Leaving cert maths Post author By Kevin O’Rourke Post date June 7, 2011 The news this morning isn’t great. Categories In Knowledge economy 109 Comments on Leaving cert maths ← Review of top-level pay → Professor Sinn Misses the Target 109 replies on “Leaving cert maths” Nor is it surprising, in fairness. I left school 2 years ago, I spent 5th year with various substitute teachers in my honours maths class, none of whom were qualified. Many maths teachers are qualified in things like engineering and computers that had Math modules at University, they don’t necessarily have degrees in Maths. I found the following a little alarming. “one in five students drop down from higher to ordinary level maths on the morning of the exam.” When is this decision made? I presume it is not made on the morning of the exam, at least not in most cases. Still, it is a little disconcerting that the decision to take one paper or another is left until so late in a two-year programme. the Dept of Education have been a sleep at wheel on this and other issues much like the Dept of Finance when the s**t hit the fan over the last five years 1. great many maths teachers are completly at sea away from the math text books and dont fully understand their brief so that students who have valid questions are simply ignored i guess may main point is that the maths teachers should be independantly accessed on their ability to A.understand fully the subject that they are to teach to a high level B.have the right communication skills that carry and inspire students also the fear of failing maths which restricts entry to third level aducation push a lot of students down to pass level maths as they do not want to take the chance of failing higher maths The leaving cert is all about incentives. Maths consumes more study time per point gained therefore people opt not to sit it. Maths also contains greater risk because a failure to pass means a failure to matriculate. Maths teachers are conscious of this and warn borderline students. A number of things can be done to change this: 1. Remove the risk of non-matriculation by allowing honours maths students to take the pass maths leaving cert in fifth year. It will be child’s play to most of them. (Some of the fancier schools allow students to matriculate in all necessary subjects in fifth year so they can score points in 6 easier subjects in their final year). 2. Give bonus points for maths. 3. Ensure that all honours maths students are also offered the opportunity to take Applied Maths. This will help them re-use their study time and lower the study time per point. They should also be offered as physics as well for its cross-over with honours maths. I think the curriculum should also explain how honours maths can be used in real life. Honours maths students will understand the examples. I sat my leaving more than 15 years ago. It is only in the last year that I have discovered how honours maths can is actually used in finance and social science. Students need to be told where maths can take them, and where they can never go without it. meant to say: “They should also be offered as physics as well for its cross-over with applied maths.” @clintideal That is a good point. How many good honours maths students go on to be teachers? Close to zero imho. Many many honours maths students take grinds. This will be happening less as families have less money. We need to look at providing additional or substitute tuition for honours maths students (and let them out of school early to get to it – make maths the last class twice a week.) The new figures are a blow to Government efforts to boost maths; it has long identified the subject as key for the “smart economy”. Emperor and New Clothes come to mind. While the topic of the LC is still on, is it not remarkable that despite the consistent interest shown by the best performing LC students, entry to all the medical schools is very restricted to Irish and EU citizens? Places made available for non-EU students are candied by large cheques presumably – of course this means fewer Irish and EU students can take up a place but no government has been too bothered by the fairness or otherwise of the process. Are the entry standards re matriculation the same (equivalent)? I reckon we are at the point where there are increasing returns to scale for the average leaving cert cohort. (For the 16% with the higher maths, I think we are suffering from a convexity problem) If there are less numbers studying higher maths, schools are less likely to devote a teacher for the handful of students studying higher maths, discouraging more students from taking on the subject. I think this is particularly a problem for smaller country secondary schools. You could have only 5 people doing higher level maths, so the school won’t put in the necessary resources. So the students won’t get the same tuition as if they chose gnáth leibhéal. We are on a downward spiral. @ Seamus Coffey In my personal experience (did my LC six years ago but have given grinds in maths since then) the decision to drop down on the morning of the exam is indeed often taken the morning of the exam. Many students only stay in honours due to pressure from teachers, friends and parents in particular, who have shelled out a lot of money for grinds. However, once you’ve seen the honours paper you can’t give it back and ask for the pass paper, so a lot of students make a snap decision on the morning that it’s not worth the risk of failing and ask for the pass paper just in case something on the honours paper mystifies them. As well as that, once they’ve done paper one at higher level, they have to do paper two at higher level also, and there’s a common consensus that paper two is harder than paper one. @ clintideal, SByrne +1. I lost count of the amount of times I asked my maths teacher a question and was told ‘You don’t need to worry about that’ or ‘That’s not on the course’ or ‘They won’t ask you a question like that’. Only a very small percentage of maths teachers are qualified in mathematics and most teachers focus solely on covering the maths course, rather than teaching mathematics. I might add that this problem is found among teachers of many subjects, not just maths. Honours maths students should be given the option of dropping another subject, or even two subjects. But can we expect more from Education then we have seen at Finance? (National Achievement in Mathematics Agency) For those interested in math education Check this link out: http://www.khanacademy.org Or his presentation at TED http://www.youtube.com/watch?v=gM95HHI4gLk He makes a great point that we learn by making mistakes, but only get rewarded the other way! The fear of honours maths in the general population is something I always noticed. Maths is so strange to so many people. So many people think they are not good enough. It goes with the Irish way of doing things, I think. Specifically the Irish approach to secondary teaching. The whole mess around the knowledge economy is part of the same problem. If you don’t acknowledge the way the system works and try to change it how can anything change? I always liked tennis. I used to play as a teenager during the school holidays but I never got any coaching. I decided to take lessons a few years ago in Switzerland. I thought I could do with 2 or 3. They went on once a week for 6 months. By the end I could see the difference between a decent shot and a know nothing one and the backhand isn’t bad either. I had a fantastic teacher. All of this stuff can be learnt and it doesn’t have to be left to those with astonishing talent. I often think what it would have been like to have had such a coach as a 9 year old . It is the same with maths. Teach the teachers. It’s a question of attitude and also of self confidence. If they can do it in Singapore why can’t it be done in Ireland ? Writing as someone with a kid going into sixth year….. the extra points being granted for honours maths from next year should make a difference. It has definitely changed the incentives a bit and made them think twice about dropping to ordinary level. As a previous contributor said, it is all about incentives. Honours maths is generally thought to involve the work of two other subjects and to have a significant risk of failure attached. @seafoid: “Teach the teachers.” Ah! But that would be too rational and logical. Problemo? Yep! Who is there to teach them pesky teachers? Like, teach them to teach the math. Not learn the math! Been there, tried to do it. 5 years attempting to climb Hamburger Hill. Very obdurate folk are teachers when it comes to being back in the desk! Know all the answers with 101% accuracy. Haven’t a clue what the questions are! Extra points is the Way of Defeat. Totally useless. But sure its a successful and losing strategy. So drive on! Problems: Political – don’t scare parents or annoy teacher unions. Parental – my little Mary is a genius! Demographics – 16% of population are good a formal, abstract thinking. Remainder are good at sums. Teachers of math – totally untrained cohort. Syllabi – totally off the wall stuff. I like math, but am not good at it. Have to learn it the hard way. Dismantle the examples and work backwards. NB: doing copious examples is NOT the way to learn math. 🙂 “If they can do it in Singapore why can’t it be done in Ireland?” We’re full of academic and ideological s***e! We need cranial enemas. Brian Snr. “How many good honours maths students go on to be teachers? Close to zero imho.” A decent point. Do we have data about the undergraduate qualifications of teachers? I would expect a bias towards humanities, and away from maths/engineering/CS, relative to other subjects like sciences and social sciences. The opening paragraph in the IT article is: “THE NUMBER of students registered to take higher level maths in the Leaving Certificate this week is the fewest ever. New figures show just 10,435 have registered to take the exam on Friday, the lowest figure recorded by the State Exams Commission.” The claim is completely meaningless unless the number taking higher level maths is given as a percentage of the population age-group who normally take Leaving Certificate. The fact that the IT Education Editor doesn’t do this shows that he’s not too hot on maths himself. Its an elementary point. The number of births in Ireland reached an all-time high (to that point) of 74,064 in 1980. It then fell almost every year, reaching a low of 48,255 in 1994. So, since the age at which Leaving Certificate is normally taken is 17 or 18, we would expect the number taking each Leaving Certificate subject to fall from 1997/98 onwards, reaching a low around 2011/12. If someone could produce figures for the number taking higher level maths as a percentage of the 17-18 age-group, then intelligent analysis could be done. I don’t know what those percentages are. Maybe one of the other posters can provide them? In the absence of such percentages, it is meaningless to focus on the number taking any particular Leaving Certificate subject, when the age cohort for the Leaving Certificate as a whole has fallen 74,064 to 48,255 in the previous fourteen years. Of course, the number taking any Leaving Certificate subject in 2011/12 is going to be the ‘fewest ever’, when the number of births in 1994 was the ‘fewest ever’. http://www.cso.ie/statistics/bthsdthsmarriages.htm Looking to the future, the number of births in Ireland hit its all-time low of 48,255 in 1994. Contrary to predictions at the time, the number then rose almost every year after 1994, hitting around 75,000 in 2008, surpassing the previous all-time high of 74,064 in 1980. Again, contrary to predictions that the recession would cause a sharp fall in the birth