Honours maths question

Permabear

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Webmonkey

Well back when I done LC, the maths did indeed seem a lot easier than it did in the early 90's/80's papers.

LeixlipRed

Haha, of course. Everything is dumbed down nowadays. Google "The Mathematics Problem".

Permabear

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Fremen

I remember the earliest past papers from the leaving cert were most difficult, too. The earliest papers I was were from about '94, I think.
Didn't you get 120 points for an A1 in Hons maths at one stage, though?

Pherekydes

Never did the LC, so I can't really comment, but when my son brought home the JC Maths paper in June I thought he had done the Foundation level paper (It was honours). Yet, I only got a HLC in my own Inter Cert. There seems to be a completely different ethos about education in general these days. In written work, spellings, grammar and punctuation are simply unimportant. Just write your ideas down. Any old way will do.

Projects? Why are primary school children doing projects? Why shouldn't they learn the basics first before they move onto stuff like projects and planning and coordinating?

I'm afraid it's the same with second level maths. Kids can memorise all the formulae or theorems, but they can't transpose a formula, perform simple cancellations, or write down a logical series of steps leading to an answer.

The whole education system is being dumbed down. The introduction of foundation level is evidence of that. You can add some numbers. Great, well done, here's a certificate.

LeixlipRed

donegalfella wrote: »

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Not referring to a report necessarily. Just the problem in general. I'm doing research on a small aspect of it myself at the moment. It's a huge issue, especially when we cant produce engineering and science graduates with basic mathematical and problem solving skills!

Permabear

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LeixlipRed

Yeh, it's a crazy problem that starts in primary school and just spirals from there. Hopefully with Project Maths comig online soon the long term picture will improve.

Michael Collins

What are people's opinion on the Project Maths inititive actually? I've read a little on what Project Maths is about, but it's hard to get a real idea of what effect it will have. I'll probably have to wait until the rest of it is decided. I've heard people complaining about the integration being cut down - is there any truth to this? From what I can see stages 3-5 arn't finalised yet. Are there any teachers out there who care to comment?

I think that it's hard to sex maths up without dumbing it down too. That's not to say it is impossible, just requires very careful thought.

I think for anyone who's interested in maths the current curriculum is quite good - quite challenging, but doable. If you know the honours course well you'll have a good grounding for further study involving maths. I'd very much hate to see certain parts just taken out to make it easier or more appealing. Apart from the obvious dumbing down reasons, it doesn't really tackle the heart of the problem anyway which is why are so few people interested in maths?

Big Lar

Michael Collins wrote: »

why are so few people interested in maths?

Well I can answer that from my own experience, Although in fairness it was 21 years ago when I sat my Leaving Cert.

I had four maths teachers while I was in secondary school, Some of the teachers were quite boring and just rambled on about various equations which made the whole class boring and there was a complete lack of interest.
I had one teacher who constantly gave practical examples of how one would use the equations in real life and more or less gave a reasoning behind them, That guy made classes very interesting, well for me anyway.

I suppose what I am trying to say is the the way the subject is taught needs to be changed.

Of course like I said, It's been a while since I have been to school so I could be very wrong.

Jokesetal

There is no doubt that the current LC Hons Maths course has been "dumbed down". In particular there have been major changes since around 1994.
Working in the third level, I can say that fractions are still posing problems for degree students! There are a couple of reasons IMO:
1. Less time being devoted to technical subjects
2. Too many teachers with sub-standard mathematical abilities
I know several biology teachers who have to teach maths, while acknowledging that they have very little interest in the subject other than what's given in the text books!

LeixlipRed

I think the ethos behind Project Maths is to use practical applications and history of maths to make the subject matter more interesting. Also, afaik, the "chalk and talk" method of teaching is thrown out with the new curriculum. What exactly replaces it I'm not sure.

Fremen

Maths really isn't that appealing at secondary level. It's not that the problems are necessarily "easy" but they don't require much original thought. I only really got interested when a friend showed me some olympiad problems. As things stand, it's more a case of "read the worked example then grind through thirty questions".

Leaving cart maths doesn't really cover many of the surprising or beautiful theorems either. As far as I remember, one of the only nice theorems you cover is divergence of the harmonic series.

