Hi everyone, this isn't a maths question but a request for comments. Today the government will, apparently, announce a review of maths education for 14-19 year olds, and it is expected that it will lead to a report calling for reforms to make it more "relevant" and "employer friendly". In practice, this apparently means that there will be less algebra, geometry and trigonometry and more statistics, probability and calculation.

What do you think of this idea? Are students at school likely to be more or less motivated by learning mathematics which would be more "relevant" and "employer friendly"? Would learning statistics, probability and calculation be more or less "useful" than learning algebra, geometry and trigonometry? If you were deciding education policy, what would you focus on, bearing in mind what would motivate students and what would be useful, and why? Any other thoughts?

It would be nice to get some responses from teachers and students.

In case you want to do some background reading (they are very tedious):
Sir Gareth Roberts' March 2001 review of science and engineering skills in the UK

• Institute of Directors - look for "Education and training: a business blueprint for reform"

This actually depends on the specific student. Personally, I wouldn't like this kind of change, but on the other hand it WILL motivate most students to work harder in mathematics, because it gives you something to connect to, something that relates to the real world.
Here in Israel, the advanced math students in high-school don't learn probability and statistics, and I feel like I'm missing something, because they are (most of the times) pretty interesting questions.
I don't know exactly what you mean by 'calculation', but it could help if the teachers put more emphasis on it (if you mean arithmetic), because by the time you finish high-school (and I see that in my class mates) most students don't remember how to do long-division.

Personally, I find algebra, geometry and trig more appealing, even if they don't bear a tight connection to the real world (geometry does, a little). Actually this is exactly the reason why I like those subjects!

This is, ofcourse, the opinion of a math student of Israel and not of the UK.


Yatir

I think it would help in GCSEs to include more about "why we do what we do", I remember not really understanding why I was doing certain things, however, they shouldn't cut down on the Pure Maths at all, Statistics isn't the only route from doing Mathematics at school...

It's my personal opinion that A-Levels should be made "harder", not because I want to be mean, but rather I think atm there's little differentiation (no pun intended) between people who do truely understand the maths and those who just know how to apply formulas - I'm sure many people on these webboards who are very very good at maths will agree that they're not really *that* proud of getting an A at A-Level Maths, simply because you don't need to be exceptionally good to get one... I think the exam boards should consider inventing an A* grade, or an "S" grade (to parallel will STEP grading) by which completion of a few extra *HARD* question on a Maths A-Level would result in that...An example of implementation would be something like this:

Section A: Tests ability to reach Grades C and below
(Choose EITHER B or C)
Section B: Tests ability to reach Grades A and below
Section C: Test ability to reach Grades A*/S

Section B would ensure proper A candidates could complete all questions fully - ie satisfying the syllabus and the requirement for A Grade. The questions in Section C could be more challenging, like the standard of A-Level papers from the early 80s.

Julian

Just another point: Presenting questions in prose tests the candidates understanding of the use of mathematics, most A-level papers now say things like ''Solve 2x=ò_x¹ 2x dx'', which although is a good type of question to have on a paper, the paper imho shouldn't be consisted entirely of these aesthetically pleasing-robotically-solvable questions.
Julian

Probably the hardest question I have to answer is "Please Sir, when will I use this after I've done my GCSE"? I think there IS a need for more relevance but please let's not be too utilitarian and please let's not have more fractions!

As a retired employer who headed up a large department of staff whose job entailed processing numerical data I would like to see students leaving school with less dependence on calculators. Many young people have no "feeling" for numbers. The silly answers one hears on TV quiz programs to mental arithmetic questions dempnstrates an absence of any real numeracy appreciation. I was educated in the forties and have frequently been very grateful for having instant recall from the "times tables". I have often heard the comment that people have never used algebra again after leaving school - I do not believe it. I think people often use the principles of algebra subconsciously.

It seems that the GCSE is crammed with both "relevant" topics such as statistics and "traditional" topics such as algebra and trigonometry. Why don't universities and employers look at what students can do such as problem-solving and investigation work instead of complaining about what they can't do. Students already comment that Maths is the hardest and fullest GCSE subject, and it is now acknowledged that it is the hardest AS and A level subject.

As always in a discussion of this sort, I'll forward that I'm American, but that shouldn't matter much (spare my abbreviated spelling of mathematics).

"What we are taught has no relevance" is, admittedly, a common complaint in schools, and perhaps not a bad one. In general, what is taught in school, particularly in a math class, will probably not be used, or even need to be used for that matter, in an industrial setting.