rate, it has held steady at that higher level since. So, we would expect the number taking each Leaving Certficate subject to rise from 2011/12 on. But, again, it would be the percentages that count. BTW I love the line under the heading – “the news today isn’t great”. I love that construction. “Not ideal” is another one. How are the banks? “not ideal ” . @JtO “The claim is completely meaningless unless the number taking higher level maths is given as a percentage of the population age-group who normally take Leaving Certificate.” If it isn’t in an out of context percentage, it is no use to you? Paragraph three, first sentence: “Some 55,550 candidates will sit the Leaving Cert this year.” I presume you can work out the percentage yourself… In the short term I think we should consider offering points to students that fial higher level (and relaxing matriculation requirements so that a fail of >20% in higher is sufficient) In the medium term I think we should consider restructuring the higher papers so that there is a section pitched at ordinary level and then the remainder pitched at the regular higher level (perhaps a common paper 1 between higher and ordinary?) – this would still give us the correct sorting but allow borderline people to demonstrate that they are very capable at the ordinary level. I think for many people the fear of failure combined with the knowledge that they can definitely do quite well in ordinary prompts the last minute change and the huge drop in level of the material exacerbates this. Teaching maths is hard. Not many people combine an adequate knowledge of the subject with an ability to communicate with teenagers. Teaching maths is unrewarding. People with the relevant skills mostly have better things to do with their time. Given these facts, are we sure we actually want to bring about an improvement in this area? I really don’t think the will exists. And as that wonderful maths teacher W. W. Sawyer used to say, where there’s no will there’s no way. So the first question to address is: do we really care? If so, why? I was lousy at maths at school. I learned at university. Is there a problem with that? The lecturers who taught calculus and matrix algebra in first year didn’t assume we had learned anything much at school. They started at the beginning, with definitions of functions and limits, and how to add, multiply and invert matrices. Strong students were a bit restless for a few weeks, until they noticed that the pace was picking up. I’m not convinced that there is a problem here. @hoganmahew As would be extremely obvious to anyone who knows anything about maths, one would need to know the percentage each year in order to determine whether or not the claim that the number taking Leaving Certificate maths is the ‘fewest yet’ has any substance. So, 55,000 took Leaving Cert this year. Based on the number of births in 1980, it must have been 70,000 to 75,000 taking Leaving Cert in the late 1990s. Therefore, it is not all surprising that the number taking Leaving Certificate maths, or indeed any Leaving Certificate subject, is much lower this year than in the late 1990s, when the 17-18 age cohort was in the region of 40 to 50 per cent greater. If someone can produce a time series of the percentage of the relevant age-group taking Leaving Certificat maths (rather than the absolute number), then let’s have it. Only then can an intelligent analysis begin. I am certainly not going to comment on the trend until I see such a time series, as only then can I see what the trend is. Maybe Seamus Coffey can produce one, as he seems to have figures for almost everything? Until such time as a time series showing the percentage (rather than the absolute number) taking Leaving Certificate maths is produced, its a brouhaha about nothing. @KD “I was lousy at maths at school. I learned at university. I’m not convinced that there is a problem here”. ? maybe im wrong but the whole point of having an education system is to educate our kids look at the waste of resources going in to the education system if the educaters are not up to scratch better still look a the waste of the next generation who are the real losers @hoganmahew For euro1.80 is it too much to ask our IT journalist to do the math for us? But anyway having the percentage for one year would not answer JTO’s very valid point. A quick visit to the Department of Education’s website (http://www.education.ie/servlet/blobservlet/Key_stats_leaflet_05_06.pdf) suggests that the total taking the Leaving Certificate peaked at over 64,000 in 1998-99 -so the pool of potential Higher Maths candidates is now 14% lower. Moreover, the pool of ‘core’ candidates (that is Leaving Certificate School candidates) has declined by almost 20%. Another example of superficial IT journalism! @ jto & hoganmahew Looking back through birth statistics is probably not going to get you an accurate picture, you’ve no way of taking into account the numbers of people who would have left the country with their children in the 80’s or the numbers of children who entered the country in the last decade with their immigrating parents. I’m pretty sure accurate numbers are kept of those sitting the leaving cert every year, somebody on here must have knowledge of how access to them. And as for fewer kids doing honours maths….most predictable stat ever…irish kids are lazy, pampered and too easily distracted by facebook/ twitter/Iphone b*llshit…I’m sure for a lot of them, once they discovered there wasnt an app for honours maths, they didnt want to know. @ JtO, etc Also the number of students who stay in education beyond Junior Cert is an issue. This appears to have shot up. http://www.irishtimes.com/newspaper/breaking/2011/0513/breaking17.html @ Jarlath “irish kids are lazy, pampered and too easily distracted by facebook/ twitter/Iphone b*llshit…” This is not an accurate characterisation of the kids I work with. They are bright, articulate, thoughtful, engaged, curious – perhaps it’s because they’re from Tallaght. Looking at this from a student’s point of view: There is a serious difference between pass and honours maths, so much so that I feel you have a great many people dropping down from honours and aceing the pass test but with only 50/60 points as a total obtainable goal. I think we need an in-between for Pass and Higher Level – some sort of intermediate level with total points obtainable at 80. It won’t solve the problem of not enough people doing honours but I feel it would still increase the overall competency. @ Jarleth’n’all “I’m pretty sure accurate numbers are kept of those sitting the leaving cert every year, somebody on here must have knowledge of how access to them.” A brief phone conversation later. http://www.examinations.ie/index.php?l=en&mc=au&sc=pb http://www.examinations.ie/index.php?l=en&mc=st&sc=r10 http://www.examinations.ie/index.php?l=en&mc=st&sc=r10 @ Jarlath P2 (: Unfortunately, the high numbers doing the LC is most likely as its a lot more difficult to get an apprenticeship. @clintideal: “maybe im wrong but the whole point of having an education system is to educate our kids….” Now who can argue with that! However, when it comes to formulating policy, there are trade-offs to be considered. For example, Finland apparently does pretty well in this area. But most of their teachers have a Masters level degree. There is also a suggestion being floated that younger kids should do more maths, but less drama, music and visual arts. I got these two nuggets of information just now, from the response of the Institute of Physics in Ireland to the draft national plan to improve literacy and numeracy in schools. So they do grasp the fact that there is no free lunch here. Before we decide we want better-qualified (and therefore more costly) maths teachers and less fun stuff for the kids, we should clarify why it matters. I’m not saying it doesn’t matter. There may be a good reason for the annual lament about Leaving Cert maths. If so let’s hear it. @Rob S Not sure a further downgrading of the subject is the way to go either – I wouldn’t necessarily agree with a ‘soft’ Higher level paper option. The comments above regarding the quality of teachers are the real issue. The year in which I did my LC we had two classes of Higher Level maths i.e. c50 students out of a total c90 students taking the LC that year taking Higher level maths. These numbers might seem like a statistical blip but the reason was very simple the two teachers teaching the two separate classes were excellent in every respect – in fact all students got a C Grade or better (old point’s method). The maths DNA genes are no better in the Midlands than presumably they are in Cork or Donegal but the teachers were at the time – and the results speak for themselves. (That’s of course if you believe the LC results have any standing in life – which by the way I don’t). Nevertheless my understanding is that the education outcomes in Finland compares very favourably to any nation on the earth (others may know the hard facts) – the Finnish model it seems, from my reading, is very simple – improve the teaching standards and the quality of the teachers generally and the rest follows. QED. @Yields or Bust Says I wouldn’t propose that the higher level be removed as an option but I think the fact remains there are people breezing through pass who couldn’t hack honours. My suggestion was targeted to elevate those who would end up doing Pass rather than to take from those currently doing Honours. Maybe an upgrading of the pass course is worthy of consideration also. @JTO You’re right. Another thing is that this will be subject to natural variability anyway. Having said that I have no doubt that current adversity will encourage kids to work harder. It is our job, as a nation, to ensure that they have a place to benefit from it. Education is the engine of social mobility. Crooked bond marketeers are the brakes on it. @Rob S Upgrading the PASS level to me is a better suggestion. I have googled looking for the figures I wanted, but only limited success. Best I could find was this report. http://www.engineersireland.ie/public/20100211-Mathematics_and_Science_at_Second_Level.pdf Based on a very quick and cursory examination (which I am sure others could improve on), it looks as though the percentage of students taking the Leaving Certificate, who took higher maths, rose from around 11 per cent in the early 1990s to 18 per cent in the mid 2000s, and then fell to around 16 per cent in the past couple of years. However, as Gavin Kostick pointed out very relevantly, the percentage of persons of the 17-18 age-group who took leaving certificate has itself risen sharply in recent years, and the number failing to complete secondary education has fallen sharply (to well below average EU levels), so, if applied to the number in the 17-18 age-group, rather than just to those who stayed on to take Leaving Certificate, the fall from the peak in the mid 2000s is much less. I would say that this is the more relevant figure, because if previous secondary school drop-outs are now staying on to take Leaving Certificate, even if they are not taking higher maths, then this is a good thing. So, to summarise as best one can: it looks as though the percentage of the 17-18 age-group taking higher level maths at Leaving Certificate rose very sharply up to the mid 2000s, but may have fallen slightly since then, but is still at a level well above its early 1990s (and before) level. So, clearly, the claim that its the ‘fewest ever’ is bonkers. With regard to international and historical comparisons, data is hard to find. In my class of around 40 of 11 plus age at primary school in Tyrone in 1959, I was the only one who ended up doing A’ Level maths