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.

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

meant to say:
“They should also be offered as physics as well for its cross-over with applied maths.”

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)?

@ 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.

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!

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.

“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.

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 ” .

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.

@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.

@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, 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.

@ 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

Unfortunately, the high numbers doing the LC is most likely as its a lot more difficult to get an apprenticeship.

@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.

@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.

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.

Just to clarify as its a long report: the figures I took were from page 22 of the report I linked to.

“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.

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.

“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.

@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.

“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.

@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).

@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.

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.

“‘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.

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.

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.

@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.

@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.

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.

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.

@ 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.

€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.

@ Al

Know you don’t, becasue they’re not.

It really makes an argument look weak when you confuse ‘no’ and ‘know’.

& if we don’t take ‘them’ on during our current perma-crisis, will they ever be taken on?

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!

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.

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

@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.

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.

If we want to examine understanding and ability to apply, rather than memory, why not make it an open book exam?

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.

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.

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.

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!

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.

@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.

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.

@ 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.

@ 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.

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!