It's interesting to note, however, that you don't hear the same sort of complaint in, say, the fine arts. Surely these fields have far less application than math to industrial uses. Should we therefore conclude that there is a collective haze upon the people involved preventing them from seeing the lack of value in these endeavors?

Perhaps you are sane and say, "but art does have value: it entertains; it enlightens; it gives us a great amount of freedom!" Of course you'd be correct in so saying, and few people would disagree with you.

It's remarkable, however, that so many people would disagree with you were you to apply the same comments to math. Surely the right sort of math does afford the same amount of freedom and beauty as does art. And surely curiosity is a natural part of every human, to which end mathematics should be enjoyable if introduced in a decent way.

That's the problem, though; mathematics, unlike art, is introduced (in school, at least in my school) in a way that no sane person would enjoy. It's taught as a variety of formulas, and we are to learn these formulas because we have been ordered to by this or that person. Mathematics, which ought to be a subject learned without appeal to authority and which ought to stem naturally from a childs curiosity, is instead just the opposite. It is used as an instrument to beat down a childs curiosity, and the newfound lack of curiosity and absense of motivation in students is then used as an excuse for the exercise of more authority. This is, I suppose, a rather honest response you could give someone if they ask how the stuff they're taught in school applies to industry...

I've gotten off topic, and intentfully so. To answer the question, though, I don't think that the solution to math's problems is to make it more oriented towards industry. Rather, just the opposite. Humanity has more important needs than the aquisition of capital, and it seems most real needs are in direct opposition to this false one. Sir Gareth's report is a case in point.

Brad

"We need more plumbers..." Why shouldn't a plumber have a first class maths degree?

I believe that doing mathematics helps the brain learn a general system of problem solving without being distracted by relevance to non-mathematical things.

I've just gone through those two dull reports and culled about two pages worth of material from them that I think is most relevant to this discussion. It might be useful. http://www.fcbob.demon.co.uk/maths-education-stuff.html

A couple of questions that occurred to me are - what does "relevant" mean in this context? In several places, it seems as though they are using the deduction "relevant" implies "will motivate students". I wonder if there is any reason for this or if it is axiomatic (and hence dubious). Either way, I don't think it's clear what they mean.

Another question: is the ability to do calculation relevant today and will it remain so? Bill Smith gives the example of times tables being very useful to him. I wonder, will this sort of mental calculation remain useful as the sorts of calculations that are relevant become ever more complex and computers become all pervasive and more sophisticated.

For example, I was having a discussion with someone about mortgages the other day, we were trying to work out how much you end up paying in total with different schemes. The schemes are sufficiently complicated and varied that (it seems) no method of calculation could be taught that would cover all the different types. In fact, to work out algebraically (and probabilistically and statistically if you want to take into account varying interest rates) how much you end up paying in the end is very complicated.

Do you think it would be possible to educate a significant section of the population to a level of understanding of the relevant mathematics that they would be able to do this sort of calculation? If not, are there any resolutions to this problem, that people are unable to make decisions about such important matters on their own? How does this sort of consideration (ever increasing complexity of the relevant mathematics beyond a level which could reasonably be expected of everyone) bear on the question of relevance and usefulness to employers? For example, what is it that employers want people to be able to do, and will a greater emphasis on calculation really achieve these goals?

Another example - computer programming. This is becoming an ever more important skill. In this domain, the ability to do calculations is totally irrelevant, but the things Elizabeth Dunford mentioned (problem solving and investigation) are very useful indeed.

I'd like to comment on some of the "elitism" questions raised - whether there should be more streaming, separate vocational / academic streams, more differentiation in abilities (e.g. raising the difficulty in getting an A grade) - but the issue is very political and I don't know if it would be very constructive to do so here. Such discussions tend to get ideological very quickly.

Finally (at last you may say!), I'd just like to agree with Will and Brad. Maths does have a rarely recognised (outside the mathematical community) aesthetic quality as well as it's more pragmatic side. More generally, there is a danger in considerations about "usefulness" and "relevance" in forgetting that education has value in itself, as a process, as well as a means to an end. Most people spend a significant proportion of their life at school and university. The intrinsic value of that part of their life shouldn't be forgotten in the quest for a more skilled workforce (or whatever).