There's a lot of scope for developing the nicer parts, perhaps in optional course components (the same way you can take particle physics as an option in physics). For example: students already know complex numbers and newton-raphson iteration, so why not combine them both and study newton fractals?

miss no stars

I only learned to appreciate maths in 3rd level. Why? Umm lemme see


All through school, my maths teacher did not properly understand what she was teaching. I can look back at some of my memories and say that with 100% certainty, although she could figure out where stuff came from, she didn't really "get" it. I remember asking a question about maxima and minima and why it seemed so counter intuitive that if it's a local maximum the second derivative would be less than zero... she couldn't explain why. Just said "it just is".

Someone already mentioned that they had a teacher who gave real life examples of where the maths is used. I'm in 3rd year engineering and (although I'm probably only scratching the surface) can grasp just how useful calculus is. I can look at a (not TOO complex :P) beam and know how to write the differential equations to find deflection, bending etc at a given point. So why wasn't I taught some of the actual practical uses of calculus when I was learning it in HL LC? Well if the teacher doesn't understand it to begin with.... how can they say where it's used? My own teacher was a science graduate. Maths wasn't her primary focus in college. It's just something she happened to do in college. Whereas my grind teacher did a maths degree. He understood, she didn't.

and THAT, ladies and gentlemen, is the problem with maths in education today. (Or as my dad likes to say - those that can't; teach - I say this partially in jest as I have some fantastic, and I mean completely amazing lecturers and had a good few really good teachers! but it's partially true too, unfortunately)


On another note, I found my dad's notes from his leaving cert. It's definately dumbed down to a ridiculous standard. Thinking doesn't exist. Just learn a formula, regurgitate and off ya go.

Now, I'm not saying it would neccessarily be good to go back to older standards. Maybe it was just too difficult for a 16 year old to do. 16 is a bad age to be trying to focus on school. (Let's not forget you're dealing with teenagers!)

I almost feel as though the focus of at least higher level leaving cert maths should be shifted off what I experienced as "learn learn learn" to "understand, demonstrate and apply"

paraiceen

As a secondary teacher of Maths to LC higher level for the past 26 years, I am depressed and frustrated at the decline that has taken place in the standards of Maths at second level over this time - particularily over the last 5 or 6 years. Obviously society changes and maybe our ways of teaching must change accordingly, but the bottom line is that students still need to attain a certain standard in theoretical Maths to successfully pursue certain courses at 3rd level (Engineering, Physical Sciences, Technology etc.)

The current emphasis is on students "learning-off" questions instead of understanding and having an appreciation (dare I say Love) for the subject.


The standard of Maths in the average student coming in from national school is way down from where it was even 10 years ago. Methinks this is due to the time spent (or not spent) per day on Maths. Teachers in primary schools must cover so many other topics (as the curriculum is now so broad) that time spent on basics (RRR) is much reduced. I find that kids in 1st year have no CONCEPT of many topics - fractions, percentages, algebra, numeracy among others. They have no understanding of a logical process which leads to a solution to a problem. Of course the introduction of calculators has meant that a lot of kids now cannot do basis calculations.

In a lot of cases the "window of opportunity" for learning these fundamentals is lost.

I recently spent 3-4 weeks teaching basic Sets to a 1st year class which in the not too distant past would have taken 3-4 days to cover.


This is an indication of the scale of the problem we are facing!

Junior cert Maths was "dumbed down" 7 years ago.

One of the reasons for the changing of the Junior Cert higher course was the fact that some teachers did not cover certain topics (like Trigonometry) at all. (Some of these teachers had very little background or qualifications in Maths.)

The follow-on from this was a drastic decline in the numbers trying Leaving Cert higher level, which was not dumbed down. There is now a gap between Junior Cert higher and Leaving cert higher that most students do not want to attempt to bridge!


The proposed solution for this malaise is "Project Maths".

This takes topics like Matrices and vectors off the course. What proper minded engineer would have any use for these useless concepts???

As far as I can see most students in the "Project Maths" pilot scheme seem to spend a good deal of their time doing Statistics at a very practical level.

This may be very useful and practical and Statistics is an obvious topic for practicalities, but what about any student who wishes to progress at Third level in Maths?

Mathematics by its nature is a very abstract & theoretical subject. No amount of "practical aspects" will get us away from this fact. This knowledge is required to progress in the engineering field - Differential equations etc.

Sometimes things in life are difficult and have to be WORKed at.

Some people have a natural aptitude for understanding this and some do not - hence the reason for higher & ordinary levels. "Dumbing-down" courses will not get us away from this fact!


A more obvious solution would have been to leave the leaving cert higher level course as it is, and maybe create 3 new Maths related subjects at leaving cert level and/or junior cert level - for example

-Statistics

-Business Maths

-Science Maths.

