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Applied Maths aftermath
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Hi qweerty, just getting back to your comments there - it's easy to see you have great passion for this special subject!
The exam paper is laid out unimaginatively and questions appear intimidating.
I think that's harsh
I mean the examiner is constrained to ask questions based on the syllabus given and there is an "unspoken" law that Q1 will be uniform accelerated motion etc. with little if any mixing of topics allowed (to prevent outrage on the students part). I know what you're saying about the paper lacking in imagination but, to be fair, there are only so many scenarios that can be concocted for each topic so there will be repetition through the years. I thought the tennis question on projectiles this year showed imagination and even the last question involving the economics formulae. But you could argue then that the physics paper lacks imagination also since the section dealing with experiments is fairly predictable (draw a graph, draw the appartus used etc), with the experiments themselves repeating over time. Similarly for chemistry and even for PM, there is still some lack of imagination in various questions e.g. the complex numbers question this year was "run of the mill", the theorem that needed to be proved can't be made imaginative or the construction of the triangle centroid that followed.
In relation to the questions appearing "intimidating", that's even harsher
I mean there's almost a contradiction in that sentence! I'd go as far as to say that because the AM paper is somewhat predictable in the nature of the questions that appear, it is very accessible to students who have made a decent effort to study the subject rather than be anything to be intimidated about. Again, for those students who take AM formally in class, the teacher holds an element of responsibility to ensure that students feel comfortable with the subject and the types of questions that appear.
The topics are all classical physics. Four of the ten topics are answered by <30% of candidates and are usually the worst answered. There is ample anecdotal evidence to suggest that students study only six (or maybe seven) topics, and spend considerable time practising the catalogue of past papers.
I definitely cannot argue with that! Teachers do have a certain element of responsibility though in ensuring that they do cover at least 9 of the topics and really should try to ensure that they get across how relevant those topics are - statics in designing buildings etc, hydrostatics in designing objects to ensure they float etc. Personally, I find those topics interesting and indeed I usually find the hydrostatics question very accessible - it usually makes good sense and can be worked out with a little thought. But I guess even if the teacher does cover the topics, students will still do what students often do, and take the shortest route from A to B, covering the bare minimum and taking their chances, which is a real pity.
There is almost no additional mathematical content in AM. Linear Motion relies on algebraically derived formulas. Relative Velocity uses very basic vectors and most of the questions can be answered using junior cert geometry. Projectiles uses extensions of the basic equations of motion and requires a certain level of competence with trig identities. The other topics rely on physics formulas which needn't be derived and on the ability to split vectors in axial components, which is based on junior cert maths. Only differential equations introduces something new, and those questions are formulaic. So, if the maths is no more advanced, what is the justification for AM? It is, of course, a "problem-solving" subject: the maths is kept basic so that students concentrate on the skill of applying what they know to situations.
Can't argue with most of that to be honest. The maths required for AM is very straightforward for a decent honours maths student. I wonder if there would be some merit in actually expecting students to be able to derive at least some of the formulas used in the course e.g. the kinematics formulas, the ones for SHM and circular motion, hydrostatics formulas for buoyancy, law of floatation etc ? At least it would give the students a better appreciation/understanding of where these formulas are coming from.
AM certainly encourages problem-solving, but is it sufficiently successful in that regard to justify a stand-alone subject?
Despite all its perceived flaws, I do believe that AM stands out amongst all LC subjects as the one that challenges students to think on their feet and try to problem-solve on the fly, using their knowledge of maths and mechanics to solve various problems. Whether it is sufficiently successful at encouraging problem-solving is another question for sure. I know that procedures can be almost (or totally) rote-learned, but still most questions do involve the student having to step back, think about how to tackle the problem and then get stuck in. Even if they analyse hundreds of past questions, they do still need to problem-solve to a certain degree when they get that exam paper in June. I would still like AM to remain as a stand-alone subject personally, but I do see where you're coming from.
I have to conclude at this point for time reasons, but I'll just make a few points: AM is seen as being not merely mathematical but difficult - that perception will need to change if there is to be any increase in uptake.
