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Project Maths

doc_17

Hi all. I'm a Maths teacher and just had the first Project Maths inservice last week. I was just wondering what other teachers/mathematicians thought of it? I have some misgivings about it. First of is the removal of some of the more practical and student friendly topics, such as Vectors and Matrices (both being useful to engineers and scientists at 3rd) and some of the changes to Statistics in JCert. I am not in favour of dumbing down but I would get rid rid of some of the derivations of the 20 Formulae at LC Trig. Also it's the proof of the theorems that drive students away from JC HL which then means they do not go to LC HL. I would have made changes there. Any other teachers have any opinions on this. I have no problem with the formulae being in the tables as its about using them not learning them of by heart

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LeixlipRed

You advocate removing the proofs? These proofs are so ridiculously simple. I cannot understand why they would be removed. There should be more proof on it if anything. Simple, aesthetic proofs mind you, but proofs none the less. Vectors and Matrices are re-taught a lot in 1st year Maths so I'm not too concerned by their removal. They have lots of applications though and I thought that was the whole ethos of Project Maths, to teach through applications. And there should be no extra stats on the course. Statistics is not maths.

doc_17

I don't advocate removing all of the proofs on the JC, as you say most are elementary, but the simple fact remains that they are the main raeason why students drop from HL to OL for he JC. I think that students in first year know so much less than they did 15 years ago. Students are targeting the subjcts where they can get the most points with the least work. Project maths wouldn't be needed if there was bonus points for maths. 90% of the curicculum is going to be taught the same way anyway.

Fremen

Christ, keep matrices on the curicculum. They're a ridiculously important, central feature of mathematics.

doc_17

Fremen wrote: »

Christ, keep matrices on the curicculum. They're a ridiculously important, central feature of mathematics.

At least the students understand them and can do well in them. We're taking away a popular question that LCHL students enjoy. I'm not sure that'll impress the maths teachrs of our country. But aside from matrices what do you think of the whole project maths idea anyway

clartharlear

I hadn't realised that matrices were gone too. That's an unpleasant shock.

I was at the applied maths teachers agm, and it was decided that an 'official' letter from the subject group would be sent to the NCCA frowning upon the removal of vectors.

I don't think consultation on the whole Project Maths was wide enough.

MathsManiac

I taught applied maths a bit (after school) when I was a maths teacher. My recollection is that the students never did vectors in maths until long after I needed them in applied maths, so I taught them during applied maths. It wouldn't have made any difference to my applied maths teaching whether they were on the maths course or not.

I agree that matrices are hugely important at third level, but since the last LC syllabus change, there haven't been any decent applications of them on the course, so students just find them a bit pointless. (Their use in optional for handling transformation geometry, and hardly anyone uses them for that topic. Anyway, that seems to be gone too.) The only "application" that the students encounter is to use them to solve a pair of simultaneous equations. As far as they are concerned, it's an awful lot of bloody trouble to go to to do something you can already do without any difficulty since you were in second year.

I disagree with LeixlipRed about statistics, despite my being a pure mathematician at heart. Even if you don't regard statistics as a branch of mathematics, it is certainly a closely related discipline. Second level maths isn't just about preparing people for maths at third level. Stats is probably the one area of maths that people need the most understanding of in order to be properly informed citizens, and it's certainly the area that more students will encounter at third level than any other. I think this has been a huge gap in second-level eduction for decades, and it's about time it was sorted out. If they don't do it maths class, then where? The chances of it happening as a standalone subject for everyone are zero.

It is certainly a shame to see some of the nice topics going. But if the intention is to have more time devoted to developing good understanding of material and the ability to apply it, then something has to give in terms of content. My problem is that I love ALL the stuff that's there, and I'd like to chuck a whole lot more in too.

It must be hard to decide what to leave out. But unless they're going to add in a few nice applications of vectors and matrices, they might as well leave them out as anything else.