some years later. However, lots of those who didn’t ended up much richer than me. The fact of the matter is: most people either have a talent for maths or they don’t. Its pointless trying to force those who don’t to base a career on it. They can still be extremely successful. I’d be interested to see the numbers. How much does Ireland spend per student on secondary maths compared to other countries and how do the outcomes compare? Just to clarify as its a long report: the figures I took were from page 22 of the report I linked to. I wonder what would happen if there was a free market in grades – i.e if colleges were able to award as many points as they thought prudent for each LC subject. I would be more interested in a candidates math grade than anything else – at least for a lot of courses. Lets lets say a small college said, all we care about is your maths grade, and say a pass in ordinary level English. now that would make people think about their subject choices “The fact of the matter is: most people either have a talent for maths or they don’t.” This is nonsense. Perhaps not everyone can be on X Factor but maths can be taught. Everybody uses money, after all. The Free Market in Leaving Certificate Points Has Spoken: Ireland Shall Have No Mathematics Students. Some subjects are more difficult than others. Applied mathematics is probably the most difficult (and the most beneficial) subject in the country. Most “STEM”(Science Technology Engineering Mathematics) courses are generally more difficult. However, students are not rewarded for the additional effort they must put into these subjects, and are effectively rewarded for dropping them in favour of softer subjects. I taught in a private 2nd level college in this country for a time. This was a “grind school” in every sense of the word, where the children of parents who could afford the fees studied from 9 in the morning till 7-9 in the evening. The school hired (some might say poached) the best teachers from the public system and made much of its average LC point quota and the improvements in points seen by repeating students who joined it. The most popular optional subject at the college was honours level Home Economics. The Points System is actually a perfect little example of an “Incentives Based” system, and a perfect example of how these systems utterly fail to deliver on promised results. When competing for courses, students play and game the points system to their points advantage, not their educational advantage. If a good student can get 90+ points from honours Home Economics, why would they spend the additional time and effort to get only the same result from STEM subjects like honours mathematics, Physics, or the insane choice of Applied Mathematics? The government claims to want more students doing STEM course, but then talks out the other side of its mouth by rewarding those who choose other courses. If you’re going to give students their choice of courses, then you have to give them a reason to choose the course you’d prefer them to study. There’s always a torrent of complaints and lip certain quarters when it is suggested that hard science study be rewarded more than other subjects(usually from the intelligentsia who flunked such studies). But the fact remains that people trained in STEM are the foundations of industry and innovation, particularly in the modern age. We can’t attract multinationals or grow our own companies without them. Poets and playwrights might impress art critics and review magazines, but they don’t provide jobs. Ulysses never put food in Dubliners’ mouths, or coins in their pockets. (I also note that perhaps if we had more logically, analytically and scientifically trained people in the country, we might be able to actually understand our current national crisis and calculate how much we in fact owe. But I digress) And I’m not going to get into the Project Maths debacle except to say that–compared to the previous course–dropping it is loss to the LC students who elected not to sit it this year. It’s only at about the level of the old JC course anyway. Some great points here. I’m an undergrad who sat the honnours maths and applied maths papers 2 years ago. I had a great Maths teacher who got a B1 in his leaving cert. He said people who get A’s in LC honours maths don’t go on to teach maths. @SByrne I would be more worried about JC maths teachers with biology degrees being qualified to teach maths. For my Junior cert I was taught the bare minimum in order to solve a problem, for leaving cert in a different school with a different teacher, I was thought how to understand what I was doing. Both my results and enjoyment of maths improved tremendously. We need to employ Maths teachers who have a good understanding of maths themselves, not teachers who just teach the book. Also weaker students often have difficulty with the introduction of algebra in 1st year. I don’t see why simple algebra cannot be integrated into the primary school curriculum as it isn’t really a difficult concept. Students find it difficult in first year because they always associate masths with numbers. The problem does not occur in 6th year or even secondary school. My nine year old – who understood the concept of multiplication at age five or six – has just spent an entire year being ‘taught’ multiplication through pointless repetition of examples, leading to the eventual construction of a multiplication table. Her homework usually looks like this: 6 x 1 = 6 x 2 = 6 x 3 = etc. In other words, she’s learning how to add again, or to count by x. But the concept – multiplication is scaling or repeated adding – has never been a part of her instruction. This failure/refusal to teach conceptually retards learning throughout the curriculum, but is especially damaging in mathematics, as that subject is about the application of concepts to problems that (may) yield to numerical understanding. Anyway, kids know when their time is being wasted. Those with mathematical aptitude make the rational decision to switch off very early in their education. “However, students are not rewarded for the additional effort they must put into these subjects” It would be interesting to see how well those with honours maths fare on the labour market in comparison to those with pass maths. On incentives: elite colleges and universities in the US give serious weight to the difficulty of a student’s course load in making admissions decisions. Because of the extreme competition for all places – not just in certain subjects – in these institutions, the norm is for anyone who wants to get into a top school to take math through calculus, even if it jeopardises grade point average. Someone who aces algebra and geometry, but does not go on to do trig and calc, is not going to Harvard. They’re not even going to a good state college. Yes, there are problems with more qualitative approaches to 3rd level admissions, but getting students to try to learn challenging subjects is not one of them. @omf The physics course has absolutely no calculus on it. It’s totally ridiculous. Applied Maths is the only course that hasn’t really been dumbed down. It would be great to see people encouraged to do subjects like physics but without any real maths on the LC paper, you could easily get an A in physics in the leaving cert and be totally unequipped to do it in third level. The exam is about how well you can learn off definitions and equations. ‘Anyway, kids know when their time is being wasted. Those with mathematical aptitude make the rational decision to switch off very early in their education.’ Very True. @ ObsessiveMathsFreek “Poets and playwrights might impress art critics and review magazines, but they don’t provide jobs. Ulysses never put food in Dubliners’ mouths, or coins in their pockets.” Hold on there a sec., the arts do provide jobs and revenue. In the sense that Dublin is now a Unesco World Heritage city of Literature, and attracts a lot of visitors for such reasons and that the hotels are packed for the various festivals through the year (70,000 attending the Fringe alone), I would say that Ulysses does put coins in Dubliners’ pockets – what Joyce would have made of that is another matter. I’m a big Maths fan, but the mistake being made here is the old-fashioned trade-off view. We need a bright, creative educated people who, as far as possible given the miseries and anxieties of human existence, can live full, flourishing lives and that means a variety of subjects and educational proccesses well delivered. After all, innovation in Maths, Science and the Arts are all creative acts. The Arts Council pubished an Indecon study on the economic impast below. http://www.artscouncil.ie/Publications/Arts_Council_Economic_Impact_Full_Report.pdf “Poets and playwrights might impress art critics and review magazines, but they don’t provide jobs. Ulysses never put food in Dubliners’ mouths, or coins in their pockets.” This strikes me as being incorrect. Many tourists will arrive in Dublin in one week’s time inspired by Ulysses itself! We do not see similar numbers making a pilgrimage to Broombridge station to commemorate the quaternions. Advocacy for mathematics training must not be based on attempts to lower of the status of others; that is the route to acclaim from one’s sectoral peers and an emotive negative reaction from those whom one ought to convince. (Disclosure: I am a maths graduate as well as an economist.) – I think the threat of failure is important for the borderline student. We can consider a very simple model of the student’s decision. Assume that the student faces a pair of truncated normal distributions of results, one for each difficulty level. He/she assigns two means and an invariant standard deviation to the underlying non-truncated normal distributions. Assume further that the mean is higher by 40 in the case of the ordinary-level paper compared to the higher-level paper; this agrees with the CAO points scale, and it does not produce perverse results in the case of the borderline higher-level student. When we do this, we can see that the high probability of getting zero points at Higher Level, relative to getting zero points at Ordinary Level, is a big inducement to choosing Ordinary Level. This is before we consider the added cost of getting zero points in maths, i.e. the requirement to have passed a maths paper on the part of university applicants. I see a big role in this decision process for the steep drop in payoffs for higher-level students who get 38% relative to those who get 42%. Bonus points beyond the current CAO assumption about difficulty will help, but if we assume the added cost of failing beyond getting zero points, and risk-aversion on the part of students, it is hard to see whether increasing payoffs will be effective in inducing marginal students to choose Higher Level papers, as opposed to merely rewarding those who would have taken Higher Level papers anyway. Perhaps that has merit in and of itself, but most people seem to think this debate is about increasing participation rather than rewarding talent, so we should choose incentives to achieve that goal. @Gavin Kostick If you want to escape “the old-fashioned trade-off view” you’ve come to the wrong site. Economics is all about trade-offs. But I agree with the gist of your comment. Kids need to see that maths is a creative activity. Where it differs from music and drama is that there is no point in sitting in the audience. The only satisfying answers are the ones you find for yourself. @All In many sports where a judge is required to grade or mark the effort of a participant the ‘degree of difficulty’ forms part of the marking structure. Diving, ski jumping are some examples. I cannot see why