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Method Marks - This needs good clarification!

Discussion in 'Mathematics' started by David Getling, Dec 6, 2015.

  1. David Getling

    David Getling Lead commenter

    This was mentioned in passing quite some time ago, but the exam boards need to make the policy on this VERY CLEAR and very easy to find out. I get the very strong impression that it's not just students, but most teachers who are not at all certain about this: and, of course, those who mark the exams are recruited from those teachers.

    My understanding is that unless a specific method is asked for, or working is specifically requested, then a correct answer gets full marks. The method marks, together with follow through, are effectively a safety net which allow candidates who make a silly numerical slip up to still, deservedly get most of the marks.

    With the availability of GDCs students, and markers, need to be very clear on the rules. For instance, if one is given the mean, standard deviation, and a couple of values, then a GDC will allow you to get the area by simply plugging in these four numbers. Now, while it is often good advice to show working, the working out of normalised values is, in this case a waste of the student's precious exam time. This is just one of many examples I could cite.

    Of course, I realise that there are jealous and spiteful teachers out there who resent students using powerful GDCs, and thus relish this state of ignorance.
     
  2. MLMaths

    MLMaths New commenter

    There's a useful post here, unfortunately spoilt by another biased, inflammatory troll-like parting shot.

    Even if we have a huge chip on our shoulder, we need to reduce the amount of useless sniping. The board is less welcoming, less visited and therefore less useful because of it.
     
    colinbillett likes this.
  3. Piranha

    Piranha Star commenter

    I agree that it needs to be clear, and some teachers may not know where to look. I doubt if somebody teaching the MEI A-level specification for the first time would find this document http://mei.org.uk/files/pdf/Use_of_Calculators_in_MEI_A_Level_Examinations.pdf which suggests that your understanding is not always correct, David. Their definition of a correct method is not the same as ours! I am not trying to justify this policy, and don't know if other exam boards are similar.

    I have seen worse. The Maths paper in the Engineering Diploma asked students to use "an appropriate method" to solve 7^x = 2401 and the examiner's report then said that those who used trial and improvement got no marks.
     
  4. David Getling

    David Getling Lead commenter

    Thanks for that Piranha. Yes, that MEI document certainly seems to insist on working. Unfortunately, AQA seem to say that correct answer gets the marks, unless a specific method is called for, and Edexcel seems to be closer to AQA, but is somewhat vague. So, are the criteria for each board different, and should we therefore advice our students based on what board they are being examined by. Of course, this would reinforce the suspicion that some boards give students an easier ride than others.

    ML what I said is based on observation! On more than one occasion I have either had to personally intervene, or encourage a parent to intervene because a teacher has been deliberately hassling a student for using a GDC. Only that intervention but a stop to it.
     
  5. Skillsheets

    Skillsheets Occasional commenter

    My calculator solves equations. I work as a private tutor so don't know the full ins and outs of what is allowed in exams. One of my students had the same model and claimed his teachers had said he could use it in A-level modules. Is this right ? It seems to me to be a way of getting an unfair advantage on solving quadratics etc very quickly
     
  6. JaquesJaquesLiverot

    JaquesJaquesLiverot Established commenter

    I suppose it depends on whether you think that answering the questions is the important thing, or knowing how to answer them. The logical extension would be to ask why you'd need to even use a calculator if you can just get someone who's good at Maths to answer the question for you.
     
  7. Piranha

    Piranha Star commenter

    Provided that it doesn't do Algebra, then it probably is allowed. The only way to be sure is to look carefully at the exam board's website, which anybody can do if they are interested enough. Not being a private tutor, I don't know what would be expected; as a teacher I thought it my duty to read and understand the regulations.

    Is it an unfair advantage? Probably yes, I would say, but it is allowed. You can buy a calculator which solved many equations for less than £20. although a decent graphical calculator would cost a lot more.

    If exam boards were serious about this, they would have calculator and non-calculator exams at all levels, as the IB does. Even careful phrasing of questions can be used to make students do the Algebra.

    I agree that students need to understand how to answer questions but, in an exam, I would like them to do things as efficiently as possible. When my school started doing the IB, it took me a while to adjust to doing something on a calculator without even thinking about how to do it by hand, because it was quicker and had less opportunity for errors.
     
  8. David Getling

    David Getling Lead commenter

    This is precisely my take. As regulars are tired of hearing, I strongly recommend the TI-Nspire CX. The fact that I managed to write (and successfully sell) 3 books about it should give an idea of just how much help such a calculator can be. For instance, using lists, one can do a trapezium rule question very quickly, with the minimum chance of introducing an error: then using numerical integration one can very quickly check to see if the result is in the ball park.

    Unfair advantage for some (rich) kids? If it's allowed then I want to make sure that my students are the ones with that unfair advantage.

    But my reason for starting this thread is that I don't want to see any kid disadvantaged because they might be wasting time they can ill afford on working that won't gain them any marks.
     
  9. BillyBobJoe

    BillyBobJoe Lead commenter

    It's worth being aware that for Scottish exams correct answers without working will often earn zero or only 1 mark. Graphical calculators have their place for checking answers but that's all. I would also say that, even for English exams the risk of a mis-keying makes reliance on calculators without working very dicey indeed.
     
  10. Karvol

    Karvol Occasional commenter

    Whether we, as mathematicians, like it or not, the nature of mathematics teaching is undergoing a change.

    Most of us have a strong background in analytical mathematics. Yet, I have to ask, for what purpose are we teaching the mathematics that we teach? Is it for understanding or is it for knowledge?

    I am increasingly inclined to believe that the mathematics we teach is not for understanding. Understanding may occur, but it is only as an accident; a by product of the pupils' engagement in the learning process and not as the focus of the process itself.

    I attended a workshop on calculus with computers, which (almost) completely did away with the need for analytical mathematics. From the basic definitions of differentiation, to looking at continuity and smoothness, the whole process was concerned primarily with understanding. Any technique that was introduced was purely so that understanding could take place.

    It left me feeling profoundly uneasy with the way that we teach mathematics and that, if we are not careful and forward thinking, the future methodologies of teaching will leave us standing behind.

    It used to be the case that no individual was considered educated unless they had a strong knowledge of Greek and Latin. Yet, those languages have now become minority subjects. Could the method of teaching that we employ for mathematics also lead to the slow death of our subject?
     
  11. David Getling

    David Getling Lead commenter

    Absolute rubbish. As my example above shows, they can also help one get the answer a lot faster and with less chance of mis-keying. Then there's the joy of reading the wrong entry in a statistical table, or bugg@ring around to find areas under a normal curve when Z < 0. Students with GDCs miss out on these character building exercises.
     
  12. Piranha

    Piranha Star commenter

    Doesn't this suggest that exams are lagging behind technology? Why would one want to use the trapezium rule when a more accurate answer is available more simply from the same calculator?
     
  13. PaulDG

    PaulDG Occasional commenter

    It's all part of the argument that begins with "why learn number bonds / multiplication by 10, etc., etc." when a calculator can do all those things?

    And the answer, despite what Conrad Wolfram says, is that if you don't learn those things, you tend to be unable to access any of the higher level stuff that's really of use to scientists & engineers or even have a clue that you've mistyped a figure or two into your calculator (or the bar code scanner / optical recognition package on your smart phone was fooled because the wrong code was on the item..)

    Trapezium rule is just an example of a simple numerical integration process. It should be taught, but experience shows that if topics are not examined they don't get taught in our exam-factory education system, so it has to be examined too.

    (Part of the brief for the new A levels was that there shouldn't be marks for just calculating Standard Deviation - typically worth 2 UMS in current exams - as all scientific calculators have had built in functions for it since the 70s).
     
  14. GeordieKC

    GeordieKC Occasional commenter

    Just writing answers is not something teachers should be encouraging. Apart from anything else clear method is a good indicator that the student has understood the concepts. Ideally I like students to both show their method and take advantage of capabilities of their GDC, it does not have to be one or the other. In a 1-1 tutoring situation you have the privilege of watching and discussing the method.

    What David is suggesting is probably very effective examination technique, and certainly when approaching exams getting students the most marks in the minimum of time is important, but to me the highest quality mathematics will always include the method used.
     
  15. David Getling

    David Getling Lead commenter

    I totally agree. Whenever possible students should understand the maths and be able to do it without a GDC. As you rightly surmised I encourage the use of GDCs because I honestly believe that students who can use them well have a significant advantage in their exams.
     
  16. Piranha

    Piranha Star commenter

    Sorry - I was not saying that there was no point in learning about the trapezium rule. My point was that if we accept an answer taken straight from a calculator, then we might as well just get the definite integral from it. If understanding is to be tested, then exams have to be written differently; as I pointed out earlier, the IB succeeds in doing this.

    By the way, and coming back to David's original point, it is harder as a class teacher to give the minority who have a GDC support in lessons, as that would take teaching time away from the rest of the class. I was prepared to spend a little time on it with individuals, but more detailed teaching had to be done outside lessons.
     

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