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New maths and further maths A Levels

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Original post by PhysicsKid
And perhaps I didn't articulate that very well, but what I meant is compared to the current A Level timeline, as Maths & FM AS often spans 2 years. Apologies if I've confused you or am constructing a somewhat circular argument, I'm just really passionate about this area and was interested in good debate/seeing how such an idea might work from experienced teachers. :smile:


A level always took 2 years

You are not clear what it is you are passionate about ... It would seem that you want 16 year olds to be taught a level maths ... Why
The problem with maths is that its content is so vast, you really have to be brutal with what you include and what you omit.

I guess it would be nice to have maths targeted at each uni subject, whether it be chemistry/physics, psychology/biology, engineering, etc. (yes I know we have mechanics) but I don't know whether there are enough lessons or competent teachers to do it in just two years. And what if someone wanted to change paths? Most people haven't picked their degree when they decide on their A levels.

As has been said, when students don't know basics like changing the subject, manipulating fractions, and simple trig, there's no point even going there.

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Original post by TenOfThem
No ... Did you not read what I did and did not study


I read that you didn't really do Stats/Matrices or any deep Complex Numbers, but some content could be removed that is no longer deemed appropriate, as could happen in the NC progressions. Where are tessellations useful for example? Similarly, how does the average student benefit from studying loci? A Further Mathematician definitely would! At the time, I really hoped you Maths teachers had some justification for it :wink:
(edited 9 years ago)
Original post by TenOfThem
Ok ... Schools with 2 a level sets are rare ... If there is a bottom group they should be doing something different that does count

Your field trip comment does not seem relevant ... I thought we were doing what was good for the students


Doesn't that depend on whether what is best for the students is giving them the greatest mathematical knowledge and skill they can handle or maximising their examination grades?

If universities are not downgrading international or Welsh qualifications against new (harder) English ones, then what may be in the students' interest is to have them sit the examination that will get them the best grades.

In essence the DfE is seeking to strongarm schools into possibly not doing what is in their students' interest by threaten to come round with a baseball bat and duff up the school's league table position.

One could say that a school acting properly ought to ignore the implications for its league table in choosing whether to enter pupils for these new qualifications or not but that is a tough call for any head. It would be so much easier if what is in his students' interests happens to improve his league table position.
Original post by Mr M
MEI's income is not dependent on A Level mathematics (and there is no reason to believe they won't be a big player for the new A Level anyway). They are contracted to run the Further Maths Support Programme and raked in a tidy few million for developing Gower's ideas into the Critical Maths element of the new Core Maths qualification. You don't need to fear for their future!


Caught my eye. Looking it up, it seems like an appropriate pseudonym may be 'Foundational Statistical Concepts'. Interesting idea, and a good one I think.
Original post by PhysicsKid
I read that you didn't really do Stats/Matrices or any deep Complex Numbers, but some content could be removed that is no longer deemed appropriate, as could happen in the NC progressions. Where are tessellations useful for example? Similarly, how does the average student benefit from studying loci? A Further Mathematician definitely would! At the time, I really hoped you Maths teachers had some justification for it :wink:


Interesting choices

Tesselation is half a lesson at ks3 so dropping that will barely scratch the surface

The geometry understanding in loci is valuable ... The number of people who struggle with co-ordinate geometry and vectors is a testament to how poorly this topic is understood

The new GCSE has removed content that is deemed inappropriate ... Sadly this is a lot of stats ... After financial maths stats is probably the most useful element ... So how are you going to decide what is useful and what is not
Original post by TenOfThem
A level always took 2 years

You are not clear what it is you are passionate about ... It would seem that you want 16 year olds to be taught a level maths ... Why

I'd hopefully be far better in sketching this out in person; it's incredibly difficult to describe a sort of framework like this over the Internet :smile:

With regards to the first bit, I am suggesting the 6 units are taught over Years 10 and 11, with 360 hours or so recommended teaching hours, not on 3 hours a week- more like an hour a day on average.

In response to the second bit, I'd like the opportunity of a challenging, 2 consecutive AS difficulty Maths courses to be afforded to KS4 students who would benefit from it/could cope, hence why I suggested limiting it to the top quartile or so of students. My argument is that with a weaker student base at A Level, these results are achieved, so with a far more restricted KS4 student base (mathematical maturity notwithstanding), similar results *could* be achieved. Even an E grade would be something to be immensely proud of, due to the student's enhanced skills compared to those similar to them in the past who were artificially capped at an A* at GCSE. Those who got less than a B could continue studying it in Year 12 and maybe get on to some Further Maths, where the average modules would be far 'harder' than present.
Original post by nulli tertius
Doesn't that depend on whether what is best for the students is giving them the greatest mathematical knowledge and skill they can handle or maximising their examination grades?

If universities are not downgrading international or Welsh qualifications against new (harder) English ones, then what may be in the students' interest is to have them sit the examination that will get them the best grades.

In essence the DfE is seeking to strongarm schools into possibly not doing what is in their students' interest by threaten to come round with a baseball bat and duff up the school's league table position.

One could say that a school acting properly ought to ignore the implications for its league table in choosing whether to enter pupils for these new qualifications or not but that is a tough call for any head. It would be so much easier if what is in his students' interests happens to improve his league table position.



I think we are talking about different things ... If a student is not capable of doing a level ... Why would they do a level?
Original post by PhysicsKid
I'd hopefully be far better in sketching this out in person; it's incredibly difficult to describe a sort of framework like this over the Internet :smile:

With regards to the first bit, I am suggesting the 6 units are taught over Years 10 and 11, with 360 hours or so recommended teaching hours, not on 3 hours a week- more like an hour a day on average.

In response to the second bit, I'd like the opportunity of a challenging, 2 consecutive AS difficulty Maths courses to be afforded to KS4 students who would benefit from it/could cope, hence why I suggested limiting it to the top quartile or so of students. My argument is that with a weaker student base at A Level, these results are achieved, so with a far more restricted KS4 student base (mathematical maturity notwithstanding), similar results *could* be achieved. Even an E grade would be something to be immensely proud of, due to the student's enhanced skills compared to those similar to them in the past who were artificially capped at an A* at GCSE. Those who got less than a B could continue studying it in Year 12 and maybe get on to some Further Maths, where the average modules would be far 'harder' than present.


I have already pointed out that only 5% of students really master the current GCSE ... There are suitable courses to extend them

Why do you want 25% to spend less time mastering that work and instead starting harder topics that they are ill-prepared for ... I find the idea that a student age 16 is better served by an E at A level than an A* at GCSE ridiculous ... Why would they be?


Oh and ... A level maths in my school has more hours a week than GCSE so I did not understand the 3 hour comment
(edited 9 years ago)
Original post by TenOfThem
Interesting choices

Tesselation is half a lesson at ks3 so dropping that will barely scratch the surface

The geometry understanding in loci is valuable ... The number of people who struggle with co-ordinate geometry and vectors is a testament to how poorly this topic is understood

The new GCSE has removed content that is deemed inappropriate ... Sadly this is a lot of stats ... After financial maths stats is probably the most useful element ... So how are you going to decide what is useful and what is not


I'd get a large team of teachers and experts together to decide- I'm in no way qualified to do that lol.

As I said a large number of posts back, separating Maths into 2 separate, setted strands of Numeracy Skills and Maths would help.

Things like scale drawings and L7/8 percentage problems could have much less emphasis in the latter while being a worthwhile area for greater scrutiny in the former, given reports of large numbers of adults having the maths skills of an 11 year old and current students supposedly being even less equipped.
Original post by TenOfThem
I think we are talking about different things ... If a student is not capable of doing a level ... Why would they do a level?


Presumably we are expecting grades to fall overall under the new dispensation.

If grades do not change under say the exams set by the Welsh board to the old spec, then you may have a student who will get a D under the new dispensation who would get a C in the land of someone else's fathers. That student hasn't picked the wrong A levels. He is just a D student sitting English A levels and a C student sitting Welsh A levels.

If the DMU or the Anglia Ruskins of this world don't have different offers for Welsh and English A levels then doing the Welsh rather than the English board might be the difference between going to university or not.
Original post by TenOfThem
I have already pointed out that only 5% of students really master the current GCSE ... There are suitable courses to extend them

Why do you want 25% to spend less time mastering that work and instead starting harder topics that they are ill-prepared for ... I find the idea that a student age 16 is better served by an E at A level than an A* at GCSE ridiculous ... Why would they be?


Oh and ... A level maths in my school has more hours a week than GCSE so I did not understand the 3 hour comment


I receive 3 hours a week of Maths where I've essentially self-taught A Level, so I wasn't sure whether you thought I meant forcing everyone to cram 6 units into 3 hours a week or something silly like that :smile:

I wouldn't want GCSE topics to be glossed over, but they are quite often revisited in C1/C2/S1, I'd just want the A/A* topics brought in during Year 9 where Level 8 topics are currently developed (in top set).
(edited 9 years ago)
TenOfThem
.
I think it all comes back down to KS2, where good work is often done. I wonder whether the KS2 SATs could test Levels 4-6 with a 5b or 5c expected of the 'average' student instead of 4b. That would grant crucial extra time at KS3 for harder topics to be brought in earlier; with the necessary foundations.
Original post by nulli tertius
If a school has two A level sets, surely not counting the bottom set in the league tables by teaching them something else improves the school's overall performance.

Isn't it the same as sending the disruptive kids on a field trip on the day of an inspection?


I'm a bit confused and don't know if you are talking about teaching A Level to pre-16 or post-16 students now but ...

Pre-16 - students' Progress 8 point score falls triggering a visit from the Grim Reaper (Ofsted)

Post-16 - students' Programmes fail to meet 540 approved hours and the Bride of Frankenstein (EFA) slashes funding
Original post by Mr M
I'm a bit confused and don't know if you are talking about teaching A Level to pre-16 or post-16 students now but ...

Pre-16 - students' Progress 8 point score falls triggering a visit from the Grim Reaper (Ofsted)

Post-16 - students' Programmes fail to meet 540 approved hours and the Bride of Frankenstein (EFA) slashes funding


I am referring to A levels so I am referring to post 16. I realised that pre-16 any head attempting to game at least those GCSE subjects which Gove Dec'd cared about was going to have Ofsted problems.

Thank you for pointing out the funding issue.

I wonder to what extent the government will be be able to hold a line here, particularly with, what is it, 25% of VIth form students in the private sector and most of their providers not being the likes of Westminster.
Original post by nulli tertius
What is the scope for schools saying "sod this for a game of soldiers" and entering pupils for something Welsh or international?


Original post by TenOfThem
zero scope for state schools as they will not count in the Dfe measures


Isn't this the real issue? I think there were two fundamental problems with the current Maths A-Level. The first is that even with Further Maths, they are just not adequate preparation to get into a maths course in a top university (hence the prevalence of STEP). The second is that it is failing even as a facilitating subject for quantitative courses at university.

The proposed reforms go some way in helping with the second problem (note that the changes to the actual content are minor, but there are encouraging signs the exams will differentiate more). As long as participation doesn't drop, this can only be a good thing.

But we're kidding ourselves if we think that we are stretching our brightest with the current system. For those who are aiming to study maths at university, the current content is nowhere near as helpful as it should be.

There are huge chunks of content which would both be challenging and helpful to a wide range of people. For example, learning to count properly (permutations/combinations, inclusion-exclusion principle, using De Morgan's laws, pigeonhole principle etc.) could be a starting point for both mathmos and those who do stats, so that they get a proper feeling for probability. Similarly, modular arithmetic is a hugely interesting topic that can be taught straight out of GCSE, not least because it starts of very simply.

Why not create multiple courses which properly meet the needs of those who take maths at A-Level? This should include viable and respected alternatives for people who won't (or shouldn't) take A-Level maths in its current form - my gripe extends both for the brightest and weakest in maths. As a nation we need to get over this culture of A-Levels being the only qualification worth having pre-university and actually help people gain the skills or education that will help them in the long-run.
(edited 9 years ago)
Original post by shamika
Similarly, modular arithmetic is a hugely interesting topic that can be taught straight out of GCSE, not least because it starts of very simply.


Modular arithmetic used to be part of SMP O level (along with a lot of other "modern maths" concepts). Then what happened was that the 'educational experts' came along and said "look at all this Modern Maths being taught in schools - it must be why we have such poor levels of numeracy." So they took out all the modern maths in the 1990s, and what happened? The 'innumerate people' carried on being innumerate, whilst those who had mastered numeracy and were ready for some more challenging concepts were forced to spend about 2 years counting squares under histograms or answering patronizing questions about how much change Jenny and Ahmed received when they went to buy dog biscuits.

Original post by shamika

Why not create multiple courses which properly meet the needs of those who take maths at A-Level? This should include viable and respected alternatives for people who won't (or shouldn't) take A-Level maths in its current form - my gripe extends both for the brightest and weakest in maths. As a nation we need to get over this culture of A-Levels being the only qualification worth having pre-university and actually help people gain the skills or education that will help them in the long-run.


Unfortunately there's just too much politics involved for realistic suggestions like this to work - every qualification has to be "equal to" some other qualification now, or you get accusations of two-tier systems etc.

Most non-graduate jobs (and quite a few graduate ones too) could be done using the knowledge of a 14 year old with a 'Certificate in Numeracy' saying they could add up, measure things and work out percentages, just like the old CSE qualification. The current GCSE contains far more content than is necessary for most jobs, but lacks the rigour and content needed for preparation for A level, which is why it's a struggle to reform A level maths without risking take-up rates. I suspect Michael Gove would happily have brought back the CSE/O level distinction, but for Nick Clegg's interference which means we have this awful wishy-washy 9-grade compromise qualification to look forward to :smile:
Original post by davros
Modular arithmetic used to be part of SMP O level (along with a lot of other "modern maths" concepts). Then what happened was that the 'educational experts' came along and said "look at all this Modern Maths being taught in schools - it must be why we have such poor levels of numeracy." So they took out all the modern maths in the 1990s, and what happened? The 'innumerate people' carried on being innumerate, whilst those who had mastered numeracy and were ready for some more challenging concepts were forced to spend about 2 years counting squares under histograms or answering patronizing questions about how much change Jenny and Ahmed received when they went to buy dog biscuits.



Unfortunately there's just too much politics involved for realistic suggestions like this to work - every qualification has to be "equal to" some other qualification now, or you get accusations of two-tier systems etc.

Most non-graduate jobs (and quite a few graduate ones too) could be done using the knowledge of a 14 year old with a 'Certificate in Numeracy' saying they could add up, measure things and work out percentages, just like the old CSE qualification. The current GCSE contains far more content than is necessary for most jobs, but lacks the rigour and content needed for preparation for A level, which is why it's a struggle to reform A level maths without risking take-up rates. I suspect Michael Gove would happily have brought back the CSE/O level distinction, but for Nick Clegg's interference which means we have this awful wishy-washy 9-grade compromise qualification to look forward to :smile:


The nine grade system, just makes me want to :facepalm2:
Original post by davros
awful wishy-washy 9-grade compromise qualification


Do you have any idea how this will work? Will the 1 grade require higher than 90% for the current A* or will it effectively be a renaming? I can't see the highest grade being pushed lower than it currently is.
Original post by davros
Modular arithmetic used to be part of SMP O level (along with a lot of other "modern maths" concepts). Then what happened was that the 'educational experts' came along and said "look at all this Modern Maths being taught in schools - it must be why we have such poor levels of numeracy." So they took out all the modern maths in the 1990s, and what happened? The 'innumerate people' carried on being innumerate, whilst those who had mastered numeracy and were ready for some more challenging concepts were forced to spend about 2 years counting squares under histograms or answering patronizing questions about how much change Jenny and Ahmed received when they went to buy dog biscuits.


Agreed with all of this.

Unfortunately there's just too much politics involved for realistic suggestions like this to work - every qualification has to be "equal to" some other qualification now, or you get accusations of two-tier systems etc.

Most non-graduate jobs (and quite a few graduate ones too) could be done using the knowledge of a 14 year old with a 'Certificate in Numeracy' saying they could add up, measure things and work out percentages, just like the old CSE qualification. The current GCSE contains far more content than is necessary for most jobs, but lacks the rigour and content needed for preparation for A level, which is why it's a struggle to reform A level maths without risking take-up rates. I suspect Michael Gove would happily have brought back the CSE/O level distinction, but for Nick Clegg's interference which means we have this awful wishy-washy 9-grade compromise qualification to look forward to :smile:


Agreed with all of this too. It makes me sad that political ideology is hurting the majority of people. I believe in Germany, vocational education has become increasingly respected. We need a similar culture shift here; it's ridiculous that those who aren't as good at maths are being shortchanged by being forced to struggle with a qualification which isn't really useful for them. Is it any wonder people get disillusioned with the educational system?

Similarly, I cannot stress enough how much I am in favour for a more rigorous qualification that is similar to the old Hong Kong A-Level for our brightest...

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