such a basic ‘degree of difficulty’ award system cannot be built into the points system here (other than the normal teacher blacklash of course). Rory O’Farrell Says: “It would be interesting to see how well those with honours maths fare on the labour market in comparison to those with pass maths.” I would love to know how many of the failed developers and CEOs of the Tiger Experience did honours maths. Did Seanie Fitz, for example? @Edward: “…most people seem to think this debate is about increasing participation….” Where ‘participation’ means having a go at the Higher paper! That’s exactly why I think the debate is silly. What matters is whether students have the appetite to go on and study further. @ Kevin Donoghue I think ‘participation’ and access is a factor. I was lucky to go to a large school, which was big enough for 2 higher level classes. But if someone goes to a school where only 4/5 people are doing higher level, are they really getting a fair crack at the whip? A few things to please keep in mind about teaching ANY subject, but especially for a subject which does require an additional level of formal (abstract) thinking – as opposed to the concrete. Each of us possess both, but in vastly different measures. Which of ye can read an engineering drawing and clearly understand the spatial constructs within it? Ever see the Boheringer Mannheim map of intermediary metabolism? I have no problem with either, but please keep me away from dy/dx and the like. Teaching something successfully requires two very different skill sets. You are a subject scholar (NOT A SUBJECT EXPERT!). You can place yourself within the shoes and minds of those whom you are teaching. Maths consists of two parallel topics: sums versus cognitive problems – straight-forward calcs versus decrypting text and transposing it into math notation – then you do the sums. You can learn the former by rote, the latter only by engaging in a meaningful intellectual manner with the course material. Everyone has to be able to do sums – and this includes percentages and exponents, both of which are tricky to understand. Neither are intuitive. Those who will teach maths need formal instruction in how to teach the subject. They need to teach a curriculum which makes sense (our current primary and secondary are almost useless). A small proportion of pupils are mathematicall savvy. You can spot them between ages 5 – 7. JI above mentioned that their 9 year old was doing simple multiplication. At that age a Montessori schooled child would be tackling complex division, area and volume. Ye are getting what ye neither need nor want in respect of math ability. The pygmies are in charge, and have no interest whatsoever in reforming (aka: upgrading). The fact that so many young persons do actually succeed in math is a minor miracle. “They are not dumb – but they are different”. The idea of a Higher paper in any LC subject is totally daft. But try selling that piece of snow to the Irish educational eskimoes. Brian Snr. We need to be teaching about bonds, CDS’s etc in LC. Not just in economics/bus studies/accounting but as a separate subject (financial maths?). “‘Anyway, kids know when their time is being wasted. Those with mathematical aptitude make the rational decision to switch off very early in their education.’ Very True.” Absolutely correct. A couple of national school principals have told me with real belief, that children at age 4/5 should not be taught to use numbers over 10 because they have no real concept of what they are – any apparent ability to manipulate higher numbers is mechanical coincidence. Similarly, children 6/7 should be limited to numbers up to 20. 3rd class is said to be the point where some can genuinely move ahead. There is a woeful lack of ambition by Ireland’s (very expensive) junior school teachers in Maths. It is a similar picture in science. The LC points system is silly. As others have said it is daft that all “points” are deemed equal. There is also the question of whether it is sensible in a world dominated by English, Spanish and Chinese for so much time to be spent by Irish 18 yr olds to get “points” or “extra points” by studying the Irish language. “There is also the question of whether it is sensible in a world dominated by English, Spanish and Chinese for so much time to be spent by Irish 18 yr olds to get “points” or “extra points” by studying the Irish language.” I spent a total of 45 hours studying Irish on a Gael Linn course 15 years ago and my Irish is only a little bit worse than the average native. I don’t think most people are spending ‘so much time’ on Irish in secondary school. If they were they’d be at least as good at it as I am at Latin. JtO: “it looks as though the percentage of students taking the Leaving Certificate, who took higher maths, rose from around 11 per cent in the early 1990s to 18 per cent in the mid 2000s,” The leaving cert was dumbed down after the early nineties. The last year bonus points were awarded was 1993 afaik. I expect that is one of the reasons more people took it from then on in. ObsessiveMathsFreak: “Applied mathematics is probably the most difficult (and the most beneficial) subject in the country.” Applied Maths was not that difficult for an honours maths student when I did it. I remember 3 or 4 other guys leaving the applied maths LC exam and joking that it was a definite “A” in the bag. Students should not be put off by the suggestion that it is very difficult. If you have a decent teacher it is pretty much a cake-walk for a good honours maths student imho. The problem is that it is not available to most students. In particular, it is available in very few all-girls schools. The wide range of LC subjects (including the Honours Home Economics option for the financially willing) combined with the lack of opportunity for some to choose particular subjects, or to matriculate in 5th year with a view to gaming the system in 6th year, make the LC an unnecessarily uneven playing field. @Eureka “We need to be teaching about bonds, CDS’s etc in LC. Not just in economics/bus studies/accounting but as a separate subject (financial maths?).” Are you not conflating ‘maths’ with the use of it? Hands up anyone who is in either financial IT or financial market trading who has ‘invented’ a new algorithm? If all you are doing is applying existing known functions, then pass maths is probably enough. No? In the sense that Dublin is now a Unesco World Heritage city of Literature, and attracts a lot of visitors for such reasons and that the hotels are packed for the various festivals through the year (70,000 attending the Fringe alone), This strikes me as being incorrect. Many tourists will arrive in Dublin in one week’s time inspired by Ulysses itself! Tourism is all very well, but the country cannot rely on the tourist industry as a basis for the economy. Bloomsday festivals are all very well, but I would prefer to see companies like Intel and Blacknight placed higher on the scale of national economic importance. This country needs industries apart from agriculture and tourism if it is to progress anywhere in the modern world. I’m a big Maths fan, but the mistake being made here is the old-fashioned trade-off view. Advocacy for mathematics training must not be based on attempts to lower of the status of others; Look, those are all very fine views, but what we have right now is a situation where every student in the country is making those trade offs, and where over 80% of them this year have effectively elected to close off many future careers in modern, high tech industry. Our educational policies are smothering our future industries in the womb. If the government wants a shot at a modern, industrialised economy, of the kind found in Germany, then it must take a heavy handed approach to STEM subjects in its education system. Yes, other subjects must be disincentivised or discouraged in comparison to those subjects which are more important to the national interest. I do not see that the arts, humanities, Gaelic, or business subjects have ever brought much to this country; certainly, they have not brought lasting prosperity of any kind. They have had their day, and I believe it is time for the government to make a serious effort towards creating a science and technology saavy workforce in Ireland. But first the government must acknowledge that some subjects are more valuable than others. Only then can we even begin to move away from this “100 points fits all” model for the leaving certificate. Applied Maths was not that difficult for an honours maths student when I did it. …. The problem is that it is not available to most students. In particular, it is available in very few all-girls schools. I also take this opportunity to note that there is a chronic lack of availability in STEM course in many all-girls secondary schools in the country. Very few offer applied mathematics, and most do not offer separate physics and chemistry courses. This is a legacy of old, conservative attitudes towards women’s education compounded by church control over secondary schools(Admittedly most schools have taken steps up from teaching girls to sew, but they’re still behind in their attitudes.). Effectively, almost half of the population are being removed from the pool of potential engineers, technicians and scientists the moment they set foot into secondary school. This is a prime example of just how poor the STEM education system is in this country. No other attempts at reform can be taken seriously while this egregiously outdated situation continues. Ireland’s education system has real problems, but like most other problems, the first hurdle of actually getting people to even acknowledge that a problem exists has not yet been overcome. @Jon I Don’t lots of second level schools insist Irish is studied as one of the LC subjects. @Hogan Not sure what you mean by “inventing”. I am fairly sure that lots of people are bamboozled by the maths embedded in “tools” they “use” – because they have no real feel for or confidence in maths. For example the execs in banks who hired physicists to write their trading programmes. Real emperor’s new clothes stuff. A lot of this fretting over LC maths is misplaced in the light of wider failings in the Smart Economy strategy. It doesn’t seem that long ago that the media was leading an short-lived bout bruhaha over low standards, grade inflation and plagiarism in Third Level. Kettle and Pot come to mind. @OMF: Thanks for reminding me about STEM. Its a while since I first encountered it. That’s reality, but not that it makes a blind bit of difference to those who – do not teach, but make significant educational decisions nonetheless. They live in an untethered undersea capsule drifting in the abyssal darkness of their own ignorance. They make the Luddites look positively Nobelian. @ Grumpy: Also heard about the ‘inability to comprehend number’ and the dreadful primary school maths syllabi. This is a truly disgraceful situation. I know of several 7 year olds who can do mental arithmetic with hundreds! They’r slow, but accurate. Ever see the rubbish that poses as primary school math workbooks? Its appalling. Brian Snr. Even though the the articles ‘lowest ever’ claim is a very poor angle for an article on the topic, we are getting hockied in the OECD tables. Labour thinks it’s not that we’re getting worse but everyone else is getting better, and that may be, but we’re getting hockied none the less. I like to make a couple of points that I think aren’t covered. -Increase Male teachers (for primary Maths especially) Teaching is by in large a female activity in Ireland in National school, and more and more at secondary school. Men seem to me to be either uninterested or frightened