Also, regarding consultation not being wide enough, it's hard to see how much more they could have done. There was a discussion paper, a review of current international practice, a national consultation in which anyone who wanted to got to make their views known, a syllabus development process at which the world and his mother is represented, and a trial run in 24 schools.

fh041205

I've discussed this somewhat with others and the general concensus is one of utter disgust really. The whole of JF year in 3rd level will have to be spent teaching student basic mathematical operations. The LC is already miles behind the A-Levels and European Bac exams, this perpetuates the problem.

Honestly, if it were ever implemnted nationwide, the entire 3rd level system would have to be restructured to cater for it. IMHO anything that focuses a Maths exam more on Statistics and Probablility is sac-rilegious.

Core topics such as matrices, differentiation and integration are missing. They are needed in almost every course at 3rd level. Engineering, Business, Economics and Science all need these basic skills. I think its a huge step backwards for the countrys schoolkids.

RoundTower

I'm not a maths teacher but I'd like to reiterate what I said in another thread.

There should be an "Advanced Maths" or "Extra Maths" or "More Maths" course that would bring back all the things that have disappeared off the curriculum over the last 20 years, and the Project Maths curriculum should become the standard Maths curriculum.

This course would prepare students for mathematical courses at third level, while the Maths course prepares students for non-mathematical courses at third level and for the use of maths in non-mathematical careers. After all that is the rationale for the emphasis on statistics.

If students chose this course, they would be spending twice as long studying maths courses and get up to twice as many points (as it used to be). Not every school could or would implement this course, but that is a terrible reason not to introduce it.

rjt

I wonder what the purpose of the maths curriculum is, at least in the eyes of the Department of Education. I'd always assumed it was preparation for third level - and more 3rd level graduates in science and engineering is good for the economy (or something like that). But Project Maths seems to remove most of the stuff that is important for science and engineering students.

MathsManiac

rjt wrote: »

As a bit of an aside, what's the point of having mandatory maths after JC anyway?

Maths after JC is not compulsory as far as the Dept of Ed is concerned, by the way. Schools treat it as though it were, because most 3rd level institutions require it for matriculation for many if not all of their courses. Also, choosing not to do it would make many employers in Ireland think twice, since it's such an established norm.

RoundTower

rjt wrote: »

I wonder what the purpose of the maths curriculum is, at least in the eyes of the Department of Education. I'd always assumed it was preparation for third level - and more 3rd level graduates in science and engineering is good for the economy (or something like that). But Project Maths seems to remove most of the stuff that is important for science and engineering students.

a very good question, I think there are two needs to be addressed and you simply can't address them both with one course.

clartharlear

RoundTower wrote: »

a very good question, I think there are two needs to be addressed and you simply can't address them both with one course.

But that's the case with all the "compulsory" subjects. English and Irish is about being able to use the languages properly (communication) and about appreciating the literatures. These are two very different needs too.
It's crazy to have only 100 points going for Maths, English and Irish. All of these subjects should have bonus points.

fh041205

RoundTower wrote: »

a very good question, I think there are two needs to be addressed and you simply can't address them both with one course.

True but with two courses theres a huge risk of the advanced course being thrown by the wayside similarly to Applied Maths. That option wasn't there in my Secondry school and I fear that any advanced maths topic would suffer a similar fate.

doc_17

Ir's difficult to compare LC Maths with A-Levels. You'd expect A-Levels to be more demanding as in the UK you only have to do 3 or maybe 4 topics whereas here you do minimum of 7. So not as much time. I just think we're missing a chance here.

I'm teaching 4th year pass this year and there's a girl in my class who should be doing HL. But she kicked up a fuss, parents had meetings with the principal and she got moved into the OL class. She has made a decision that she will be able to coast at OL and devote more time to other subjects in order to maximise her points, as she has the opinion the work you would have to put in to get an A in maths far outweighs some other subjects.