I really think a solution to this lies in actually trying to raise the standards of Maths from the bottom up, firstly at primary level, and then at 2nd and 3rd level, instead of lowering standards from the top down at 3rd and 2nd level.

Our ability to build a sucessful economy will hinge on the real quality of our Science, Maths, Technology and Engineering graduates.

If we do not get our act together soon we will be left behind.



P.S.

Leaving cert Maths was far more difficult 30 years ago. The course covered almost 150-200% of what is covered now and far more difficult concepts like convergence of series, hence the reason why it was worth 2 honours (Double what other subjects were worth - for younger readers!).

The course was changed in 1983 and again in 1994 which was the last revision.

Apologies for the long post, but I do feel very strongly about what we are doing with Mathematics in our country.

As a final anecdote, I had a conversation recently with an American teacher who moved to Ireland in the late 1990's. When she started teaching here first, she could not believe how much more advanced the Irish students were at Maths compared to American kids, but now she says that first year students in Ireland are at the same level she remembered American kids were at when she left America!

SaganScience

This project maths thing is a ridiculous idea in my opinion. If they continue to dumb down our education system where will it end? At this rate people will be getting A1's for being able to add by 2020.

Maths is not easy and it never will be but it doesn't give everyone the excuse to stop striving to reach a decent level of mathematical knowledge.

If they wish to bring in project maths for ordinary students that is fair enough but under no circumstances should they change the Higher Level syllabus. The extent to which many of our subjects have been dumbed down already since the 80s and 90s is shocking.

Then of course we have the new Leaving Cert. Log Tables this year with pretty much every formula for the Physics and Maths exams. It would appear that the department of Education don't want us to think for ourselves at all.

In fact this problem does not only apply to second level. Since 1994 there has been a 140% increase in the number of First Class Honours degrees in third level institutions. Again, courses are being dumbed down to facilitate people who make very little effort. It is disgraceful that many courses in universities offer marks for simply attending lecturers. That is simply making a mockery out of people's intelligence. It is as if to say "ah aren't you just great for coming to your lecture! Here you go, here is 20% of your marks because you are not capable of getting them any other way." It's even more embarrassing when you consider that the taxpayer is actually handing third education to us on a plate, free of charge.

It is time that people stand up for the standard of education in our country. Education is the way forward and it is time we give it the respect it deserves.

PS I am a Leaving Cert. student who finds LC Honours Maths very challenging but I am most definitely pleased to be sitting my exams before I am forced to do a project instead which will certainly not provide me with the opportunity to reach my full academic potential.

MathsManiac

What makes you think the new course is going to be less challenging than the old one?

In my experience as a teacher, students find the application of their mathematics to new and unfamiliar problems, and the extraction of mathematical meaning from text-based problems to be quite difficult.

Any development that seeks to put more emphasis on understanding and application than on the execution of well rehearsed routine procedures deserves a fair crack of the whip before I would dismiss it. I wouldn't describe it as dumbing down, even if the trade-off is the removal of some content.

Time will tell whether this effort will be successful or not. Certainly if they chop the content and don't achieve greater undertanding and ability to apply, then that would be a bad move.

Valmont

miss no stars wrote: »

I only learned to appreciate maths in 3rd level.

I studied ordinary Maths for the LC and it was only during my third level education that I really began too appreciate maths (statistics especially) and it annoys me now as I know that I was more than capable of doing well in higher level but with the prevailing attitude being "only the best students do Higher level" I avoided it. Mostly my own fault, but you get the idea. My Grandfather lent me this book which I really enjoyed during my final year of college.

RoundTower

paraiceen wrote: »

The proposed solution for this malaise is "Project Maths".

This takes topics like Matrices and vectors off the course. What proper minded engineer would have any use for these useless concepts???

As far as I can see most students in the "Project Maths" pilot scheme seem to spend a good deal of their time doing Statistics at a very practical level.

This may be very useful and practical and Statistics is an obvious topic for practicalities, but what about any student who wishes to progress at Third level in Maths?

Mathematics by its nature is a very abstract & theoretical subject. No amount of "practical aspects" will get us away from this fact. This knowledge is required to progress in the engineering field - Differential equations etc.

Sometimes things in life are difficult and have to be WORKed at.

Some people have a natural aptitude for understanding this and some do not - hence the reason for higher & ordinary levels. "Dumbing-down" courses will not get us away from this fact!


