OCR FSMQ Additional Maths 6th June 2016 Official Thread

Let me ask you a question: How many times are you planning to sit C1 and C2?

Because if it's only once then there is no answer to your question.

If I throw a fair coin 20 times and get 20 heads, what's the likelihood that the next throw will be a tail? Answer: Still 0.5.

Luckily in exams there is a high degree of certainty about the questions that will be asked and even how they will be asked. Humans generate the questions and they are creatures of habit so the choice of questions on papers are far from random - they have low entropy ( https://goo.gl/OAHwRz ). That's why students complain when an exam paper doesn't quite fit the past "pattern", last week's Add Maths paper being an example.

I would almost say that entropy for most papers in the past has been close to zero but with the occasional perturbation. That perturbation could arise from political criticism of an exam board for being too predictable. So it puts some "more difficult" questions into its next lot of exam papers.

A perfect example was the Edexcel C3 paper from June 2013. I remember students came out of that exam in tears. In my naivety while invigilating the exam I had thought "That's a nice set of questions," not realising that students would have difficulty interpreting the questions (I hadn't at that point actually taught A-level - long story not for now). The grade boundaries dropped dramatically from around 68 out of 75 for an A* to 57/75.

Rather than try and predict the likelihood of certain types of questions appearing (and I'm sure you know maths teachers who do probability analysis to an extreme degree), you should focus on developing a desire to tackle more difficult unusual problems. Not because they are more likely to appear on papers, but because that builds resilience and confidence in the exam room.

Julie Andrews (yes, she of The Sound Of Music) was once asked, with all her experience, what was the most important message she had given her children. Unexpectedly she said "Be curious." And she's absolutely right. If you don't have curiousity - an interest in - the subject you are studying at A-level, then you are less likely to do well at it, and that is particularly true of mathematics.

When sports men and women train for the Olympics, they don't simply do the same basic circuit in the same way day after day. They push themselves and try and do better each day. That's what you have to do to excel in anything, not just sport.

Anyway... One final question: Did you follow that link on entropy to find out what it was about? If you did, and if you watched the video, you were exhibiting curiosity.

Thank you so much for your advice, I am really willing to tackle more difficult unusual problems but where can i find this kind of exercise please?

Reeshar what would you expect the grade boundaries to be this year? Thanks in advance

It's worth thinking about what made the questions hard and what you might have done in the exam to tackle that difficulty. Because the underlying maths in every single question was well within the scope of what is taught as part of the Add Maths syllabus.

My guess - but you tell me - is that you were thrown by how some questions were phrased. Once you interpreted/understood the question the rest should have been relatively easy.

For Q.7 for example, do you know how to use Pythagoras? Do you know that a right-angled triangle with the other two angles 45° is isosceles? Do you know how to find the inverse tan? You only had to apply those three bits of knowledge individually to three linked triangles. That was it!

For Q.13, if I tell you that 12 oranges cost £3.60 and that I would get 3 fewer apples for the same price, can you work out the price of an orange and an apple? Essentially you only had to do the same thing for that question but using algebra.

My experience with students is that many a) don't read through the paper completely before starting and mark up the questions they can do easily and then work on those first, b) rush into problems without contemplating first the best way of answering them by letting their minds relax, and c) get stuck on problems and find it difficult to move on, thus losing time that would have been better spent on questions they could answer. You need to build confidence in an exam so why destroy it by doing hard problems too early? Just ignore them and focus on stuff you find relatively easier!

All this is exam technique. And the great thing about this Add Maths paper (if we can call it "great" ) is that it may have raised an awareness in you guys of the need to develop good exam technique. Although your Add Maths result seems like a big thing now, it's not really. It's a dress rehearsal for doing A-level, so if you've learnt something from this paper then you can apply that learning to doing really well when/if you move on to A-level maths.

Real life is full of hard knocks. The art of coping or being successful is to pick yourself up afterwards, learn from what has happened and do better next time. Keep positive!

*ROTFL*

That is an exceptionally good question and one guaranteed to put me on the spot!

Let me say first that difficulty at A-level doesn't tend to be of the "roof problem" sort. It tends to be about understanding how to link multiple mathematical concepts. Applying higher maths requires three linked skills:

1) Procedural: How do perform a specific well-defined task eg, applying Pythagoras

2) Conceptual: Being able to interpret a problem and determine how to solve it in an abstract sense

3) Utilisational: Understanding what mathematical tools to use to tackle the problem.

You'll know (1) since that'll be how you've been taught for GCSE and Add Maths. If you've had a good maths teacher you may have been taught (2) - certainly it should have formed part of teaching Add Maths. (3) is more tricky and derives from familiarity with mathematical tools.

I do find students struggle, though, with understanding (2). If I ask students "How would you tackle this problem?" I tend to get very explicit statements (eg, divide by 5, take the sine, etc) which I usually cut short as that isn't what I want. This is akin to me asking "How do you build a house?" and getting the answer "Well, I'd dig a trench, fill it with concrete, and then start laying bricks..."

What I want is bigger picture stuff - and this really is key to doing well at A-level maths - which describes the overall approach, not the detail.

(3) can be really difficult. For example, what integration method should you use in C4? Not a good idea to jump for the one with which you're most familiar because it could be wrong and not work. Students that I tutor look surprised when I tell them that "integration by parts" can only be applied to appropriate problems; it isn't a universal integration method and using it wrongly can waste huge amounts of time in an exam to no avail.

So at A-level I (and all maths teachers) recommend lots of practice - don't skimp on homework because you think you understand a given technique. Work especially through the mixed exercises in the Edexcel books (if you're doing Edexcel) because these combine multiple techniques.

Find other books that have difficult problems, albeit topic-by-topic because they develop your understanding of those topics and when to apply techniques. I really like Understanding Pure Mathematics which covers the whole of A-level pure maths, although it's quite old-fashioned in having very dense type. It's not a picture book! It's £40 full-price but you can get cheap second-hand copies at Amazon from about £5: https://goo.gl/pqRIIW. Another, again a bit old-fashioned, book you might like to consider is Mathematics - The Core Course For A-level which is available from 97p (!!): https://goo.gl/tgXEIo.

Both these books work best once you've got a basic foundation of understanding on a particular topic. They also cover more than currently needed for A-level single maths, but that may change with the new A-levels in 18 months time.

Online I'm a huge fan of Solomon worksheets that you can find free online eg http://goo.gl/x4gh6G.

But really a big component is going to be your teacher. Do they really know, live and breathe maths such that they can handle any question you throw at them? Are they enthusiastic? Do they regularly set you problems that cut across multiple topics?

You raise a good point. I wouldn't say I had given up but by the end, but I was certainly resigned to my fate of a lower grade than I had been anticipating.

Funny you should point out the two questions that I was able to complete with ease. The questions with differing acceleration values however, were, in theory fairly simple but inevitably I panicked when SUVAT didn't produce any answers.

You seem sceptical about the difficulty of the exam, yet how the questions are asked are surely a factor of that difficulty. If they are worded in a way that would take longer to understand and recognise the underlying technique needed, then it is more difficult, surely?

Ah sorry if I gave the impression that I didn't believe the paper was difficult. That'd be wrong. But I do find it hard to know what students are going to find difficult - and I suspect the same is true of exam boards. I'm sure OCR didn't set out to produce a much harder Add Maths paper than usual.

I picked questions I thought might have caused difficulty and clearly picked the wrong ones! But if you look at my MS you'll notice I dodged creating two SUVAT equations by looking at the difference in acceleration (0.5) and the time taken to cover the 100m. So for me that was simple but I appreciate students would not have realised it could be that easy.

Did you stop that question and leave it to the end, though, once you realised things weren't working out?

Thanks for your information, I will take the edexcel as next year, is the pure maths book from Amazon suitable for me pls?

Yeah, and spiralled into a depression after leaving whole pages deserted and empty. Went back and I guess was just in the wrong state of mind for considering other options/methods. It's as much a mental game with yourself; also panicking because it was only question 6 in Section A (which I had previously stormed through in past papers).

Anyhow, despite all this I'm not completely out of the running for an A after seeing your mark scheme - the questions I did, due to the care I took with getting the marks I could, were all correct.

I really empathise.

IMO regular testing in class can help get round exam jitters, but not testing in the way you might understand it. For me the value of testing is to help students (and me) understand where they are weak so that they can focus their attention on those areas. Too often testing is seen as punitive rather than to build up resilience.

I also put questions in mixed order with easy questions later in a test and more difficult ones earlier to force students to read through the test first. (Yes, I can be a bit devious!)

Both those books are general A-level maths textbooks so, yes, they're suitable for Edexcel with the caveat that they're not as "user-friendly" as the Edexcel textbooks which you will either be lent by your school/college or you'll have to buy. All the books I'm suggesting are additional to the standard textbooks, not replacements.

For a more friendly book aimed specifically at the current maths A-level, look at Pure Mathematics C1 C2 by Rayner & Williams https://goo.gl/1MGqPN. Be warned, though, that there are a few errors in the answers to questions as there are also in the standard Edexcel C1 and C2 books. It's also not as challenging as the other two books. Horses for courses, as they say.

By the way, this paper was nothing like the past papers. The other past papers my friends and I got As and Bs easy and this one it is expected that 48% of students get a U instead of 26%. Just beware that this one is the most difficult paper that has been set by OCR

I think the problem is more how mathematics is taught. Judging by how some people have reacted, they expected to do well because they had done past papers and importantly, they felt they knew how the questions would be asked. This technique lacks conceptual understanding which is of paramount importance when studying maths. I think that if you understood all the topics from first principles, then you could logically deduce how to tackle a problem quite easily, the problem was most people tried to use rote learning for maths.

Probably true but rather unkind to students who have studied diligently only to find that their efforts haven't borne fruit.

Wilshaw (Ofsted) has recently said he wants to see schools with more maverick teachers, of which I am definitely one. The trouble is that school management don't like people like me. My students are enthusiastic supporters of my teaching but I only get criticism from lesson observations which I refuse to modify to make them fit the school's model of what an Ofsted lesson should be like. This despite getting a Good borderline Outstanding from a real Ofsted inspector who commented on how enthusiastic my students were.

The point here is that there aren't many teachers willing to fight the system. And there is also a lack of maths teachers who really know their subject and are willing to go "off-piste". Very frustrating.

What would be really interesting to me would be what in particular you found hard. Not simply the question number but what was it about that (or those) questions that made them seem so impossible. Insight like that is very useful to a teacher like me cos I can then use it to fix the problem!

I think I'm pretty much okay, but I need to brush up on a couple of topics before I'll feel really comfortable about doing the exam. I got a B on the mock I did in December, so I'm pretty sure I can get up to an A by the time of the exam. I essentially have to get an A: there's no point in doing it early if you get anything less! What about you?

Probably true but rather unkind to students who have studied diligently only to find that their efforts haven't borne fruit.

Wilshaw (Ofsted) has recently said he wants to see schools with more maverick teachers, of which I am definitely one. The trouble is that school management don't like people like me. My students are enthusiastic supporters of my teaching but I only get criticism from lesson observations which I refuse to modify to make them fit the school's model of what an Ofsted lesson should be like. This despite getting a Good borderline Outstanding from a real Ofsted inspector who commented on how enthusiastic my students were.

The point here is that there aren't many teachers willing to fight the system. And there is also a lack of maths teachers who really know their subject and are willing to go "off-piste". Very frustrating.

What would be really interesting to me would be what in particular you found hard. Not simply the question number but what was it about that (or those) questions that made them seem so impossible. Insight like that is very useful to a teacher like me cos I can then use it to fix the problem!

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Fair enough, well it'll be interesting to see what OCR decide. - if only my maths teacher had such forethinking as you, O Holy Reesharr (thank you for contributions to the thread )

This is quite interesting actually, I am a student by the way. I'll address a few issues:

You said it was unkind but I think you have to tell people to change their way of study, which would be an important lesson. For example, if a student were to revise only by reading a textbook, several times and idly mulling it over a few times, then they would not see the same gains than a student who works for the same time that took part in what schools like to promote, so-called 'active revision'.

The same principle can be applied here, namely a different style of learning, which seems particularly applicable to maths, where rote learning will not suffice.

In all honesty, I'm sorry if you thought it was unkind (I am not taking offence) but let's be real, we are talking about 16+ year olds who should be able to endure some criticism and should therefore have the emotional resilience.

Besides, we need to help them for A-level. I am also led to believe this sort of criticism can take place in the 'real world' as well -- working hard does not imply you will succeed.

As for the comment about creative teachers lacking support I have to say I agree. I think lots of students should understand maths from a fundamental level, understanding the core building blocks of mathematics(especially algebra) at a deeper level with an emphasis on application. I've noticed that most of my friends who consider themselves "bad at maths" have a limited understanding on how maths actually works and take things for granted without understanding and therefore, will not be able to apply their knowledge in novel circumstances. Maybe olympiad style maths could help here...