We should have bonus points for Maths and every applicant for primary school teaching should have to do HL Maths. If thats the way it is for Irish then why not Maths?

Fremen

RoundTower wrote: »

I'm not a maths teacher but I'd like to reiterate what I said in another thread.

There should be an "Advanced Maths" or "Extra Maths" or "More Maths" course that would bring back all the things that have disappeared off the curriculum over the last 20 years, and the Project Maths curriculum should become the standard Maths curriculum.

This course would prepare students for mathematical courses at third level, while the Maths course prepares students for non-mathematical courses at third level and for the use of maths in non-mathematical careers. After all that is the rationale for the emphasis on statistics.

If students chose this course, they would be spending twice as long studying maths courses and get up to twice as many points (as it used to be). Not every school could or would implement this course, but that is a terrible reason not to introduce it.

The UK does this, it's called "further maths". It's exactly what the Irish system needs.
Edit: requiring both maths and a second "further maths" course would probably reduce the drop-out rate for technical courses at third level, too.

frido

I've only had a bit of an overview of what project maths is about. Which is apparently to introduce more real life scenarios to the students and to make it more relevant to them.
I found a school maths book from the 70s in the attic, whose aim is to introduce more real life scenarios and to make it more relevant to students. Plus ca change. The result was that teachers were hugely enthusiastic for a while and eventually students were learning off 'the running tap question' or 'the grain silo question'.
I'm all for improvements such as Dr. Merriam to mechanics and dynamics making a dry subject interesting. But it was appropriately interesting, and there's a difference between 'interesting' and 'entertaining' which some people are unaware of.
With the improvements that I hear many propose for maths, I personally have quite a big issue. The English government has been improving the curriculum every three years for decades requiring teachers to reskill continually. The most recent 'improvement' brings the curriculum back to the early eighties curriculum in England - Check out the questions in the book - They are the same. Meanwhile, the pass level for the GCSE (A* to C) is nationally about 50-55%. The pass level on an equivalent exam here (they're hard to compare but cover a significant amount of the same stuff - C there is NOT equivalent to a C here) is over 75%. Good schools in England struggle to compare to our national average even though the teachers I met there were just superb. It's not a path we need to follow. All the students may understand the how and why and wherefore of multiplying and adding and other mathematics. This may seem like a good idea, but in the end you must learn them off by heart in order to have them as a tool. Understanding how a tool works when it is shown to you is one thing. Having a dozen tools ready to tackle a problem requires significant practise in application.
How can you do factors, or even division, if you don't know your tables BY HEART.

My recollection is that the maths curriculum was designed for a purpose. The JC(or rather the inter) possibly followed by Ordinary Level leaving provided you with all the skills needed for all branches of the Civil service and some professions. The LC higher level provided you with all the skills necessary for foundation in other professions or as the foundation for every other college course. There is a purpose to it all.
The requirements have changed only slightly (Numerical algorithms aspects really)