of it. I did well in Maths, I work as an engineer, my class was 85% male in university, my classmates work in engineering or finanical services. None are teachers. Unfortunately I don’t have time to source the numbers but I would suspect that increasing male teachers would increase the quality of Maths teachers. Not because men are better at Maths than women, you could probably prove the opposite, but because men tend to do more technical degrees than women or put another way, most nerds are male. Then again, I’m pretty sure the female to male ratio is 3:1 in Finland, and they do just fine in Maths. -Cultural On the other hand I know loads of teachers. Most choose to do an arts degree (at 17), picked none technical subjects and afterwards decided to do a hdip becasue ‘they didn’t know what else to do’ and ‘sure the holidays and pension are great’. I don’t believe all teachers think like this but I think a significant amount do. I’ve spent some time in Finland, and there people want to be teachers, it’s an honourable profession, I visit there a bit, when I talk to people about teaching, they talk about it with pride, most can talk about it with pride in at least 3 languages fluently (but that’s another debate), they remind me of how we used to talk about our ‘celtic tiger’. I feel Irish society to some degree buys in to ‘Those who can do and those who can’t teach’. Or perhaps it’s a money thing. How to remedy that. Well, I’d say we should create a competitive teaching profession. In most jobs in engineering you get more pay increases faster, you get rewarded for talent, you get less holidys and you get a define contribution pension. Why not start this ‘Competitive teacher’ on the same wage circa 35,000 (I believe), but bench mark with a mixed bag of technical professions, so the highest mark is say 150%-200% that of the current highest teacher salary. Where yearly pay in/decreases are based on performance. The teacher forgoes all his/her defined benefit pension and ‘job for life’ status. He/She also has to work most of the summer. i.e. no extra for correcting papers. So a teacher could opt for either profile, with the ‘competitive teachers’ increase in pay offset against his/her worse pension. I’d say this would attract more talent, probably more men and might have the added benefit of attracting those who’d like to teach but not for life. I think that we can forget the idea that any more resources are going to be put into teaching math. The reality is that resources are going to be removed from the education sector for the next five years at least. @John Foody I’m tremendously sceptical of the idea of performance related pay in education. It seems like it would drive good teachers out of bad schools, reinforcing the class divisions in this country. In a recent radio programme there was mention of young fully qualified maths teachers (albeit women) who were working in London. All available competent maths teachers should be hired and the Croke Park agreement used to move people around so that they replace unqualified or ineffective maths teachers. Many of these existing teachers who are not maths qualified are well able to teach something different and even if they are not able there are many subjects in which they will do less damage. Basically maths teachers should be hired above all other disciplines, if they are available. When the supply of teachers is achieved require all schools to offer Applied maths etc. Gotta start in our Pre-School System. @ Kevin It doesn’t have to be an absolute measure of performance. I’m sure performance can be measured relative to the average performace of the school of teaching. There’s ways of factoring it in. We could have a money follows the pupil system either. Go as far as providing more money for those from demographics proven to hinder education progress. It’s the same old story in this country, we want great performance from our civil cervants. So in order to achieve it, we destroy their ambition by rewarding medicority as much or in some cases more. I’m sure a lot of contributors to this blog that lecture or tutor have plenty examples of the same mediocrity thrieving in our 3rd level institutions. @ John You would have to assume all students are equal! equally good or equally bad. I heard a plumbing instructor one say: “Give me timber and I make you tables” obviously in reference to the caliber of his class. But why a plumber would want to make tables, I dont know! €180Billion = Manageable €70Billion = Systemic €19Billion = IMF €500,000 = Not enough €200,000 = Taoiseach €40,000 = One for everyone in the audience 4-10% = Ebbs and flows It’s the ones with honours maths who seem to be our problem. WGU Is that on the honors or pass paper this year? @ Al Know you don’t, becasue they’re not. @ JF: ” … we destroy their ambition by rewarding medicority as much or in some cases more.” Whose the ‘we’ John? Would ‘they’ be the self-selected group of vested insiders who endeavour to persevere to maintain their positions of control? Joe Lee spotted ‘them’ well! @ DO’D: “Gotta start in our Pre-School System.” Yep, spot on! Trouble is that when they get to primary its downhill all the way except they have the good fortune to go to a genuine Montessori school. Then they come out with a two-to-three year advantage and it stays that way for most of the rest of their schooling. Achieving high standatds in math teaching is no great mystery. The principle impediment in Ireland is an ideological executive mind-set and gutless politicans. We’ll be back here again in 12 months time. Its truly depressing. Brian Snr. It really makes an argument look weak when you confuse ‘no’ and ‘know’. @ Brian Wood Snr. Yes, them. & if we don’t take ‘them’ on during our current perma-crisis, will they ever be taken on? @ JF If one has non homogenous inputs, then how can one measure and/or reward outputs? No what I mean? I’m not sure about this one. Is it really that important. As JTO pointed out Honours Maths is not a pre-requisite for success at all. The only number we need to know for FDI is 12.5% Whatever talent they can’t recruit in Ireland they’ll bring with them. And then that talent will have kids and those kids can go on to do the honours maths! @John Foody In principle, it’s possible to measure improvement in individual classes and individual pupils, and local management are, in principle, motivated to reward good performers. However, would that actually occur in practice? Is it not likely to be the case that teachers who spend more time politicking and padding their cvs than teaching would be the winners from a performance related payscale? Seamus Coffey wrote: I found the following a little alarming. “one in five students drop down from higher to ordinary level maths on the morning of the exam.” When is this decision made? I presume it is not made on the morning of the exam, at least not in most cases. Still, it is a little disconcerting that the decision to take one paper or another is left until so late in a two-year programme. I have brought up the subject of secondary school mathematics before on the Irish Economy blog site. Quite recently too, if memory serves me. The reason is very simple. No one is allowed to have the privelege of learning mathematics in Irish schools. What generally happens, is that the majority of students (including the very best btw) bomb in their exams at Junior Cert level, owing to the way in which they are presented with maths as a subject, from primary (national) school level, up until the date at which they sit a Junior Cert paper in mathematics. Most students have made up their mind at that stage, that having the privelege of being able to study maths in Ireland at undergraduate level, is like the green grass on those faraway hills. The fact of the matter is, a few students do manage to pass through that filter by a roundabout means. Namely, a few students develop some understanding of mathematics via one of the two pillars (Algebra and Geometry), which is technical drafting. By learning how to measure, draw properly to scale, understand angles and intersections and use a set square properly – those (male, and a few females), are given the rarest of rare opportunities. To participate in an education in mathematics in the Irish schooling system. I have to stress again, that even the most gifted students in Ireland are unable to crack mathematics, unless they chance upon a good teacher in tech drafting, in which case they learn through the geometric route as I described. So it is not a question of lack of academic ability. It is a problem in the way in which the science of maths is delivered to the student. The fact is, in order to learn mathematics as a young person in Ireland, you need to completely stop listening to the paid staff, from a very young age, and simply follow your own instincts. That is precisely what is done by those young folk who do wish to pass a degree in engineering. They generally do grinds, and open their grind homework in front of their teacher in their Leaving Cert class, and ignore their teacher. The teacher is generally teaching a ‘higher level’ LC maths class, who will switch down to the pass paper, a week, or a day before the exam. The odd thing about it is this. Not even the brightest and best young people bother to sit the maths examinations in Ireland. But their is terribly resentment at the same time surrounding the subject, and any daft young people who might attempt to sit a higher level paper. Even the teachers in otherwise good-ish secondary schools, barely manage to hold back their resentment of the few foolish young people who do dare to challenge and Gods, and sit the higher paper. It is like: Who does s/he think they are? There is terrible, terrible snobbery and resentment surrounding the whole mythical sciences of maths in Irish education. It is like, how witch craft or pishoges, would have been viewed a century ago. I could say plenty more, but maybe people here get the picture I am painting. BOH. @ All, There have been a few times in my lifetime, when I performed some deed, or acted in some manner, for which I was later ashamed of myself. One of those instances, still lodged in my brain was an occasion on which a young lady (a very nice, gentle youngster from home), was asked to the blackboard during my Inter Cert maths class in 1990. She was asked by the maths teacher to perform some simple operation in basic geometry using a piece of chalk and a large plastic set square. Draw a line at right angles to an existing line. Something that basic. Us fellas in the class, thought that was great gas. To watch a young lady try various ways to manipulate the set square implement, without success, in trying to draw a right angle. Looking back at that incident twenty years later, it may serve as a demonstration of my points above. All of us fellas (as tech drafting attendees), felt very smug about ourselves, with our understanding of basic geometry. On the other hand, I can safely say, that twenty years later, my algebra is atrocious and possibly non-existent. Not to mention what crimes I might commit, if presented with Calculus. It’s coming against me now though, as I try to wrap my weary brain around statistics and probability with some basic functions thrown in, and trying to execute it using digital tools. There has been a visit to the attic of late, and some old text books were pulled from the heap. Yeah, that bad. BOH. Incentives can be useful but unless there is an enthusiasm for maths, what is the long-term benefit? Much of the work in the IT area for example can seem mind numbing to people who haven’t the enthusiasm for it. The combination of an enthusiasm for science and entrepreneurship, should be encouraged