A more obvious solution would have been to leave the leaving cert higher level course as it is, and maybe create 3 new Maths related subjects at leaving cert level and/or junior cert level - for example

-Statistics

-Business Maths

-Science Maths.

I really think a solution to this lies in actually trying to raise the standards of Maths from the bottom up, firstly at primary level, and then at 2nd and 3rd level, instead of lowering standards from the top down at 3rd and 2nd level.

Our ability to build a sucessful economy will hinge on the real quality of our Science, Maths, Technology and Engineering graduates.

If we do not get our act together soon we will be left behind.

It seems like there are two different goals here.

Do you educate the future engineers and go over the heads of the smart students who will not go on to use maths at third level? Or do you want to give everyone a mathematical grounding in areas that will be applicable no matter what they study? Let's forget about the less academically inclined for this discussion - they can do pass maths.

It would be great to do both, so why not have three courses?

- Ordinary Level Mathematics
- Higher Level Mathematics
- Higher Level Extra Mathematics

let the Mathematics courses be something like the proposed Project Maths. Higher Level will be for smart students and those who need the points, Ordinary Level will be for those who just aren't up to it. "Extra Maths" will be more advanced stuff such as the topics that have been taken out of the Maths course over the years, typically maths-minded students will do Higher Maths AND this more challenging course, just like Applied Maths but with a different focus. So Maths will go back to being worth two honours.

I don't know how many schools would offer this course, but it at least seems to address the needs of both groups. Of course there are some details to be ironed out.

Calina

RoundTower wrote: »

...

- Ordinary Level Mathematics
- Higher Level Mathematics
- Higher Level Extra Mathematics..

We already have three sets of maths, called, I believe, Foundation Maths, Ordinary Level and higher level. I did higher level in 1990. Since then, I believe, the higher level syllabus has been streamlined not once but twice. I, from my position, would call this "dumbing down".

There are issues with numeracy and unlike literacy related problems, there is no social stigma attached, comparatively. So it's acceptable for people to pop up and say "I'm useless at maths".

There's a difference between making mathematics accessible and making it easy. Unfortunately, this difference is not seen. I'm not really sure how you go about changing this however because to be honest, there is a disconnect between how we value people in this respect. The question is, should people who are mediocre at maths be teaching it, should people who are good at maths but bad a teaching it be teaching it, and how do we get people who would be good at maths and teaching it to teach it when they could be earning way more money doing potentially far more interesting work elsewhere. Actually, this is true for every subject but that's a side issue.

I'd a super maths teacher for 4 of the 5 years I was at school. Do we keep people like that teaching instead of rewarding them through promotion? Is that fair? I don't think so, really. We don't reward great teachers except by putting them in positions where they ultimately wind up not teaching.

You can only address how people learn maths at school if you also address how it is taught. There's a bigger picture but like everything in this country, there's very much a piecemeal approach to finding answers.

We need people to make more efforts in maths. Making it easier is counterproductive.

Bhoy_

I think results and discipline go hand in hand. As discipline diminishes so do the results. If the exams are getting bad results they are marked easier and the year after the exam is "easier" than the last. This spirals into the gap we have now from the 80's say, to now. That's not saying the Honours maths course now isn't still very difficult.

xiggyplushie

I'm a current LC Higher level maths student who this year will have to sit a paper two that is based on the new project maths course and a paper 1 from the old revised in 1994 course. In my opinion the new idea of 'project maths' is stupid as even my maths teacher, who is really enthusiastic about the subject itself, does not understand all of it and has said on many occasions that we are a 'trial'. I recently had a look at one of the sample papers and even the layout is bad, section A is 150 marks over 6 questions, section B is also 150 marks spread over 2 questions, all questions are compulsory. Section A is okay, there are sections for writing the answers on the paper though now, Section B on the other hand, is different. On this particular sample the second question was on statistics, taken from a graph of the heights of tsunamis and the strength of the earthquakes that caused them. It was all writing, there were hardly any calculations at all it was all based on analysis of the graph, basically it looked like a geography paper, except it wasn't coloured in... While trigonometry, statistics and graphs were never my strong point, I would still prefer the layout of the old paper than the new one they've brought in. And don't get me started on the bonus points...

equivariant

I think that many if the ideas behind the project Maths initiative are good ones. Eg less choice in the exam, less predictable papers, more emphasis on understanding concepts. However they key issue with project maths is the implementation. Unfortunately it seems that many teachers band possibly some publishing houses are campaigning against reform. The reasons are clear. If your teaching methods are based on the predictability of the LC exam then PM is very bad for that. The same thing goes for the publishing houses. I have looked at some of the 'new' textbooks and found them to be very poor. Mostly rehashes of the old material.

IMO the basic problem is this. You can have the perfect syllabus, but it is no good if there are not sufficiently many high quality teachers to deliver it. Good mathematics graduates tend to be highly sought after by employers so unless there is some incentive to become a teacher it is unlikely that a good maths graduate will pursue that option. I think that the teachers unions and the teaching council have a lot to answer for in that regard (and I say this as someone who would naturally sympathise with the trade union movement)

LeixlipRed

Good post, it's simply the case that about less than half of the maths teachers teaching in schools right now are qualified maths teachers. Some have never done any maths at university. Not all of those teachers are incompetent or lacking the knowledge needed by a significant number are.

Also, what's not addressed is the poor standard of maths that those teachers who are qualified possess. I recently thought a module to 2nd level teachers on basic statistics. 30 teachers on the course, all had done a maths or maths studies or statistics degree. Most of them struggled with the pace of the class, the emphasis on concepts and understanding.

The whole education system needs reform and in NUIM we're implementing changes at a slow rate and we've had some success. However it's clear to me that to prevent the cycle continuing there needs to be a huge amount of funding dumped into the maths education sector at all levels to fund cross level research into how we can all work together to fix this issue. I couldn't care less about the economic side of things, this is a deeper societal issue, many people leave school without the most basic numerical skills. That's a shocking indictment of the education system.

equivariant

Agreed. I find it amazing that you will often hear some university lecturers complaining about the poor standard of the leaving cert when we (in 3rd level) churn out Maths studies graduates with poor mathematical knowledge knowing full well that they are the Maths teachers of tomorrow - what do we expect? I think that the idea of 40% being acceptable to pass a university course is crazy. Especially given that many 3rd level exams are even more predictable than the LC

LeixlipRed

It's not even the pass percentage that's an issue. It's the content of many of these courses and how it's presented. Too tired to rant, time for a nap.

nothing

I've just started to teach at a grinds school (maths degree, no teaching qualification) and I have to say I think PM is a brilliant change. I did LC in 2002, and the fact is, the math is the same, it's not any more or less difficult, it's just presented in a different way and the emphasis has changed. The teaching is much more in line with how university math is taught, which will hopefully reduce problems that arise when students have to change from rote learning to abstract concepts.

Honestly, it seems like the people who are complaining most are either teachers who haven't got the capability to teach it in the way intended and students who have "bad" teachers.

doc_17

LeixlipRed wrote: »

. I recently thought a module to 2nd level teachers on basic statistics. 30 teachers on the course, all had done a maths or maths studies or statistics degree. Most of them struggled with the pace of the class, the emphasis on concepts and understanding.

.

Was this for Project Maths? Or was it that course that is for teachers of Maths who aren't qualified?

nothing wrote: »

I've just started to teach at a grinds school (maths degree, no teaching qualification) and I have to say I think PM is a brilliant change. I did LC in 2002, and the fact is, the math is the same, it's not any more or less difficult, it's just presented in a different way and the emphasis has changed. The teaching is much more in line with how university math is taught, which will hopefully reduce problems that arise when students have to change from rote learning to abstract concepts.

Honestly, it seems like the people who are complaining most are either teachers who haven't got the capability to teach it in the way intended and students who have "bad" teachers.

My beef with PM is that it is taking away some useful aspects of the previous curriculum and the totally annoying way it is being implemented.

LeixlipRed

For Project Maths. All those teachers were qualified.

PurpleFistMixer

Was chatting to a friend of mine yesterday about this. His dad is a maths teacher so he knows a fair bit about it. He said one thing they're doing is trying to make it more "flexible" somehow, and less dependent on text books, so teachers can fill in the gaps themselves. This seems like a good idea on paper, but in reality can only serve to punish students who have bad teachers. Seems like a very difficult thing to get right, though.

Anyway, my personal opinion on project maths (from what I've heard of it) is that it's dumbing down the subject by removing anything which might possibly be abstract (god forbid abstraction in mathematics - dear lord, the children might get some taste for what the subject is actually about) and replacing it with "the statistics you'll need in your business degree, with added micro$oft excel". Surely higher level maths should be for people who like maths. I mean, there's so little abstract maths on the LC as it is, students are going to think it's all about statistics and Real World Problems. A terrible shame.