The next main issue is teaching in schools. The Engineers of Ireland have been recently questioning academic standards. I don't mind this. It's a million times preferable to government interference. I'll admit I'm suprised, as the results I read in the irish times indicates an overall points imrovement (Those getting more than 550 points have increased from 0.5% to ~2+%) and the maths results seem to have held within a reasonable distance of their prior norm). Regardless I think there are some logical and practical inconsistencies.
One is the notion that we can use unemployed engineers as teachers. If there's such a demand for engineers why exactly are there enough unemployed engineers to provide teaching services.
Secondly is the notion that the current crop of teachers are incapable of teaching high quality maths. All teachers are graduates. Most recent teachers have master's degrees. I know of an ex-engineer with a Maths and Computing Masters and years of work experience who is struggling to get teaching hours. The vast majority of teachers are extremely dedicated professionals working in a challenging environment. Once you start questioning that too much and try excessively to ensure 'measurable quality' you remove the power of teachers (or rather the principals/bosses) to ensure the best results, you reduce their status and motivation, and you get a completely different result to what you expected. Anybody who has been through a quality incentives process or read 'Joel on Software' will know what I'm talking about. (I admit there could be a better induction and mentoring process).
The reality is that most mathematical quality differences are socio-economic. In one school I can discuss the various meanings of infinity and do difficult puzzles involving piles of coconuts and five monkeys. In the next, when I politely ask a girl if she could take out her headphones and sit in her chair rather than the shelf so she doesn't hurt herself (again), she tells me to get out of her face, or (on a good day) goes 'excuse me I'm trying to have a conversation here'. How do you teach high quality maths in this situation. For real-life maths how do you bring this person into traffic to do statistics with minimum casualties.
I'm not sure that many people are aware of this reality. The Engineers that I went to college with almost without exception played with lego and mechano as a kid. They knew who Archimedes was and did puzzles from books at home. Their parents encouraged them and had high expectations of them. Shouting was not the norm.
On the project maths side of things I do agree that there are large numbers of kids for whom the current maths curriculum is pointless, and for whom something else would be certainly preferable. I do not think that modifying the curriculum for the entire population is a solution. I do not think that it will in any way raise standards in maths.
- My apologies if that turned into a bit of a tangential rant or if I'm completely off base on the project maths thing, but I'm a bit terrified that a well respected system is about to get shredded. If your objective is to improve the uptake of maths and the results scored in it, the simple and obvious solution is to make it easier and easier.
Q.'How do get a kid to run the 110m hurdles in under 15seconds'.
A 'You make it 50m and remove the hurdles'.
..and for the sweet love of God keep the government out of it, we've all seen what their improvements look like.

Davidius

Not sure how many have seen the HL sample paper 2.

I died a little inside but what do I know, I'm not a maths teacher.

Podge_irl

Davidius wrote: »

Not sure how many have seen the HL sample paper 2.

I died a little inside but what do I know, I'm not a maths teacher.

I'd like to see Paper 1 to judge fully, but that appears to be an awful, awful paper. Students coming into third level are poor enough at maths as it is, and this is not going to help at all.

Fremen

Davidius wrote: »

Not sure how many have seen the HL sample paper 2.

I died a little inside but what do I know, I'm not a maths teacher.

That's shocking. Absolutely brutal. It's better suited to be set as a Junior cert. paper.
Have they dropped calculus from the curriculum? Do they expect the entire student population to turn into social scientists?

All that's going to happen now is that we'll see a spike in the drop-out rate in technincal courses like engineering and computer science.

The examiners don't seem to realise that you don't get better students by making easier papers. You get better students by increasing potential rewards, which makes students more inclined to put the work in.

LeixlipRed

I hope it's a practical joke. It's just a JC standard paper. For shame.

RoundTower

Fremen wrote: »

The examiners don't seem to realise that you don't get better students by making easier papers.

But you get better marks! Which is just as good if you're a civil servant and your boss has been at you to do something about the falling numbers of Irish students who can pass Higher Level Maths.

equivariant

The topic of bonus points for mathematics is a thorny one. My personal preference would be to have ordinary maths and a separate advanced maths course, rather than have bonus points.

I think that part of the problem with reform of the maths curriculum is that there are too many hidden agenda at play. Everyone recognises that their is a big problem with 2nd level maths, but everyone has their own agenda when it comes to changing the syllabus.

The basic issue is that second level maths is trying to be all things to all people. It is meant to give students that basic mathematical skills that they need in everyday life, it is also meant to introduce them to mathematical thinking and abstraction, it is meant to give them problem solving skills and it is meant to cover basic calclulus and linear algebra so that students are prepared for 3rd level courses in science and engineering.

I think that we really need two courses to cover all the material that is (inadequately) addressed by the current LC syllabus. This will have the added effect of allowing mathematically gifted students gain extra points from their mathematical skills (thus addressing the bonus point issue for maths).