and last week Peter Thiel who invested in Facebook when Mark Zuckerberg was 20, announced a plan to to make 20 grants of as much as $100,000 apiece to teenagers who have promising ideas for technology businesses. His venture capital firm will act as advisers and mentors to the grant winners. I wrote last week about an insert in the FT promoting Ireland as a centre for entrepreneurship. Two of the 11 article contributors were entrepreneurs: http://www.finfacts.ie/irishfinancenews/article_1022419.shtml Foe the ‘it’s all gone downhill’ merchants, here, from the rather excellent State Examination Commission website, is the Higher Level Maths paper 1, 2010. http://www.examinations.ie/archive/exampapers/2010/LC003ALP100EV.pdf and for comparison the 1996 version (as far back as it goes). http://www.examinations.ie/archive/exampapers/1996/LC003ALP100EV.pdf @ BoH If that’s the worst you did, then fear not, my childhood was crammed with far more cingeworthy incidents than that. @Gavin As indicated above the maths teacher who thought 25 of us Higher level in the mid 1980s (all gaining Cs or better – 11 As from that one class alone) always suggested that the higher level maths papers from the early 1970s were the most difficult – I remember these questions seemed to appear on our Christmas tests etc with great regularity – he suggested that they were actually more difficult than what appeared in the 1960s or 50s when he was learning his trade. So for a real case of showing the dumbing down effect I suggest pulling out the papers from 1972/73/74 – which from memory were pretty savage – these papers (having studied Maths in the interim) look easy street in comparison. This thread has diverged from its original point. It isn’t about the standard of maths education, or about how necessary it is to be good at maths to be successful. These are obviously important, and worthy of a thread on their own. But, this thread is about the number taking higher level maths in the Leaving Certificate, and the reasons for the fall in that number in recent years. Both the IT Education editor and the author of this thread suggested that the fall in the number was bad news, with the implication being that it resulted from students having less interest in higher maths than in (possibly) easier subjects. I butted in and said that this claim was wrong, and that the fall was almost entirely due to the fall in the number of persons in the age-group who sit Leaving Certificate. I gave some figures for the number of births years before to indicate this. Some more figures support this. These are the figures for the number of persons aged 15-19 since 1996 (ideally, I’d have liked figures for the number aged 17-18, but these aren’t available – however, the trend will be virtually identical to that for the 15-19 age-group). 1996 339,536 2002 313,188 2006 290,257 2007 286,000 2008 283,900 2009 278,600 2010 273,300 2011 not published yet So, the number in this age-group fell by almost 20 per cent betweem 1996 and 2010, and is still falling by around 1.5 per cent a year. Just to be clear, this fall has nothing to do with migration. There was high net immigration for most of this period. It was due to the afore-mentioned fall in the number of birsths years previously. But, obviously, if the number of persons aged 15-19 (and 17-18) falls by 20 per cent, it is not surprising in the slightest that the number sitting any Leaving Certificate subject should fall. It is no big deal. Ideally, I would like to have figures for the number taking higher maths over the same period and relate them to the population figures, but I was unable to find them. However, the same IT article gives a figure of 10,457 for 2007 and 10,435 for 2011 for the number registered for higher level maths – in other words, almost identical (a fall of just 0.2 per cent). However, between 2007 and 2010, the number in the age-group 15-19 fell by 4.5 per cent, and is very likely to have fallen further in 2011. In short. It is another tedious IT brouhaha about nothing. Another phoney IT ‘crisis’. The proportion of the age-group 17-18 taking Leaving Certificate higher maths is rising, not falling. It has risen by about 5 per cent since 2007. Of course, it could be argued that the fact that neither the IT Education editor, nor the author of this thread, had the gumption to relate the figures for the number of persons taking higher level maths to the number of persons of the relevant age-group, is itself an indication of poor mathematics awareness in Ireland. I wouldn’t disagree with that in this instance. It is rather elementary, after all, that that should be done. Jto wrote, This thread has diverged from its original point. It isn’t about the standard of maths education, or about how necessary it is to be good at maths to be successful. These are obviously important, and worthy of a thread on their own. But, this thread is about the number taking higher level maths in the Leaving Certificate, and the reasons for the fall in that number in recent years. Emphasis, my own. Nice, spin doctor-ing. Why aren’t we talking to 16/17/18 years old’s today, and asking them what they think? Nobody asked me twenty years ago, and I could have given them the whole skinny on mathematics and education. Saved Craig Barrett some speaking time, right now. But no one did consult me, or any of my generation. No one does today either. That hasn’t changed. We have still got the ear plugs installed. It is funny sometimes, in Ireland, how we can ignore a huge elephant in the room for decades, and then suddenly, out of the blue, for no better reason that political expediency, someone magically discovers the problem – and it is described using that phrase in recent years. As if, real young people attending real educational programs on the island of Ireland, could not see the problem for themselves two decades ago, as I could. But the teaching profession is such a massive vested and protected interest, everyone in communities were afraid to speak out. And I find it very, very interesting, the way in which the debate has been framed. That it is the students who spontaneously decided by go off the rails. Which averts the focus away, from the part of the problem, which is to do with the teachers and what/how they teach. It was Craig Barrett who made this an issue. It was Craig Barrett who made it an issue. Before that, it wasn’t on the political radar at all. But that doesn’t mean that generations and generations of young Irish people, could not see for themselves the prejudice that exists within the education system, against mathematics (and science in general lets point out), and the bias towards the humanities. The discussion about level cert mathematics is a bit pointless too, now that we have one. Even though Craig Barrett has succcessfully put the issue on the radar, the spin doctors in Irish journalism, have decided to confine this to a problem that exists only in those final two years of the secondary education cycle. Nothing before that point is considered to be at fault in any way. It is a lot like the failure in the Irish language. Which there is invested, a lot of years of teaching time prior to secondary level. Yet, we seem to be making no progress on the Gaeilge front either, despite decades of problematic teaching methods. We don’t talk about that either. In fact, just about anything that is broken in education in Ireland, we ignore, and we don’t talk about. Until a multinational ex. boss, decides to pull the plug. Then we ‘jump’ to some extent. It is all to do with confidence, that a young person develops in a language, in themselves and in their use of language (mathematics is simply an international way to communicate, in a modern global economy, which leaves Ireland further cut off from everything else, in addition to cashflow). Young people must develop a degree of confidence in a language, be it maths or Irish, or French, of Physics, a long ways prior to getting to Leaving Cert level. If you don’t offer that in education, then it is pointless the teacher at the top of the classroom ploughing down through a syllabus. BOH. @ All, In a way, I have never left behind one side of mathematics. The geometric side. Being involved in architectural design projects all of my life. But even there, the anti-mathematical or geometric bias reigns very strong. It is perhaps a coincidence, that much of my geometric tuition in computer aided design, was received from an ex. Intel employee, who was responsible for drafting and setting out of Intel fabrication labs at Leixslip for many years. In fact, in memory serves me, this man who taught me in computer aided design, would share breakfast with Mr. Craig Barrett to discuss project details, when Barrett was in Ireland on trips. Yeah, you could say, I received my advanced geometric (zero millimeter tolerance construction design), from the man who did drafting for Craig Barrett. Bear in mind, what I have mentioned above about confidence in mathematics, about learning maths through the backdoor of technical drawing training, and about that poor young lady, who lacked the ability to even draw a right angle on the blackboard in 1990. Those are all critical plot points, on the scatter diagram we are trying to analyse here. Now fast forward to late 2008, during the time I was one of the senior architectural staff members of a developer here in Ireland. It was interesting how there was a new paradigm coming in, in computer aided design at that time, which enabled designers to move beyond two dimensions, and beyond the third dimension also, into that of planning, scheduling and logistical/resource & cash flow management of complex construction projects. It was interesting to me, how the senior architect involved, deemed fit to fire all of the Irish staff, and hire Europeans instead, who it was considered, knew best how to manipulate software within the new paradigm. Not to mention the years of on-the-job experience some of the Irish staff had, they were all (including myself), put out in the cold. I spoke to a colleague of mine at the time, who worked on the national Childrens’ hospital project (approx. 600 million euro), in terms of the computer aided design, and it was the same story there again. Rather than invest the confidence in the Irish staff, the senior architects engaged carpetbaggers from somewhere in middle America, who could use the software tools. The reason why myself, and colleagues of mine were any good at all, in computer aided design was because we had mathematical brains. What we didn’t have were the employers who had developed enough confidence to allow us to exercise those same brains. You can see that we are retrenching in terms of our confidence in Ireland. You compare the era of Craig Barrett, and my friend who gave me instruction, to today’s case, where we outsource it to the carpetbagger instead. BOH. If we want to examine understanding and ability to apply, rather than memory, why not make it an open book exam? @ RO’F: Now, now, don’t spook the marke…. Oops! Sorry! I meant the Vested Ones. 