You know the old saying "JACK OF ALL TRADES BUT MASTER OF NONE"...However in the last few decades this opinion has undergone a drastic change...Today,we should not be a master of single field nor should we be jack of all trades but we need to be masters of as many trades as possible....This is the key to survival today in this growing world full of competitions...This means that student should have sufficient understanding of each and every field...This can only be achieved if and only if education in its entirety is produced before students....

In other words,the talk of "relevent" and "irrelevent" maths is absurd and irrational..There is nothing like irrelevent maths..everything is going to be useful but it is for us to decide how are we going to use it....Every part of maths is useful in some or the other field....like for example my computer engg syllabus is completely based upon applied maths and discrete maths....

Some people talk of explaining students,the use of maths, so that they take more interest...but i don't think that's possible.....In my school days,the only thing that i took seriously was to come home from school and not to miss the 6'o clock show of disney cartoons and ofcourse at 7'o clock go outside and play cricket....My friends and i used to talk about careers a lot but hardly we ever took them seriously until we were 15 atleast...

Therefore,according to me,the syllabus should be such that it must give students an idea of each and every part of mathematics....(i.e give them each and every possible options so that it is possible for them to switch fields quite easily)...I know that this could be like overburdening the students with studies but i think you have to "HAMMER THE ROD WHEN ITS HOT"...

Note:i am talking, keeping in perspective the changes in world economy and corresponding changes in indian economy....

But i am quite sure that everyone agrees with me....

love arun

I believe the government is wrong to make maths more applied - I would hate 'A'-Level maths if it became more "applicable". GCSE and 'A'-Level maths already contain large amounts of probability and statistics and they don't need to be crammed with any more.

I agree with Elizabeth - universities, employers and the government should be focusing on teaching investigation and problem solving skills in maths, which help students to think in different ways about puzzles and would be both interesting to the students and "applicable" to industry, rather than teaching them to regurgitate formulae that they don't understand.

Removing algebra and geometry from the curriculum appears to be yet another example of [what seemingly is endless] "dumbing down". The new AEA papers are another example - I have only seen the maths AEA, but it's much easier (and much less interesting) than any STEP paper I've seen, which makes it difficult (or rather impossible) to differentiate between the best candidates and means more people will be expected to take the exams and so more pressure will be put on students.

Students now face exams in years 11, 12 and 13, and possibly the following year at university - it's no wonder they're always trying to learn formulae and always complaining that they're subjected to too much pressure. And this is the key: students do face too much pressure, and the disastrous introduction of the 'AS'-Levels has simply added insult to injury. School children should have sufficient time between examinations to explore maths outside of the curriculum - that is what will spark their interest, and that is where the government is going wrong.

In response to William's comment, plumbers don't need first class maths degrees! A large number of jobs quite rightly require employees to have degrees. Plumbing is not one of them. I completely agree with the IoD - this country needs fewer media studies graduates. The government should scrap its 50% target of young people in universities by 2010. Call me cynical, but the only reason why they invented that target was to keep unemployment figures down.

I believe, as Brad said above, that maths should be curiosity driven and studied for its own sake rather than as a prelude to employment. Maths is wonderfully elegant subject, and should be taught thus.

Paul

Following on mostly from what Brad said, there are a couple of issues here.

Firstly, it is obvious, I think, that the what needs to be tought to children is how to think coherently and crititcally and how to increase their quality of life through the appreciate in of beauty in all forms, from painting to mathematics. And you do need to learn both these things. By deemphasising these aspects of teaching in favour of "employer-friendliness" (more on this below) one is essentially designing a society where people do not think often and do not have the tools to appreciate some of the great achievements of humanity. I would consider this a substandard existence and it is hypocritical of anyone who has both of these things (i.e. ministers or employers writing the reports on education) to suggest that others shouldn't.

Secondly, it seems clearly wrong to suggest that learning "practical" things is the best way to be practical. It's like teaching someone about a certain computer operating system in depth without teaching them the fundamentals of computing interface, which will mean that when the operating system changes, they will have to start from scratch again! They are then at the mercy of the other people who know what is going on. Knowledge is power, let's not deprieve anyone of it. Training for the specifics of a certain job is not difficult (indeed it used to be something that the employers themselves were expected to do), instead what needs to be taught is a solid background.

This isn't to say, of course, that one shouldn't struggle to present maths in a way that links with the world and practically, but this really isn't too difficult (althought here are a lot of bad maths teachers out there). The point is not to move away from teaching people to think in favour of teaching them how to perform certain mind-numbing calculations that may (or probably not) get them a job later.