Eliot Rosewater

The Governments goal is only to increase grades, and instead of improving teachers or students they just dumb it down.

That paper annoys me. Its so retarded - Maths shouldn't be made that easy. What are these students going to to when they get into college? Such a stupid stupid thing to do.

The only thing this will do is improve marks on paper. The students will be less able. The average students will remain the same, while the talented students will not get the opportunity to excel.

MathsManiac

I spent over ten years as a maths teacher, teaching to LC higher level, and marking LC higher level exams. That paper is certainly a significant change in emphasis. I think that the students that I taught and who were successful at higher level would have had severe difficulties with that paper. It's very easy to point to a few things and say it's dumbed down, while ignoring the fact that there are some things there that are far more searching than before.

My guess is that most students on the traditional course would be completely clueless as to how to start that question about the pylon. If they had been given all the details about what had been measured, etc., then yes, they could have done the trig, but they would not have been able to see in advance how to begin. So that pretty much wipes out 50 marks for a start.

Also, in my experience, the lack of choice makes a paper much more demanding than it appears. If you're gunning for an A, then all it takes is a couple of things to trip you up and you're a gonner.

It's an interesting development. Hard to say whether it's harder or easier.

Podge_irl

I'm not a maths teacher so I'll freely admit I can have some difficulty judging the level of LC papers as I'm not really used to looking at maths at that level, but the paper seems quite easy to me. I like the pylon question as it requires some proper thinking but I don't think there should be questions such as that there at the expense of some good old fashioned maths slog. There needs to be a better balance. There just aren't enough calculations. I realise students find them tedious and difficult, but its a vitally important skill to have if you're doing anything remotely maths/science based at 3rd level. I get a little tired of the concept of "just getting the idea right" and while I appluad trying to make it more than just a memory test, students have to be able to get stuck into long calculations and get them right!

I'm not sure increasing the difficulty be removing the choice element is a particularly good idea either. It makes it too easy for one slightly odd question to wreck everyone's exam.

There's also too much stats/probability on it.

LeixlipRed

MathsManiac wrote: »

I spent over ten years as a maths teacher, teaching to LC higher level, and marking LC higher level exams. That paper is certainly a significant change in emphasis. I think that the students that I taught and who were successful at higher level would have had severe difficulties with that paper. It's very easy to point to a few things and say it's dumbed down, while ignoring the fact that there are some things there that are far more searching than before.

My guess is that most students on the traditional course would be completely clueless as to how to start that question about the pylon. If they had been given all the details about what had been measured, etc., then yes, they could have done the trig, but they would not have been able to see in advance how to begin. So that pretty much wipes out 50 marks for a start.

Also, in my experience, the lack of choice makes a paper much more demanding than it appears. If you're gunning for an A, then all it takes is a couple of things to trip you up and you're a gonner.

It's an interesting development. Hard to say whether it's harder or easier.

It's an interesting viewpoint and I admit that the pylon question is excellent and would be found difficult by most current LC HL students. But what are your views on the rest of the paper? It seems awfully easy, choice or no choice.

Fringe

Does the pylon question really belong on a maths exam though? It looks like a nice question but it seems more suited to a puzzle book.

MathsManiac

LeixlipRed wrote: »

It's an interesting viewpoint and I admit that the pylon question is excellent and would be found difficult by most current LC HL students. But what are your views on the rest of the paper? It seems awfully easy, choice or no choice.

Well, since you ask: speaking on my experience of the HL students I taught in the last few years before I left teaching:

Q1 is straightforward, provided that you understand the notation and know what "independent" means. That material is not on the existing core, but I did do the prob & stats option with some classes I taught. In such a class, I'd have expected the better half to handle that question properly.

Q2 requires a fairly sophisticated understanding of statistical distributions and how various summary statistics are related to the shapes of the distributions. My lot would have happily calculated means and standard deviations till the cows came home, but I think they'd have really struggled with this.