🙂 Brian Snr. R O’F writes, If we want to examine understanding and ability to apply, rather than memory, why not make it an open book exam? In the past year, I have witnessed in my own experience the changed nature of third level education of undergraduates, where the lecture notes are uploaded to a system online, where students can access it through their student login. What tends to happen, when assignment work is un-coordinated, and over-assigned (seven subjects in the course I attended last term), is that students stop going to the physical lecture, and instead adopt a strategy, based on the fact that they know the lecture notes are available to them – and rather than attend a physical lecture – they divert time instead to completing assignments, and simply, memory cram the lectures notes available online before exams. In effect, it has the effect that the major component of capital investment in the third level education system, the professor and the lecture space, to which the class is allocated a time slot each week of term, becomes sort of redundant, with the professor addressing an empty room. It was an ironic, and possibly un-intended consequence, of allocating more PROJECT-BASED assignment work to student(s), that in the end, resulted in an increase in the techqnieue of memory-based, last-minute information cramming by the student (non-) attendees! But rather than accept this fact, and try to assess the situation as a manifestation of complex demand-supply systems behaviour, of numerous free-willed agents, who are trying to optimise given the parameters, the staff in effect sticks its head in the sand, and continues to bellow away to the empty chairs in front of them. I know, it is not exactly like an ‘open book’ exam, but it is an open lecture notes course, using new web technology. As more lectures are distributed via podcast, webcast and so on, it becomes even still more problematic. I can imagine a time, when students enter an exam with a video iPhone, and engage in some pathetic attempt to scroll down through available webcasts, in search of answers! Open iPhone exam. You heard it here first. BOH. @ JTO Well said. I’m not sure many on this site would be shocked by the poor sandard of journalism in this country. Which of course, in its medicority helps hinder the real issues from being tackled. Though I don’t think there’s much doubt we are getting worse at Maths. From that PISA report published in December last year. Covering 15 year students examined in 2009. http://www.erc.ie/documents/p09national_summary_report2009.pdf ‘Changes in mathematics performance are examined for 40 countries between 2003, when mathematics was last a major domain, and 2009 Ireland’s mean mathematics score dropped 16 points, from 502.8 to 487.1. Most of this decline (14 of the 16 points) occurred between 2006 and 2009. Just one other country, the Czech Republic, experienced a greater decline (24 points). Ireland’s rank dropped from 20th to 26th among countries that participated in both cycles’ Of course this ranking is based on test administered to 15-year-olds. However I would say it is unlikely that students in Ireland become more Maths literate than students in other OECD countries once they reach 16/17/18 years of age. Ireland is nowhere on the PISA test for maths at age 15 http://www.michael-holzapfel.de/fortbildung/pisa.html This is on the ball ( in German but there is always google translate for that Doolin style English) http://www.nzz.ch/nachrichten/hintergrund/wissenschaft/so_viel_rendite_bringt_ein_kind_1.10658954.html A Swiss economist reckons if Switz can improve its PISA test scores for the weakest 13% of students and get them above the 400 point mark it will feed directly through to higher GDP growth . Crap teaching costs Ireland jobs. @BO’H: Been there Brian. Best attended classes are the mid-semester examinations (usually held in lecture rooms). Lectures at 09.00s are also interesting. However, two of my lecturers took class attendances at every lecture. A couple made half-hearted attempts. BlackBoard is indeed a useful source, except that some fiendish lecturers asked exam questions on material that was not posted, but was dealt with during class or that was assigned as reading. Now wrt to maths. UCD has a superb and dedicated Maths Support Centre. Five hours per day, five days per week during semester. Always packed out. Message there somewhere. Brian Snr. I am a 17 year old Higher Level maths student and I’m worried about how the subject is taught. In contrast to the national figures quoted, 42% of students in my school (High School Rathgar) take maths at higher level. This may in part come from the extra class each week that the school allocates to maths or to the teachers the school employs in the maths department, most of whom are competent and qualified. I also study physics and applied maths and it is only in applied maths that ‘Vectors’ are studied, surely key for anybody who wants to go into engineering or science. Project Maths is seen by teachers and students as contriving to make maths more accessible but only serving to make the subject more difficult for gifted maths students, by taking away numbers and introducing more wording. That doesn’t sound like maths to me. @ BW Snr, A comment of mine possibly had a mistaken tag included or something and disappeared. Here is a blog entry I created in order to try and tie together a few themes and ideas. BOH. http://designcomment.blogspot.com/2011/06/open-book.html I’m taking higher maths tomorrow and looking for an A. Only two higher classes in my school and 7 ordinary because the course is too long not too hard! @ BO’H: Got it. Thanks. B. @Shane: The theme mandated by LC curriculum designers is “quantity over quality”. Its completely daft, but that’s the mindset of those who control the design of the curriculae. When your exams are over (and the best of luck by the way, and yes, luck does come into it!) find out where and when your constituencey TD has his/her office. Go down and lobby them! Then follow it up with a letter to their Constituency Office. Bring some friends with you. You ARE voters – or almost! Register ASAP. Brian Snr. Colm Finlay writes, I also study physics and applied maths and it is only in applied maths that ‘Vectors’ are studied, surely key for anybody who wants to go into engineering or science. Tim Joyce’s tutorials at Engineers Ireland are really good I thought – I only viewed one or two of the webcasts. He looks at Vectors a bit I know. But if your teachers are able to deal with the material, you are probably well taken of, for tutoring etc. Still though, an online resource such as that, on Engineers Ireland, is always available afterwards, when you go onto third level etc, and want a quick refresh. Then the webcasts are quite useful. In my case, it is like knocking away old cobwebs. I believe, that without students who wanted to do Engineering after secondary, the subject that is higher maths would have died off, about three decades ago. In fairness, it is like lobbying in politics. The smaller lobbies generally have an uphill battle to maintain adequate resources and standards. I take Shane’s point above also, that higher maths is not too hard, but too long. I do recall now, back to the days twenty years ago, when I sat the higher paper and I only had roughly half of the course covered. So effectively I did the paper, on half the questions only. I managed to the get through the Algebra question and a couple of others I recall, in the exam. But only scraped out with a bare C-minus. Tim Joyce mentioned the fact in his tutorials online, that many students only do half the paper also. Definitely, it seems that many students have only half the course done, even today. In my old school in north Kerry years ago, there were three ordinary level classes and one higher level. But what happened there was quite interesting. In the final Leaving Cert year, the higher level class split into two. One half doing higher and the other doing ordinary level maths. But both groups stayed in the same classroom with the same teacher. So the teacher would teach half of the class ordinary maths, and the other half higher level maths. That is basically how I got half of the higher level course done, and managed to grab a C-minus in the exam. But I was only one of six students out of 120 in the school who even passed the higher paper. The other three students who got an honour in the higher maths exam, went on to do engineering as they intended to do. For all of the final LC year, they were in an outside grind class together, and they simply took out their grind homework in school maths each day, and worked together on it, while ignoring the teacher at the blackboard. She gave out one day about it, but they did not care, and probably still don’t. I assume my experience was repeated again and again, all over Ireland. Like I said, higher maths is a small lobby, and generally tied up with the Engineering course choices. The three guys I referred to above, took on Applied Maths as an extra subject too, in Leaving Cert, just to get familiar with some of the material. It was their Physics teacher actually who taught them. I did Physics too, but not the applied maths. If you do Maths and Physics, the Applied maths can work out quite well. Kind of like an overlap. BOH. Above should read: But I was only one of six students out of 120 in the YEAR who even passed the higher paper. That is a ratio for the that year’s LC students of 1:20. So I think, Shane’s ratio as mentioned above still sounds about right. Once you work past the ratio, it is only a case of providing teaching resources for the thin end of the wedge. As we all know, the thinner end of the wedge is seldom, catered for very well. You have to be really careful about that one or two higher level maths classes in a school. Because all the kids want to get into those classes after Junior cert. Not in order to sit the higher maths exam at the end of the day. But rather, because the teacher in the higher level maths class, teaches to a much higher standard for the two years. And then, the smart people simply ratchet back down to ordinary level, a few weeks (or days) away from the exam date. It is a smart play when you think about it. But it ends up drawing away too many resources away from the de facto, higher level candidates. And as I say, by that late stage, the ordinary level students are left sitting where they are, and generally consume vital teaching resources in the final months prior to the exam period, as the higher level class becomes hybrid-ized downward. So the potential engineering candidate student gets caught in a vice grip, of decreasing availability of time, and teaching resources, when they most need both. BOH. @BO’H: Not sure this is the correct place to debate this issue, so I shall be brief (leaving a whole lot out). The idea of H and O papers in LC – in any subject is totally daft. Daft! So what is the solution to the math problem. Well it depends on what THE problem actually is! So many folk know with 101% accuracy what is NOT wanted, but have 0% idea what they do want. It is No. of outputs or the quality of the outputs or what? Approx 16% of any cohort are math savvy – ie: have the required proportion of the abstract v concrete cognitive skill set. That is more than sufficient for our purposes. Some of the remainder, if they apply themselves, will achieve a good understanding of abstract math. So, the former and this latter are our target. Say 20% of cohort – that’s it. You design pre-instruction math ability tests – at entry to 2nd level, to sort out the different sub-cohorts. Its not that A is good and B is not so good. The sub-cohorts are just different and you have to ID who belongs where. Now, you have to design appropriate curriculae for the different math skill-set cohorts. These curriculae must have direct application for where the sub-cohorts are going after school. This is where the real problem with the curriculae is concerned. They are designed with only one outlet in mind. This is daft! What we have with the current math curricule are completely, inappropriate off-the-wall stuff. Meaningful reform of any LC syllabus is neither possible nor probable. We will re-visit this unfortunate place again. Brian Snr. Brian Woods Snr wrote, You design pre-instruction math ability tests – at entry to 2nd