I agree 100% there. I think there is a widespread belief that the subject can only be taken my mathematical whizzkids who also do HL physics. Which is completely false. In all honesty, I believe a decent C level maths student who has a decent grasp of the basics of geometry,trigonometry,linear/simultaneous equations and differentiation will easily pick up the extra bits of maths they need to succeed and the physics covered is very accessible also for the most part (I do think rigid body motion might be difficult for a C-level student, trying to calculate moments of inertia for compound bodies etc).
It's more than a little dubious that A-students in Maths can quite easily get an A in AM. Arguably the ease with which such can do so is unmatched by any other subject pair.
I don't know about that one I would have said an A level student in maths (especially now with project maths) would be more likely to succeed with AM as I think A level maths students are more likely to be naturally good problem solvers anyway.
If AM remains roughly as is, I think written into its DNA needs to be that it is a problem-solving subject, and not mathematical physics. The redesign that is proposed in that document involves increasing the variety of topics. While I think that is (very) exciting, I also think that it represents a significant change to the premise of AM as I outlined above - introducing new content not taught elsewhere. Contrary to what you said, japester, I see such a redesign leading to a decrease in uptake. (Remember, also, that most people will take only three optional subjects, with which they hope to meet subject requirements, maximise points and pursue their interests.) The difficulty of teaching it will increase, also.
The solution as I see it is to replace the subject of Applied Maths with a Further Maths subject that the new Project Maths syllabus has left a definite need for. AM topics can be incorporated in that subject and into Project Maths, as is the case with maths in the UK. There will be great complexity to introducing such a subject, but I think it's the optimum.
Maybe if it remains in its current guise, it could be renamed "Basic Mechanics" - the "Basic" in the title might help increase uptake :pac: I'm not against the rejigging of the subject at all, but I would like for it to keep much of the mechanics on which it is currently based .... I guess I'm just old-fashioned in that sense! I'm still convinced that were options such as programming and game theory added to the mix, and it was "sold" well by the AM teachers within the schools (of course these teachers will need training too, I never thought about that part! And teaching programming would require a computer lab!) in relation to the economy, job opportunities etc then a boost in numbers could result.
Your suggestion about replacing AM with "Further Maths" sounds plausible for sure and could definitely be the route it goes down in the end. I'll look on with interest to see where all this goes over time - I'll be happy enough as long as those much-loved mechanics problems are appearing in some guise or other, be it within PM papers or within "Further Maths" papers 0 -
Someone in the LC OT 2015 thread (iirc) posted an article...
Yeah, saw that. It was an Irish Times article. I thought it was a really poor piece of journalism because it misrepresented the research and imposed a populist and simplified conclusion.I think that's harsh I mean the examiner is constrained to ask questions based on the syllabus given and there is an "unspoken" law that Q1 will be uniform accelerated motion etc. with little if any mixing of topics allowed (to prevent outrage on the students part). I know what you're saying about the paper lacking in imagination but, to be fair, there are only so many scenarios that can be concocted for each topic so there will be repetition through the years. I thought the tennis question on projectiles this year showed imagination and even the last question involving the economics formulae. But you could argue then that the physics paper lacks imagination also since the section dealing with experiments is fairly predictable (draw a graph, draw the appartus used etc), with the experiments themselves repeating over time. Similarly for chemistry and even for PM, there is still some lack of imagination in various questions e.g. the complex numbers question this year was "run of the mill", the theorem that needed to be proved can't be made imaginative or the construction of the triangle centroid that followed.
In relation to the questions appearing "intimidating", that's even harsher I mean there's almost a contradiction in that sentence! I'd go as far as to say that because the AM paper is somewhat predictable in the nature of the questions that appear, it is very accessible to students who have made a decent effort to study the subject rather than be anything to be intimidated about. Again, for those students who take AM formally in class, the teacher holds an element of responsibility to ensure that students feel comfortable with the subject and the types of questions that appear.
