar

    I’m now heading into final year engineering in UCD and without doubt it can be said that if you want to study engineering of any reputable description (I do chemical) but mech, elec, biomed etc your going to come across this all the time, its about learning the problem solving skills, because you wont be able to say q1 2 3 4 5 6 7 8 are a certain topic it will be the course as a whole and the paper wont have many trends going back 5 years, itl be slapped up and youl have to work it out with your knowledge rather than rote learning of the integration for a sphere or log tables (mostly)

    and im sure the same can be said for any heavily maths based course eg actuary, maths courses some business

    And finally, the department generally marks papers fairly, the fact its the first year will be taken into account and another part of the question may be allocated more marks

    keep the faith and good luck with whats left

    Reply
  • The wording of the questions was terrible. In some questions it took me a long time to figure out what was actually being asked, but once I realised what was being asked the maths was usual for some of the more difficult stuff we had covered in class. Apart from “causality”, which is something to do with mortgages and arrears and stuff…. Anything I didnt do was just down to me not being able to do it myself as opposed to me not being thought it. No real complaints about the difficulty of the maths in other words.

    Reply
  • ”Also, worryingly, on another news site I seen a quote from the author of one of the Project Maths textbooks who said he could not do one of the questions, did not know what it was asking. That is worrying because what the hell is he doing writing a book when he doesn’t understand the syllabus in its entireity? Joke.”

    I don’t believe that it is a ‘joke’ as the author is given topics to cover by the department as far as I know and with these topics they go and write the books. I appreciate that its the first year of examining maths like this apart from the pilot schools but if the books are not written in a manner that will cover anything that can/will be asked in the exam then there is a problem.
    This shows what i believe is the problem that there has been a lack of communication and an unwillingness from the department to tell teachers how topics were going to be asked and graded. When they did answer theses questions they were very vague with their answers almost as if they didn’t know themselves.

    Reply
  • Paul Mac 12/06/12 #

    You can get the exam papers from the SEC website. The Maths Paper II is available here: http://www.examinations.ie/archive/exampapers/2012/LC003ALP230EV.pdf

    Reply
  • Eleen 12/06/12 #

    Haha, I remember the LC higher maths for my year – one of the questions was technically unanswerable. They had a team of mathematicians try to work it out and they couldn’t.

    Reply
  • Wait until these LC students get to college…they’ll know all about the shit hitting the fan then..

    Reply
  • Had a look at it there and while portions of it are challenging I really can’t see what the issue is. There’s nothing that isn’t on the syllabus. I’d imagine the difficulties are coming from teachers lacking the knowledge/cpd to teach new portions of the course and the confusion that would cause for students. Also, worryingly, on another news site I seen a quote from the author of one of the Project Maths textbooks who said he could not do one of the questions, did not know what it was asking. That is worrying because what the hell is he doing writing a book when he doesn’t understand the syllabus in its entireity? Joke.

    Reply
  • There has been a culture of teaching “to the exam”, textbook teaching (ticking off chapters), vested interests from private publishing companies and a grind school mentality that is engrained in education. Learning by rote may have got you your honour in the Old syllabus, however was that student adequately prepared to problem solve at 3rd level/ or in engineering etc? Why does Ireland perform so poorly in PISA studies?
    I teach in one of the 24 pilot schools and can honestly say I feel my students do have a better UNDERSTANDING of mathematics and it’s applications in the real world. They’re more engaged and better able to problem solve. The problem is not with the syllabus it is with the exam. We need to change our methods of assessment. The junior cert higher level paper 2 (project maths)was a lovely paper and really reflects the new syllabus. I was disappointed with leaving cert ordinary level paper 1 (project maths one) , the calculus question was traditional and no emphasis on graphs/ matching graphs of functions to their derivatives. However my students came out of both exams ( ord level) saying they were confident in tackling and attempting questions.
    We won’t see the true benefits of project maths till the present 2nd years from the pilot schools sit their leaving cert in 2015 as they will be the FIRST cohort of students who will have done 5 years of project maths after a natural transition from primary school.
    As for CPD, teachers have the opportunity to attend evening courses that will assist them in new teaching methodologies and support in new course content. These courses are run in local education centres, I have run some myself and feedback has been very positive. This is on top of compulsory workshops that teachers attend. Some of the universities, UL and DCU are running courses for maths teachers too. One only has to look at http://www.projectmaths.ie to access amazing resources for rollout of new course. If teachers are following the syllabus (and not a textbook) checking this website, attending project maths workshops, and trying out new teaching methodologies then I believe only then will they experience benefits of new course.

    Reply
  • Damocles 12/06/12 #

    That doesn’t look too bad to me.

    Although I do have a maths degree so maybe I’m not the best person to be commenting.

    Reply
  • These people wont be happy till they get the questions in advance so they can give the answers to their friends and students.

    Reply
    • You give higher maths a go and tell me how you get on, it’s shit hard – and an even harder than normal paper is unpredictable and unfair!

      Reply
    • Stephen 12/06/12 #

      The problem with maths is it cannot be learned off as there are too many variables involved. Where students can learn off answers and regurgitate then in an exam you can’t do this with Maths. Students are so used of this type of learning in all other subjects they can’t adjust.

      And then comes the argument that “why do they have to learn this? Cher they will never use that in life” championed by every detractor of Leaving Cert Maths. Well the entire Maths course is designed to train your problem solving abilities which will be used everyday of your life.

      One last note: That Adrian Kavanagh who tweeted that L.C Maths is the most difficult exam students ever had to take clearly never had to do an exam in Continuum Mechanics as part of a UCD Engineering course!

      Reply
  • im one of the students in one of the 24 pilot schools across the country that had both papers on project maths and i may do pass but some of my friends did honours and they said that paper one was hard but as regards to the statistics questions being nothing about what the students learned is understandable as many of us did the old course for junior cert so it is difficult to adjust and the department really should have taken that into consideration

    Reply
  • doing a biomedical science degree at the moment and were doing linear algebra and differential calculus, and have to say, project maths taught me absolutely nothing, nor did it prepare me in any way for my first semester of college maths. I mean measuring the probability of rolling a one on a dice does nothing to prepare you for limits, logs, exponentials, or functions, i understand its useful for other subjects, but the thought of wasting so much time on this in my leaving cert when i have no current application for it is ridiculous. I pity the leaving cert people this year having to do a course full of this nonsense.

    Reply
  • There has been a culture of teaching “to the exam”, textbook teaching (ticking off chapters), vested interests from private publishing companies and a grind school mentality that is engrained in education. Learning by rote may have got you your honour in the Old syllabus, however was that student adequately prepared to problem solve at 3rd level/ or in engineering etc? Why does Ireland perform so poorly in PISA studies?
    I teach in one of the 24 pilot schools and can honestly say I feel my students do have a better UNDERSTANDING of mathematics and it’s applications in the real world. They’re more engaged and better able to problem solve. The problem is not with the syllabus it is with the exam. We need to change our methods of assessment. The junior cert higher level paper 2 (project maths)was a lovely paper and really reflects the new syllabus. I was disappointed with leaving cert ordinary level paper 1 (project maths one) , the calculus question was traditional and no emphasis on graphs/ matching graphs of functions to their derivatives. However my students came out of both exams ( ord level) saying they were confident in tackling and attempting questions.
    We won’t see the true benefits of project maths till the present 2nd years from the pilot schools sit their leaving cert in 2015 as they will be the FIRST cohort of students who will have done 5 years of project maths after a natural transition from primary school.
    As for CPD, teachers have the opportunity to attend evening courses that will assist them in new teaching methodologies and support in new course content. These courses are run in local education centres, I have run some myself and feedback has been very positive. This is on top of compulsory workshops that teachers attend. Some of the universities, UL and DCU are running courses for maths teachers too. One only has to look at http://www.projectmaths.ie to access amazing resources for rollout of new course. If teachers are following the syllabus (and not a textbook) checking this website, attending project maths workshops, and trying out new teaching methodologies then I believe only then will they experience benefits of new course.

    Reply
  • Exams, Exams, Exams… So much focus on the perceived failure of the process of evaluation… Yet nobody ever questions the quality of the teaching…

    Reply
  • It was not broke … why did they “fix it”?. The Higher maths paper was always a challenge but a very do able one – it just required lots of practice.

    Reply
  • My daughter is in one of the 24 pilot schools so both papers were project maths and paper 1 proved an absolute disaster. Maths is the only ordinary subject she is doing (she got a b in pass maths in the junior under the old system) but questions appeared on this paper that they had never seen before.. The lack of sample papers to practice on is an absolute joke but the main problem is that many of the questions that appeared on Paper 1 they had never seen before. How is this fair? She had done the sample paper provided by the SEC over and over again but none of those questions appeared?? I am absolutely furious. Paper 2 was much better in that the methods they had been taught at least came up. Why should the kids on this pilot scheme be put at a disadvantage and not have proper learning tools or guidelines? I think more parents should be complaining about this as the students have enough on their plate trying to focus on the rest of their exams. This project maths is not working – proper resources and learning tools are not being provided – and it is not fair on the our kids who are being used as “guinea pigs: on this pilot scheme. I hope that there is a response from the department on this.

    Reply
    • Marie, there are plenty of resources that have been made available to teachers as well as extra training so have to disagree with you there and excellent resources might I add. Check out the website I quoted above. Yes I agree it has been unfair on the student especially as they did 3 years of the old syllabus before hitting the full 5 strands in 5th year. The problem is not with the course it is with the exam.

      Reply
    • plato 12/06/12 #

      You say she had ” done all the questions on the sample paper.. And none of them came up” did you seriously think that they would? I don’t think the SEC provides the questions in advance.

      Reply

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