level, to sort out the different sub-cohorts. Its not that A is good and B is not so good. The sub-cohorts are just different and you have to ID who belongs where. I am glad that you picked up on the issue, of direct application to where the sub-cohorts are going after school. I didn’t mention this above, but I was hoping that someone here my pick up on this and mention it without prompt. I was giving a hint, in my emphasis, that without students intending to do engineering after school in Ireland, that the subject that is higher level maths would have vanished off the scene many, many years ago. It would have become a little like Applied Maths, is as a subject today. I rarity. But in putting my emphasis upon prospective engineeering course candidate, I would intentionally ignoring for the sake of emphasis how many other modern day disciplines in Ireland, and globally, in the 2010s must tie back in some way to mathematics as a foundation stone. Take the industries to do with financing, lending, borrowing, industrial investment and production etc, etc. I am glad that someone has enough common sense, to realize the point you make in relation to the various sub-cohorts, which need to be addressed in the teaching system, for maths as a subject. I remember once what Alan Kay once said about computer science, and the teaching system at Stanford university. It has become a vocational education, with the institution of Stanford caving into the vendors. The idea of a computer science to Alan Kay is a bit of an oxymoron. Kay believed, that if you had a mathematics graduate first of all, you could hire them as a software programmer, and simply teach them whatever vocational add-ons they needed to bring them up to speed. So even in computing, Kay believed it all tied back to maths. The idea you express about maths pre-ability tests is interesting, and I would like to offer you my own experience from the year 1990, when I attended secondary school. I did my Inter Cert that year, in a class of 120 students in a school. As I described above, there were three ordinary level maths classes for the LC program, and one higher level class. Here is the funny thing. We had a crowd of students in the higher level maths class in the year after Inter Cert, which is normally referred to as ‘fifth year’. At least it was in those days. Even though it is technically the fourth year of the secondary school program. I dunno. There was such a crowd in the higher level class, as I mentioned above, none of whom wished to sit the higher level paper, but who wished to gain better standard of tuition for the two years of the LC program and then sit the ordinary level exam. I vividly recall still, the teacher asking the crowd assembled in the room, which much have comprised the majority of the 120 students in the year – that anyone who didn’t score at least a ‘D’ grade in the Inter Cert was being asked to leave the class. I also vividly recall, that when all of the students had not received at least a ‘D’ grade in the Inter Cert had left the room, there were still 80 students remaining in one class, out of 120 in the whole year! Absolutely no one in the class wanted to be thrown back into one of the ordinary level classes. I still vividly recall sitting on my school bag, because I didn’t have a seat, with my maths textbook balanced on my knee for most of the fifth year of my leaving cert. In the final Leaving Cert year, I finally did get a seat, because some of the 80 had been thrown out. But I do still vividly recall, being asked to leave the higher level maths class myself during my fifth year, even though I had scored an ‘A’ in the higher paper for the Inter Cert. It was purely political who stayed or who went, in that higher level maths class, and I was an ‘A’ Inter Cert student being shoved out. Even though there were ‘D’ students still being allowed in. As I also pointed out, it wasn’t a real high level maths class either, but a hybrid-ized version, where there were only three students remaining, who wanted to do engineering, by the end of the second LC year. And those three students took out their grind homework and ignored the teacher for most of the final LC year. I believe I was the only student in the 120 kids in that year at my school, who didn’t do a maths grind, hung in there in the faux higher level maths class, and still managed to scrap an honour by managing to muddle through an Algebra question in the final exam. So you could argue the maths program in my school was entirely broken. The ratio was 120 to 1, against you. I somehow managed to beat those odds, despite having only half a course done, and sitting on my school bag for a whole year. These are the kinds of stories I would have told Craig Barrett and company, twenty years ago. BOH. This has to be my closing comments on this sad and dismal tale. The LC curriculae are the substantive issue. The fact-turd (sic) that we have H and O level courses/papers is absymal, intellectually and pedagogically. Reform is needed, but will never come. Our politicials (sic) witter on about a ‘Knowledge Economy’ without so much as a microgram of understanding what such entails. Like, a full-monty FoI Act, or absolute constitutional protection for the Ombudsman. They are do-nothing fakes, imposters and charlatans. If I may plagerise Paul Hunt’s well crafted and accurate commentary on a different (but reform related) matter on another blog; “Most people seem to confuse what passes for debate and deliberation with adverserial disputation … … Tame consultants are retained to examine tightly defined elements of … … (the) process in a way that supports the nonsense advanced … … There is no potential to contest and rebut … … the woolly-thinking (he is being excessively kind here). And anyone who has the temerity to critique … … is either ignored or vilified.” Brian, both of us (hopefully), have more trivial things to do with our day than worry over a fossilized bone. I have to mark out and set the grounds for a suspended balcony on the back wall of my house! Cheers. Brian Snr. Brian Woods Snr, We both do have a lot better things to do. There is a book on financial management sitting on my desk at the moment, that will not read itself. I suppose in writing in the above, it has made me realize something, that I don’t think I had consciously understood before now. You are present in a higher mathematics classroom the year after Junior Cert. A room that is designed to carry maybe forty students. There are 120 students in the year, in the school. There is excess demand, not for the higher mathematics subject, but for basic good tuition mathematics itself. The market for mathematics tuition in that school, had decided en masse, that the ordinary level mathematics classrooms (of which there were three, kitted out with teachers), were not the place to be. No one who designs education policy, or looks at statistics on student performance in a subject, could have predicted that a classroom would be too full of students who DO NOT WANT TO DO A SUBJECT. At least, it does seem counter-intuitive to me. It has to with the fact, that first year in many college courses becomes quite difficult unless you have gone through the paces of a higher maths syllabus in secondary. On the other hand, from a points race view of things, sitting the higher maths paper, simply doesn’t add up (pun was intended). What happens to the handful of potential mathematical nerds in the classroom I described, is that they are crowded out of their own territory by masses of non-nerds. If the medical system in Ireland is supposed to be Angola. Then what is the mathematics education system? Jerusalem? A piece of ground that religions, majority and minority fight for possession over. But no one has the ability to acquire outright. The fact is, no one has access to quality mathematics education in Ireland. Too many religions want that piece of rock. Over and out. BOH. @ All, It should be noted, actually, that the reason the National Treasury Management Agency, in Ireland was proposed as a solution, has a lot to do with the crowd struggle over possession for mathematics education I described above. It was a sad reality, that the private financial institutions in Ireland operated like gorillas for a long time. That is, have the Irish state invest the resources and time in training the financial experts that could control Ireland’s finances in that department. But as soon as the Irish state had invested it’s money, the private financial institutions were more than capable of robbing the same valuable human resources from the department of finance. So you see, you find this same kind of problem, at every level in the Irish economy and in society. BOH. The bottom line is students don’t listen anymore. They treath maths like english or geography where they think they can read the text book and catch up on what is being ignored in class. They use not understanding as an excuse for when they are not really listening. They don’t have the discipline to practise examples (throughout all school years) Only a small percentage of students have the discipline and techical competance / inteligence to do honours maths. Students who do well in the non thinking subjects expect maths to be the same and blame teachers and departments. Reality is students are good at learning boring shit off, but not so good at original thought and problem solving, maybe it’s unfair to test this as only a small percentage have aquired this at an 17 /18. Altough a lot still haven’t aquired it by 21., being terrified of any problem they haven’t seen before @ David Fens As a student who sat higher maths yesterday, it is not a case of students treating higher maths like english or geography.From my experience, typically students who do well in “non thinking” subjects do not take higher maths because the reward to effort ratio is too low. When you can learn off two poets, one hamlet essay and two other essays for english and get an a1 in english, why spend the time on maths? Whilst some students are as you described, there are many reasons I would put above that. The lack of reward compared to other subjects and the fact that your grade can depend largely on luck during the exam ie what is on the paper and what changes are made to the marking scheme. Perhaps the biggest problem though is the seemingly inaccesibility of an a1. Because honours maths is designed to prevent students failing it also prevents there being many a1s compared to other subjects such as accounting. This means many students that are capable are advised (often by maths teachers) to focus on other subjects to maximise points. It is the system that fails the students not the students that have failed the system. David Fens wrote, Altough a lot still haven’t aquired it by 21., being terrified of any problem they haven’t seen before. David, I must confess to being one of those personalities types, who does enjoy venturing into the unknown without a real plan, or a sense of where I am going. That has extracted a heavy price from me, at many times in my life. I appreciate your taking the effort to express this point. It is a quite large, and fascinating question you pose to the community here. Maybe someday, we will all get to engage with this question in some other forum, and get closer to what may be considered the answer. Regards, Brian O’ Hanlon On my website I’m at the moment creating a library of full VIDEO solutions to all the questions in the LC applied maths book (Fundamental Applied Mathematics by Oliver Murphy). I’ve the first 4 chapters up (or pretty much anyway) at the moment, so it could be of help to people you know doing the subject.. Either way, it’s a free resource so why not! Comments are closed.