Sean

i think that discussion has become stagnant here....almost everyone agrees(even me) in unison that "math should be studied for its own sake" (paul smith's words and brad's humanitarian views)

The discussions no fun if there are no points coming from the opposite side....

i would like it if some of us would take the stand of the government and defend it and then the discussion would be fun....

ANY VOLUNTEERS????

love arun

Well Arun - here's a volunteer.
It should be obvious that a maths - based discussion board is going to come down on the side of a 'purer' form of maths for school students. Most contributors seem to enjoy maths and find it useful - I don't think thats how the majority of the population see it. As a teaching colleague ( non-maths ) said to me the other day - all the maths you need to get by in most of life is number work, percentages and an understanding of graphs!
Teaching low-ability maths students is not helped by the fact that they see much of the syllabus being geared to the few going on to do maths or sciences at university and being of little relevance to their future concerns.
Perhaps relevance is not the answer to generating more enthusiasm for maths - but it sure would help!
I do agree that maths is about more than just job relevance, but we do do need to do something about raising the generally poor standard and profile of maths in this country. In primary schools surveys show that maths is a popular subject - this is not the case at seconday level.
Something is going wrong and tributes to the beauty of maths only impress other mathematicians - not the rest of the kids we are trying to reach.

Neal

Neal,

I agree that maths should not be taught as if everyone who's learning it will carry on doing it at university. That is why I am strongly in support of separting maths students (in senior school) into classes by ability (and to a smaller extent, enthusiasm). That way, the less able can be taught basic numerical and statistical skills, and the better students can be taught algebra and geometry. It is also why I like the modular system for 'A'-Level mathematics, allowing students to choose the modules that they're most interested in.

Paul

Neal, what though, seperates mathematicians that are impressed by references to math's beauty, and those that despise math? Is there a "math gene," which most the people on this board have been endowed with, or is it something else?

A similar question could be asked of nearly every field. The point is that there is probably something appealling about a particular field that brings people to it, and we should try our best to show that particular aspect to everyone. In math, I don't think that aspect is numerical computation, or industrial uses.

Brad

There is already a choice for 16-19 year-olds whether to bias towards Probability and Statistics or away from Pure.

Brad, you have a point.
I don't like a topic called: 'citizenship' it is about how the goverment operates and about rules, why not make that easier for me to like it more???

Yatir

From TonyGarwd

Hi

How do we ordinary teachers influence this potentially dangerous report?
Maths without algebra and geometry would be less interesting and hence less motivating.
Statistics can be presented as a series of number crunching rules to be learnt and
applied. Is this what the person behind this report wants to see more of in the name of
maths? We probably could train a greater proportion of pupils to rote learn calculation
algorithms to do "hard sums". Where is the excitement and where is the basis for A level
work? Perhaps this will lead to A level "hard calculations" instead of maths? I do not believe
that my pupils would benefit from such a change.

Tony Garwood

From Gordon Goodyear

My guess is that 80+% of all students have no real need for algebra, trigonometry or geometry in the course of their lives. The balance that
might go on to some professional education probably might. Those who take scientific education clearly do. So why not place the primary emphasis on mathematical tools that will be both useful and relevant to people's actual lives. A kind of Mathematics 1 that everyone has to take. From an employers perspective, future employees that can add, subtract etc are clearly desirable. The ability to solve quadratic equations is somewhat irrelevant if the individual can't perform basic order of operations.

I teach algebra and trigonometry to adult students training to be technicians, CAD operators and computer networking specialists. The relevance of quadratic equations to their lives is at best tenuous. When I teach them simultaneous linear equations, most students are terrified. When I teach them Kirchoff's rules and show them how a resistor network leads to those same equations, they "get it" and will persevere in learning the necessary manipulations to solve the equations. Once they see why they have to learn something, it becomes much easier to learn.

As a result of this realization, I am in the process of redirecting my complete syllabus towards the actual application of each and every
mathematical topic that I teach. Instead of teaching first order linear equations, I introduce Ohm's law and introduce the equation from the physical world.

Hope these comment help. BTW, I do sincerely hope that "employer friendly" and "relevant" doesn't translate into yet another lowering of standards. Our level of mathematical and scientific training is low enough without being
further reduced.