Q3: first three parts would have been straightforward for all but the weakest, but I'm not sure that all that many would be able to see the base and perp height required to do the last bit, and I note from the report that if you found the area by some other means, you got hammered, (the question said "hence".)

Q4(a) is a doddle. Those who are good at maths can't understand how questions like 4(b) could trip anyone up, but mid-level students often just don't see it. The relevance of the distance from a point to a line is not obvious unless you remember doing questions like this before. It's not a walk in the park, but still should be doable by the better half or so. On the current syllabus with its (a)(b)(c) structure, it's a tricky (b) part or an easy (c) part.

Q5 should be a breeze, but you do have to know what the range and period are, and not mix them up. Also, the word "range" has a different meanig in statistics from its meaning in functions, so that doesn't help the middling and weak student. (In stats, you need to subtract the small one from the big one and give a number as your answer; in functions, you have to give a set - usually a closed interval.) Despite that, it should be an easy 25 marks for most people.

Q6 should be straight forward for most, provided you've done your stuff and don't make silly mistakes. Weak to middling students are often not great at vectors, but the stuff that's all i's and j's is easier to handle than the "unco-ordinated" stuff, so this should be ok.

I also note, by the way, that those first six questions are only worth half the marks of a full quesion on the current course.

Q7 is content that's not on the current course, core or option, so I'm on less certain ground, but here goes: (i) is a doddle; (ii) is grand as long as you're competent with your calculator. (iii) is testing the kind of skill that's virtually untested on the current course, and I note that the scheme is quite demanding in its expectations. (iv) should be ok, assuming you know what the best-fit line means. (v) is ok, but you need to be careful not to forget the thousands. (vi) is straightforward. (vii) is challenging for students at this level; it's subtle to underrstand and difficult to articulate clearly. (viii) should be ok, provided you've engaged in discussions about sampling and bias, etc. Overall, we'd certainly have a more statistically discerning class of citizen walking the streets if a bunch of them could handle most of this question.

Q8, As I've said already, I reckon almost all of my crowd would have been completely stumped.

Q9A easily matches the standard of the current optional question on prob & stats, which very few people do, bexause teachers think it's too hard (wrongly, in my view, by the way).

Q9B is not especially difficult, but all of this content is new (not on the current syllabus) with the result that most higher level students arrive at LC having forgotten all their geometry, so it's not a bad thing that some of this stuff is back on again. The scheme for the proof is pretty demanding for full marks, so it's not a walk in the park. Part (b) should be straightforward, but experience tells me that a whole bunch of them would be scratching their heads, just not quite seeing it.

Of course, all of the above relates to the students that I was teaching the existing course to over ten years ago. I do think on balance that there's enough straightforward stuff that they'd pass this paper, but that they would really struggle to get good grades, particularly given the marking scheme. I think I would have had to teach them in a quite different way to make them really succeed on this paper. I could have done that, I think. But of course, then they'd have been less well prepared for the old exam!

The paper reflects a significantly different vision of what mathematics is all about. I'm not sure that it's aligned with my vision, but I think I'd have to concede that it's not an unreasonable one in the context of second level education.

And, after all that, I still can't decide whether it's easier or harder, but I do know it's different!

Megatron_X

I'm a 5th year student at the moment, aspiring to be a Maths and Irish teacher, and my heart sunk when I saw this 'Project Maths'.

I like the fact that Maths is difficult, I understand that statistically speaking the fact that it's difficult to some looks bad to the government but dumbing it down just dumbs the students down. I was looking forward to teaching hard maths to kids and to help them them to understand it, just as my teacher has done to all of my class which has inspired me to do the same.

Is this really what I'll be teaching? I honestly feel disappointed right now, and I'm not even a teacher yet.

ZorbaTehZ

No vectors OR matrices on the course?! Absolute insanity. The mind boggles. :eek: