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Serious foul-up on A Level mathematics exam

Discussion in 'Mathematics' started by DM, May 27, 2011.

  1. Mathsteach2

    Mathsteach2 Established commenter

    I apologise for my poor construction here, I certainly did not want to imply that I actually encourage my students to look for mistakes! I did reference my concern about the dangers of encouraging arrogance in students by this approach in my post 62. I also tried to soften the blow with my use of the word "wary", but this still did not work!

    My main point remains, however, that errors in the printed word do occur, and we must all learn to deal with them, without being too critical of the persons who make them, which is what seems to have mostly occurred in this thread, prompting me to make my first post.

    Spending an inordinate amount of time on one question in an examination is anathema to me, and any student who does this has not learnt the most elementary of examination techniques, and gets little if any sympathy from me. I mark what they have done, fairly and without prejudice across the board, assuming that they are well-schooled in doing their best to impress me with their comprehensive/broad knowledge of mathematics, in the time available.

    Imagine expecting to pass one's driving test by spending an inordinate amount of time trying to show that you are capable of reversing into a nearside side road! I do not think the examiner would be impressed. I guess after the second attempt the examiner would tell us to move on!
     
  2. Exercising good examination technique is one thing, but suggesting that this will minimise a student's loss of marks over a mistake in the exam is quite another. The loss of confidence from not being able to answer a 'banker' question because of a mistake can ruin a student's overall performance however good their answering technique.
    Are you also suggesting that you incorporate deliberate mistakes in your class teaching to try and prepare students for this eventuality? I think you are seriously deluded. At best you risk looking incompetant in front of students when you try and tell them that 'it really is a deliberate error' and at worst you can end up confusing students - totally unprofessional IMO. A Teacher is supposed to show students how to answer questions correctly, not to try and detect incorrectly written questions - a recipe for disaster in an exam as has been said above when they try and re-interpret a correctly worded question that they have difficulty with. However, we have all come across questions that are incorrect or badly worded in textbooks and if students are savvy enough to re-interpret them correctly then fine, but this SHOULD NOT happen on an exam paper. If it does happen, then the exam should be re-sat at the expense of the relevant board if possible.
     
  3. Mathsteach2

    Mathsteach2 Established commenter

    I do this not to prepare students for "this eventuality" but to make sure they are awake during my lessons.

    The arrogance of your post, FlippantFlyer, is unbelievable. I choose not to comment further, beyond your statement, IN CAPITALS!!!, that it should not happen on a exam paper. I trust you work within an ideal set-up, otherwise you might care to chill out a little.
     
  4. What is more unbelievable is your arrogance in thinking that students should just be able to deal with errors in an exam paper by simply applying good exam technique. You obviously haven?t seen the fallout from these errors on students, particularly those that suffer badly from exam nerves.
     
  5. Karvol

    Karvol Occasional commenter

    Out of curiosity Mathsteach2, where do you teach again?
     
  6. Mathsteach2

    Mathsteach2 Established commenter

    You completely misunderstand my approach with this comment, FlippantFlyer.

    My analogy with passing the driving test has not been commented on, I do not know why as analogies are always open to criticism. However, to continue with it, a learner driver suffering from examination nerves deserves to fail, and so be it with any external test, I think. Concerning examination technique, I guess the driving examiner, even though he instructs the learner to move on after a second failed attempt at reversing, will fail the candidate because to be able to reverse is an essential part of passing the test. Overall driving skills throughout the rest of the test would not be sufficient to gain a pass.

    This is one place, then, where the analogy breaks down. The competent maths candidate (competent at passing examinations, not necessarily competent at mathematics) does not "deal with the error", they simply avoid it by moving on. They may gain some marks (perhaps even all of them, depending on the mark scheme) for what they do in their attempt, even though the problem is not solvable because of the error.

    Karvol, I have been a successful teacher for 40 years, 1966 to 2006 in state maintained schools and private schools in the UK (30 years), then 10 years P/T in Barbados, which is included in the 15 years marking the CXC Mathematics (GCSE Caribbean equiv.) running into my retirement. I still do some private tuition, preparing adults and teenagers for the CXC. In all of this work I have been commended for my approach, always with excellent ratings from the chief examiner. I trust that answers your question.

    As Betamale said in post 59:

    "Unfortunately this country and its weak ways have seen education move away from kids having to take tests (and therefore responsibility for the outcome of their exams)."
     
  7. DM

    DM New commenter

  8. Mathsteach2

    Mathsteach2 Established commenter

    A quote from the OCR link reads:

    "Examiners marking the papers are aware of the incidents and will make careful adjustments so that all students receive the marks they deserve".

    Now this is very reasonable to me, but most of this thread seems to focus on the impossibility of this taking place. For me, the most significant phrase is "the marks they deserve". Therefore I repeat, a candidate, able or not, who spends an inordinate amount of time on one question in this type of examination does not deserve to receive any compensation for doing so, errors in the paper or not.

    One poster suggested above that an able student "does not want to be beaten", therefore pandering to his/her own ego instead of giving the examiners what they want to see.

    I also say again, we are not here to mollycoddle our students. It makes me wonder that this so-called dumbing-down which is claimed to be occurring in the teaching profession stems from the teachers rather than the examinations. Perhaps they do it because they want as many students to pass to keep up their league table numbers.

    As I often say, we can take a horse to water but we cannot make it drink. If the kids are not up to it, then fail them!
     
  9. pipipi

    pipipi New commenter

    Perhaps one thing this does reinforce is timing. Making sure that students look at the time they have for the whole exam, look at how many marks are available for each particular question, and divide their time accordingly.

    I used to do this, particularly when there was an A and B part with a choice of question, but I haven't been mentioning it recently. I think I will be raising it. No system is perfect!
     
  10. You're missing the point with the timing.


    The question wasn't worth 3% of the marks - it was worth 11% of the exam.


    So - if you're aiming for an A* you *have* to answer this question. You can't just leave it or you throw away your A* - maybe you need that A* for your university place. Or maybe you've just worked really hard to get it.


    Or... you're not aiming for an A*, you're aiming for a B. And you have struggled with A-level maths but this question is one of the areas that you have understood - and in effect it makes up more like 15-20% of the marks that you are hoping to pick up in this paper. If you don't get your B you don't get your university place. You'll have to re-apply next year, and the cost of your course is going to triple.


    So, we've established that this is not even remotely similar to doing a 100 mark paper with the maximum mark of 3% per question?


    Now let's assume that it's a 2 hour exam, and that you generally aim to have 15 - 20 minutes to check your working at the end.


    You hit this impossible question early, but of course you don't know it's impossible, so you use the normal amount of time to try to finish it - and maybe a couple of minutes extra out of your checking time. You assume the question can be solved, so you think you're just making a simple (or complex) mistake. Any minute now the solution will reveal itself to you.


    After a while you move on. A little distracted by the solution you haven't found. Neurology wouldn't allow you to 'put it out of your mind' - that's not how cognitive processing works. This question is important, your adrenaline is flowing, so your brain is going to leave a bit of resource working on it. Unless you are one of the tiny minority of people who is suitable for fighter pilot training, this will have affected your concentration on the other questions - you will, whether you know it or not, be using the work you do on them to try to figure out that other problem too.


    So, you finish the rest of the exam, and with 10 or 12 minutes of 'checking time' left, the rational thing to do (because it's worth 11 - 20% and you need those marks for your required grade) is to return to that unsolved question. After all, you have no idea that the examiner has made a mistake. To be honest I find it odd that you would tell kids to look out for mistakes on the exam paper, because the potential for false positives there is huge - lots of questions initially look like you don't have enough information to answer them.


    Anyway, you end up not checking through the rest of your work, so you don't get the opportunity to pick up the inevitable small working memory errors and slips of the pen you've made. All people make them, not all to the same degree. Most people make more of them when they have stress chemicals flowing, but again, not all to the same degree. This trait is orthogonal to logic, reasoning and numeracy.


    Now instead of examining your math skills, what we've also thrown in is your working memory, your handwriting fluency and accuracy (both of which would normally get largely cancelled out in the checking phase) your physiological response to stress and the extent to which the grade matters to you. If you were already planning a re-sit for another subject maybe you'll just think c'est la vie.


    You can retrofit a grade curve, but you won't guarantee that the same people are at the same points on that curve. Some people will end up the other side of a grade boundary, and that's potentially a massive impact on their future.


    So, let's be generous and make sure that anyone who ends up the wrong side of a grade boundary gets the error in their favour. That's fair, eh? Not so fair on the kids who took a different exam board, missed their grade by a lesser margin and then don't get their university place because the university is legally bound to take those who get awarded the grades they were offered.


    The system is unfair enough as it is - we should be outraged on behalf of the real human beings who are affected by this.


    So - don't be so glib or so unbelievably patronising of the students who recognised that an 11% question is not the same value as a 3% question and thus dealt with the situation differently.
     
  11. Maths_Mike

    Maths_Mike New commenter

    I agree and of all the misatkes this year this is by far the worst. Your talking a question that in itself is worth a grade - even if it ddint affect your performance on the rest of the paper (which it probably would).
    How the exam board can possible claim they are going to ensure no student is disadvanatged is ridiculous unless ofcourse they intend to give A's - and even doing this is unfair becuase the students who genuinely deserve this grade are disadvanatged by the fact that other people (would would not ordinarily have acheived this grade) are now competing with them.
     
  12. Fantastic post, lindz76! And your point about the students who didn't take this board is my worry. My daughter did the Edexcel D1 exam, and it does seem to me that she is now competing against students who will probably receive a boost, which, to ensure that nobody who should get the boost misses out, will include some who shouldn't. So there will probably be some kids with scores matching or exceeding hers who wouldn't have if the examiners had taken the time to check their exam.
    The only fair way to deal with it is to run a new exam later this season somehow. But that would take work and also cause logistical hassle for kids who may be going away when their exams finish.
    What a shambles. Sometimes I feel like I am living in a third-world country, where resources are scarce and everyone does the best they can in the circumstances.
     
  13. DM

    DM New commenter

    I agree. Top post lindz.
     

  14. Sorry no you are are missing the point. It is only a must if there is only 1 exam paper.
    It is not the case with any exam that I know of.
    In fact, if there was just one paper then there would be a lot more than 72 marks on it for an A level.
    You are wrong the 11% that you are fixated on is divided by 6. The 6 percentages are aggregated. To get an A is have 480 [or more] out of 600.
    They can be in the right place if the use <u>better exam technique</u> in the other 5 units.
    Sorry but your argument is subjective and highly emotive.
    That bit of resource is your unconscious mind.
    I guess my department all fighter pilots because we are all agreed that we would have moved on and would have coped.
    I think it is a partly a question of a sense of proportion. I wouldn't expect you to be happy about a mistake on an exam paper. However I would expect any student to follow their teacher's advice and move on.
    The amount of marks to an extent is irrelevant. Move on from a question you cannot do is sound advice, with only one proviso; that you can do some of the other questions.
    Other advice is show your working. Once you have followed these 2 pieces of advice then it the onus is on the marker and the exam board to award you the correct grade.
    As there are 6 A level units each with a paper I am ok to let the exam board award a grade.
    If you feel ' cheated' at the end the of the course and your school/teacher agrees then appeal.
    All systems have their failings, the exam system is better than awarding better grades to those that kick up the most fuss.
    It is very disappointing to hear such irrational arguments.
     
  15. DM

    DM New commenter

    You obviously are not familar with university offers that require over 90 UMS in each module with no resits then ITIQ.
     
  16. Well said DM. My offer - many years ago I hasten to add! - was dependent on getting 40 out of 40 points for both A-level Maths and A-level Further Maths. I wanted to go to Cambridge.


    In the end I got these 80 points but not my science As (too much of a focus on the maths side, or possibly the pub side).


    It was the first year of modular A-level maths (at least that's my recollection - 1993/4) - but because the per-module grades were available they wanted to use them.


    We were told that you had to get 90% to get the full 10 points. I don't remember ever seeing a raw mark so I'm not sure if that was totally accurate.


    But my point - ITIQ - is that it *is* good exam technique to return to the 11% question you haven't solved rather than scan through your answers again to pick up a handful of accuracy marks, but that discounting that 11% of the exam doesn't cover the lost accuracy marks, and so the impact on each student won't be 11% - each student will have been impacted differently.
     
  17. afterdark

    afterdark Lead commenter

    Which universities are these then?
    Cambridge, for example, quotes A* Mathematics and A in Further A level.
    The criteria for geting an A* is an <u>average</u> of 90+ and 90+ in C3 and C4...
    I do not believe that the 90 UMS requirement is that common across all universities is it?
     
  18. DM

    DM New commenter

    No it is not common but it is certainly relevant to this discussion.
     
  19. This on the Oxford website; they've been quick to adopt A* after avoiding them at the start:
    <h3>IMPORTANT: Standard offers for those in the A-level system who are applying by October 15th 2011 for entry in 2012 or 2013 will be as follows:-</h3><h3>Mathematics, Mathematics and Statistics, Mathematics and Philosophy: A*A*A with A*A* in Mathematics and Further Mathematics if taken to A2; or A*AAa with A*a in Mathematics and Further Mathematics if taken to AS; or A*AA with A* in Mathematics if Further Mathematics is not taken.</h3><h3>Mathematics and Computer Science: A*AA with A* in Mathematics or Further Mathematics. </h3>
     
  20. No, but I am familiar with A* as a requirement. That means an average of 90, including 90 or more on both the C3 and C4 papers. I still do not quite understand what you are talking about when you say a UMS over 90 on all the the units?
    That is not the same as having an average of 80 + is it?
    Please can someone give me an example of an english university that specifies 90 + on all units?
    I could required to have the answer to this question as part of my job at an international school. Some of the children at the international school where I work consider UK universities.
    They seem oblivious to the UK exams errors fiasco as most of what we do here is unaffected. However when it does impinge upon them they will want answer immediately... from me.
    Can anyone point me in the right direction?
     

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