Regards
Dr Gordon Goodyear
Theoretical Physicist and ex-General Manager of a large electronics company.
Educated in the UK and living in Arizona

I am an ordinary maths teacher - only teach up to GCSE higher level - at 57 have been through many changes of what and how to teach maths - looped the circle right round! I started with tables learning and am now repeating having gone via 'modern maths' (Nuffield) and several styles - whole class, mixed ability, setted, groups, individual learning - in fact the Government seems to have changed maths teaching more often than the salary!?! At present I am marking (yes, in my summer holiday) a heap of GCSE statistics coursework which has proved much more irksome to the students than investigative coursework has in the past. The answer to 'Why maths?' - my standard answer is always 'To train your brain.' I am sure it does - in a way that other disciplines do not. When asked to comment on their most enjoyed part of their maths this year, my year 9 students picked 'finding the gradients of the school staircases' (possibly because they were out of the classroom and my supervision!!)and 'the games we play at the beginnings of lessons' (mental arithmetic, no calcs) The Numeracy Strategy hit secondary schools this year - it already seems to be sending through students with more mental arithmetic skills and more enjoyment of maths from the Primary sector.

The new proposals (assuming that they have not been wrongly interpreted by the media I have read) seem to me to be completely ridiculous! Reducing the amount of algebra, trig. and geometry taught will not only remove the foundation of maths necessary for a maths (or, to a lesser extent, physics) A-level, but is likely to de-motivate many students. The notion that "statistics, calculations and graphs" are more interesting to study seems to be entirely groundless. We may be in the minority, but myself and a number of my friends enjoy "pure" maths far more than statistics and other "applicable" maths. Amongst those who are no longer continuing maths at A-level, most found all aspects of maths equally unenjoyable!
I agree with the posters above who have said that maths should be made more interesting by allowing students to experiment and investigate, instead of the current system of learning by rote. The new AS-levels have compounded the problem further, as the first year of sixth form (which I'm assured by teachers used to involve a reasonable amount of extra curricular study) is now dedicated solely to hammering syllabuses (sorry, specifications) into us. If the government want to increase standards then dropping these needless exams (and freeing up the inordinate amount of time that they consume) and instead allowing a broader investigation of the subjects being studied would be a far better way of achieving this than removing essential, core, maths from GCSEs.
Okay, that turned into a rant at the end, but having suffered the AS-levels to no noticeable gain I feel strongly that the new system is deeply flawed and in dire need of change. The new AS-levels (especially Chemistry and Physics) have had all questions that require thinking removed from them and have been dumbed down to the level necessary to enable them to be taught in the hort breaks between exams (as there are now exams in January and May/June).

Ok,
it seems we have had good enough points from both parties....

out of these discussions two things are quite straightforward which everyone agrees to....
THE FACTS:
1> making education entirely job oriented is unjust
2> but there are students with career oriented minds who are interested in studying only those things which are relevent to their future..

some suggestions made above are...
THE SUGGESTIONS:
1> DO NOT make math...career oriented,infact efforts should be made to make students realise the beauty of maths.....
2> another suggestion....no need to change students minds just let them follow what they are interested in by grouping of subjects....
3> another one is........make math career oriented but without removing pure math entirely....

Now......
Assuming that the govt. will not make any biased decisions and that it will keep in mind the interest of all students.....

What do you think the governments decision should be???

ANY IDEAS!!!!

love arun
P.S-> Its nice to see teachers getting involved in this discussion and i expect their interaction to continue in future as well...

From Bridget Vickers

I can't believe that the government are going to make yet more changes. I think that all students deserve to have a grounding in number in all its richness. It is the exploration of areas tangental to the national curriculum which extend and excite but they need the basics. I think that other topics aid the development of reasoning and logic and problem solving skills. They instill structures that can be transferred. The greeks thought of maths as calculation and arithmetic and one was more practical and the other more like philosophy.

I do think as pupils pursue more vocationally based subjects (as in the 14-19 education plans) that they need both a sound grounding in the basics and development of problem solving skills but they also might benefit from 'Business Maths' or Maths for the Office or Life Skills Maths. I must admit that when I have a bottom group that has covered the syllabus three times over in every way possible I do try and give them some life skills maths. eg find that job - how much take home pay, buy/rent your flat etc. If nothing else it make some of them aware of how much things will cost and why they might need further qualifications.

Bridget Vickers

A couple of comments. To Tony Garwood - the Guardian article said that there would be a consultation (if I remember correctly). As far as I know, it hasn't been announced yet, but details of the consultation and a form to send comments will become available on the DfES website http://www.dfes.gov.uk/consultations if and when one is announced. I don't know how much difference it would make, but it's worth a try.

To Gordon Goodyear, I think your view on adult learning is completely accurate. However, I suspect that the situation is different for children. Adults can be motivated to learn maths because they need (and can clearly perceive their need) to in order to achieve some other goal (e.g. technicians, CAD operators). Children don't have such a need and so that type of motivation wouldn't work. OK, they do have a need but it isn't clearly perceptible for them (partly because it's a long way off), and just telling them that they will need it isn't going to cut any ice with kids. There's another point, adults tend to (but not always of course) have a lower natural motivation to learn for its own sake, so they need to be motivated by another goal. You could say adults are goal-oriented whereas children are more process-oriented. That's not to say that the process has to be a formal learning of algebra, trig and geometry though. In my case, I came to learn and be interested in maths through my interest in programming computer games. A certain amount of mathematical knowledge is a prerequisite for programming games, but more importantly the mindset involved in programming games (and to a lesser extent programming in general) has a great deal in common with the mathematical mindset.

Yatir, your point is well taken (in that the course is, in some sense, neccessary), but why shouldn't that course be made more to your liking, if possible? Furthering the questioning, what makes you dislike the course in the first place? Could societal changes change your dislike?

Brad

I guess that looking at politicians in my country and then finding out that in most cases they act based on political reasoning only, and to not care to preserve democratic reasoning. In fact (I guess this is true all over the world) politicians are more eager to keep their job than to actually preform it!

I guess that seeing their actions stir a feeling of dislike against this subject.

I do like and enjoy the political "discussions" we hold in class, but I don't see any much point in memorizing sets of rules.

Brad, Yes. Social changes would change my views.

(I know this post kind of diverts from the math conversation)

From Gill Tucker

hi
You asked for comments and these are mine. I speak as a parent - one offspring has a degree in Maths from Cambridge and is currently halfway through an MBA in the US and the other has a degrree in Engineering, is a CE, and is working in the Netherlands.

As a Maths teacher, I have taught in a good comprehensive school in Cheshire since 1989, long enough to see numerous changes, but as I was a late entrant to the profession my own education gives me an additional perspective.

Grammar schools are too divisive, coeducational comprehensive better, but are we a two part society, the haves and the have-nots? I can really only speak from the perspective of the 'haves', I teach all abilities 11-16, but I also have the privilege to teach A level Maths and Further Maths. I like the Numeracy strategy, pupils are able to calculate without a calculator.

14-16 I have seen transition from SMP, applicable but little algebra, to current specification. Higher tier has much more content than 10 years ago, and it is a struggle to complete with all except the most able pupils.
How many state school pupils are entered for Higher Tier GCSE Mathematics?

My colleagues and I are currently wrestling with the latest specifications requirement to complete a piece of Statistics coursework. Most of my pupils have enjoyed it but what marks they will gain is not what I expect from them. This is meant to be GCSE not A level.

16-19 we have just completed the first two years of the new specifications. Students giving up Maths after AS because it is hard compared to other subjects. If students follow 4 AS courses in Y12 most do not feel they have the amount of time to spend practising and consolidating Maths that teachers recommend. Consequently after one year they decide to drop Maths so that they can gain the requisite grades for their university courses. There seems little parity between AS courses in terms of content and concept.

Has no one considered the effect of greatly reduced numbers of students with A level Mathematics on the economy in terms of lack of engineers, scientists and teachers?

To return to the question posed: For most students an ability to apply their mathematical knowledge to solving real life problems seems more appropriate than being able to learn formulae so in that sense calculations seem most sensible. The trend of the latest GCSE specification in reducing the formulae supplied seems a retrograde step. However this does not help the development of our more able students who need to learn algebra, trigonometry, geometry and statistics.

We could have a more problem solving approach at GCSE but this would require changes to post 16 education which might not be palatable to Government or the Unversities. I don't have an answer but I do have an appeal for any changes to be carefully considered with all their consequences. Those of us interested in post 16 Mathematical education are not at all surprised at the lack of applicants for Maths and engineering degree courses this year. It was
obvious as soon as it was stated that all AS courses would be more straightforward EXCEPT for Mathematics. WE need to provide attraction
for MORE students so that we can provide more technically proficient young people rather than a surplus of tham interested in IT but not able to DO anyything.

Re-reading your question, yes a problem solving approach can only be seen as more relevant, but we can only aim to develop skills, employers must
train their own employees not schools

My apologies if this is over long but this is one of my hobby horses. I enjoy Mathematics and teaching it but it is difficult to persuade more
than an enlightened few to pursue the subject as far as they are able.

I hope you have many responses
Gill Tucker