I definitely cannot argue with that! Teachers do have a certain element of responsibility though in ensuring that they do cover at least 9 of the topics and really should try to ensure that they get across how relevant those topics are - statics in designing buildings etc, hydrostatics in designing objects to ensure they float etc. Personally, I find those topics interesting and indeed I usually find the hydrostatics question very accessible - it usually makes good sense and can be worked out with a little thought. But I guess even if the teacher does cover the topics, students will still do what students often do, and take the shortest route from A to B, covering the bare minimum and taking their chances, which is a real pity.
Can't argue with most of that to be honest. The maths required for AM is very straightforward for a decent honours maths student. I wonder if there would be some merit in actually expecting students to be able to derive at least some of the formulas used in the course e.g. the kinematics formulas, the ones for SHM and circular motion, hydrostatics formulas for buoyancy, law of floatation etc ? At least it would give the students a better appreciation/understanding of where these formulas are coming from.
Despite all its perceived flaws, I do believe that AM stands out amongst all LC subjects as the one that challenges students to think on their feet and try to problem-solve on the fly, using their knowledge of maths and mechanics to solve various problems. Whether it is sufficiently successful at encouraging problem-solving is another question for sure. I know that procedures can be almost (or totally) rote-learned, but still most questions do involve the student having to step back, think about how to tackle the problem and then get stuck in. Even if they analyse hundreds of past questions, they do still need to problem-solve to a certain degree when they get that exam paper in June. I would still like AM to remain as a stand-alone subject personally, but I do see where you're coming from.
I agree 100% there. I think there is a widespread belief that the subject can only be taken my mathematical whizzkids who also do HL physics. Which is completely false. In all honesty, I believe a decent C level maths student who has a decent grasp of the basics of geometry,trigonometry,linear/simultaneous equations and differentiation will easily pick up the extra bits of maths they need to succeed and the physics covered is very accessible also for the most part (I do think rigid body motion might be difficult for a C-level student, trying to calculate moments of inertia for compound bodies etc).
I don't know about that one I would have said an A level student in maths (especially now with project maths) would be more likely to succeed with AM as I think A level maths students are more likely to be naturally good problem solvers anyway.
Maybe if it remains in its current guise, it could be renamed "Basic Mechanics" - the "Basic" in the title might help increase uptake :pac: I'm not against the rejigging of the subject at all, but I would like for it to keep much of the mechanics on which it is currently based .... I guess I'm just old-fashioned in that sense! I'm still convinced that were options such as programming and game theory added to the mix, and it was "sold" well by the AM teachers within the schools (of course these teachers will need training too, I never thought about that part! And teaching programming would require a computer lab!) in relation to the economy, job opportunities etc then a boost in numbers could result.
Hi, japester. In order...
I was referring to the layout of the paper, which hasn't changed since the beginning. I think there's scope to make it less hostile to weaker students and more approachable, like PM papers. So, to emphasise, I was not referring to the repetition of questions. But, to pick up on your comparison with other subjects, that repetition is perhaps justifiable given that the material was new to students. But, if you subscribe to my contention above, AM is a problem-solving subject, so such repetition isn't justified.
Although they're usually responsible, I don't think teachers are to blame. The subject effectively encourages it.
First, AM undoubtedly requires more problem-solving than most subjects. But the subject would be untennable if it didn't, for reasons I gave previously. I think the question is, Does it develop those skills and how widely applicable are they? In project maths, students learn relatively basic calculus and then are given an unpredictable situation and asked to apply it - one year a falling raindrop, another year an oil spill. But in AM, you go to, say, Q3 (a) and ignore all your learnt theory but for projectiles on the flat, or to Q4 (a) and ignore all theory but for a block-pulley combo. I'd venture that the skills gained aren't applicable outside a specific mathematical context. My point is, only when there is unpredictability and a requirement for synthesis of knowledge do you get higher-order problem solving.
I don't know why you took issue with what I said about A-students easily getting an A in both subjects. I think it's certainly the case that an A student in Maths can (much) more easily get an A in Applied Maths, than an A-student in English can get an A in History or an A-student in Physics can get an A in Chemistry, or possibly any other complimentary set of subjects.
It will be interesting to see what happens, but I think we'll be waiting a long time. A subject called Politics and Society, which is entirely devised, has been waiting to be implemented for years. I think unless it can be shown that there is a definite need for a further maths subject or if various interest groups stop knocking project maths and instead advocate such a subject, we probably won't see it for a while.0 -
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Yeah, saw that. It was an Irish Times article. I thought it was a really poor piece of journalism because it misrepresented the research and imposed a populist and simplified conclusion.
Hi, japester. In order...
I was referring to the layout of the paper, which hasn't changed since the beginning. I think there's scope to make it less hostile to weaker students and more approachable, like PM papers. So, to emphasise, I was not referring to the repetition of questions. But, to pick up on your comparison with other subjects, that repetition is perhaps justifiable given that the material was new to students. But, if you subscribe to my contention above, AM is a problem-solving subject, so such repetition isn't justified.
Although they're usually responsible, I don't think teachers are to blame. The subject effectively encourages it.
First, AM undoubtedly requires more problem-solving than most subjects. But the subject would be untennable if it didn't, for reasons I gave previously. I think the question is, Does it develop those skills and how widely applicable are they? In project maths, students learn relatively basic calculus and then are given an unpredictable situation and asked to apply it - one year a falling raindrop, another year an oil spill. But in AM, you go to, say, Q3 (a) and ignore all your learnt theory but for projectiles on the flat, or to Q4 (a) and ignore all theory but for a block-pulley combo. I'd venture that the skills gained aren't applicable outside a specific mathematical context. My point is, only when there is unpredictability and a requirement for synthesis of knowledge do you get higher-order problem solving.
I don't know why you took issue with what I said about A-students easily getting an A in both subjects. I think it's certainly the case that an A student in Maths can (much) more easily get an A in Applied Maths, than an A-student in English can get an A in History or an A-student in Physics can get an A in Chemistry, or possibly any other complimentary set of subjects.
It will be interesting to see what happens, but I think we'll be waiting a long time. A subject called Politics and Society, which is entirely devised, has been waiting to be implemented for years. I think unless it can be shown that there is a definite need for a further maths subject or if various interest groups stop knocking project maths and instead advocate such a subject, we probably won't see it for a while.
Thanks for your replies qweerty. I'm sorry, I misunderstood what you meant by "unimaginative" earlier - the layout of the paper should definitely have been altered over the years just to keep it fresh. In relation to making it more accessible to weaker students, I do agree also - I wrote a post last year in relation to this with a suggestion that questions could be broken into (a), (b) and (c) parts, starting off in part (a) very easy and then getting progressive more difficult in (b) and (c), a little bit like how PM papers are arranged. My suggestion was that it might aid the weaker students and allow them achieve their C grade at least, without being brilliant problem-solvers. I know what you're saying about the repetition of questions for sure and I do agree with you also that, because AM is meant to be "the" problem-solving subject, such repetition is not justified. I know there are only a finite number of scenarios for each topic (especially if they are being kept separate) but even still, there are vastly more ways in which questions can be presented so that the student has to think a bit more before putting pen to paper.
"My point is, only when there is unpredictability and a requirement for synthesis of knowledge do you get higher-order problem solving." Can't argue with you there at all, but I'd wager that if AM papers became more unpredictable in their nature, the take up for the subject would diminish even further, as students are vying for points at the end of the day and a semi-predictable physics paper (say) would be much more preferable to an unpredictable AM paper.
Sorry also about my comments in relation to students getting As in both PM and AM. Again I misunderstood what you were saying (it was late and I'm getting older) I agree with you totally that an A level Maths student can more easily get an A in AM than any other subject pair.
At least the ball in rolling a little bit at this stage on reviewing the syllabus - as you say it could take some time before it gets finally implemented but I will be interested in seeing what comes to pass. In the meantime, hopefully the examiner will try to freshen up the questions more and make it just a little bit more unpredictable over time. Still, looking forward to attempting next years paper already :pac:0 -
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Benm123 wrote:Three of my friends who did the exam also got A2's lol, has anyone/much people gotten an A1 yet??
yep, eight guys in my class did 0 -
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