Once again I find myself too busy to do a substantial post this lunchtime. However, I’ve been rescued by Prof. Philip Moriarty who tipped me off about the following video from the series “Sixty Symbols” which features this blog in a supporting a role as a source of old examination papers. The theme is the dire state of mathematics education in British schools, something I’ve moaned about on many occasions myself, so I thought I’d post it here. You’ll get a flash of my organ about 6 minutes and 15 seconds into the clip, so if you don’t want to see it please watch with your eyes closed.Follow @telescoper
Archive for education
I spent quite some time this morning going over some coursework problems with my second-year Physics class. It’s quite a big course – about 100 students take it – but I mark all the coursework myself so as to get a picture of what the students are finding easy and what difficult. After returning the marked scripts I then go through general matters arising with them, as well as making the solutions available on our on-line system called Learning Central.
Anyway, this morning I decided to devote quite a bit of time to some tips about how to tackle physics problems, not only in terms of how to solve them but also how to present the answer in an appropriate way.
I began with the Feynman algorithm for solving physics problems:
- Write down the problem.
- Think very hard.
- Write down the answer.
That may seem either arrogant or facetious, or just a bit of a joke, but that’s really just the middle bit. Feynman’s advice on points 1 and 3 is absolutely spot on and worth repeating many times to an audience of physics students.
I’m a throwback to an older style of school education when the approach to solving unseen mathematical or scientific problems was emphasized much more than it is now. Nowadays much more detailed instructions are given in School examinations than in my day, often to the extent that students are only required to fill in blanks in a solution that has already been mapped out.
I find that many, particularly first-year, students struggle when confronted with a problem with nothing but a blank sheet of paper to write the solution on. The biggest problem we face in physics education, in my view, is not the lack of mathematical skill or background scientific knowledge needed to perform calculations, but a lack of experience of how to set the problem up in the first place and a consequent uncertainty about, or even fear of, how to start. I call this “blank paper syndrome”.
In this context, Feynman’s advice is the key to the first step of solving a problem. When I give tips to students I usually make the first step a bit more general, however. It’s important to read the question too.
The middle step is more difficult and often relies on flair or the ability to engage in lateral thinking, which some people do more easily than others, but that does not mean it can’t be nurtured. The key part is to look at what you wrote down in the first step, and then apply your little grey cells to teasing out – with the aid of your physics knowledge – things that can lead you to the answer, perhaps via some intermediate quantities not given directly in the question. This is the part where some students get stuck and what one often finds is an impenetrable jumble of mathematical symbols swirling around randomly on the page.
Everyone gets stuck sometimes, but you can do yourself a big favour by at least putting some words in amongst the algebra to explain what it is you were attempting to do. That way, even if you get it wrong, you can be given some credit for having an idea of what direction you were thinking of travelling.
The last of Feynman’s steps is also important. I lost count of the coursework attempts I marked this week in which the student got almost to the end, but didn’t finish with a clear statement of the answer to the question posed and just left a formula dangling. Perhaps it’s because the students might have forgotten what they started out trying to do, but it seems very curious to me to get so far into a solution without making absolutely sure you score the points. IHaving done all the hard work, you should learn to savour the finale in which you write “Therefore the answer is…” or “This proves the required result”. Scripts that don’t do this are like detective stories missing the last few pages in which the name of the murderer is finally revealed.
So, putting all these together, here are the three tips I gave to my undergraduate students this morning.
- Read the question! Some solutions were to problems other than that which was posed. Make sure you read the question carefully. A good habit to get into is first to translate everything given in the question into mathematical form and define any variables you need right at the outset. Also drawing a diagram helps a lot in visualizing the situation, especially helping to elucidate any relevant symmetries.
- Remember to explain your reasoning when doing a mathematical solution. Sometimes it is very difficult to understand what you’re trying to do from the maths alone, which makes it difficult to give partial credit if you are trying to the right thing but just make, e.g., a sign error.
- Finish your solution appropriately by stating the answer clearly (and, where relevant, in correct units). Do not let your solution fizzle out – make sure the marker knows you have reached the end and that you have done what was requested.
There are other tips I might add – such as checking answers by doing the numerical parts at least twice on your calculator and thinking about whether the order-of-magnitude of the answer is physically reasonable – but these are minor compared to the overall strategy.
And another thing is not to be discouraged if you find physics problems difficult. Never give up without a fight. It’s only by trying difficult things that you can improve your ability by learning from your mistakes. It’s not the job of a physics lecturer to make physics seem easy but to encourage you to believe that you can do things that are difficult.
So anyway that’s my bit of “reflective practice” for the day. I’m sure there’ll be other folk reading this who have other tips for solving mathematical and scientific problems, in which case feel free to add them through the comments box.Follow @telescoper
Only time for a quick post this morning as I have to go into the department to get my things ready for tomorrow, when the Autumn Semester starts and I have to begin lecturing (at 9am on a Monday morning). Anyway, the text for today’s sermon is provided by Ed Smith’s Left Field column in the New Statesman, the latest issue of which I read yesterday. His topic is the rise of credentialism and the resulting excessive amount of examination in the British school system:
It is now widely accepted that British pupils are excessively over-examined. Teachers are so busy focussing on examinations that there is little time left for education. Exam-led cramming has become the year-round norm – like an election campaign that consumes the whole political cycle. Exams are obviously necessary. But there is an optimal amount of assessment and it has been far exceeded. Grade inflation – notwithstanding this year’s controversial “crackdown” – is simply accepted as a fact.
It’s well said, and it’s not just the school system that suffers from disproportionate emphasis on assessment over education. It’s rife throughout the university system too, starting with the reliance on A-level grades as criteria for assessing students’ suitability for university study, through the “modular” undergraduate degree programmes with examinations twice a year for three or four years.
We examine far too frequently and the effect of this has been to turn the entire education system into a meaningless exercise in box-ticking.
It is an unfortunate irony: in our age of credentialism, exams have never mattered more. And yet they have never been more unreliable as gauges of academic quality.
I’ve felt for some time that in my discipline, Physics (and Astronomy) A-levels are virtually useless as indicators of the suitability of a student for doing an undergraduate degree. Some of the very best students I’ve ever had the pleasure to teach came into my university with modest A-level scores; and some students who came in with perfect grades at school never adjusted to the different, more independent type of study required of an undergraduate.
As Ed Smith points out, the increased emphasis on examination grades hasn’t expanded opportunity either. It may appear to be fairer to base university entrance or award jobs on examination results rather than, say, interviews, but this has just led to a system that can be easily gamed – private tutors, cramming, re-sits to improve grades, and so on. He rightly concludes that the “correlation between exam results and intelligence has been steadily weakening”.
So what’s the alternative? Smith mentions the admissions process at Harvard University, which famously ignores high-school grades and relies on its own interview system. Interviews can be very biased if carried out in an inappropriate way. Subjecting a young person to a 30-minute grilling in a room with a complete stranger can be enormously stressful for applicants who are shy, and would also play into the hands of those whose educational background has involved specific training for such ordeals. But one thing I’ve found by talking to students face-to-face is that it doesn’t take very long to identify precisely those things that the examination system does not: imagination, enthusiasm for the subject, and a flair for thinking on your feet:
One teacher told me with regret that she had to advise her most academic pupil not to display her full intellectual range: in order to secure all the ticks, first you have to stop thinking freely.
If you don’t believe this, take a look at this GCSE Science Examination. A truly intelligent student would struggle to find any correct answer for many of the questions on that paper!
This is why we still place so much emphasis on interviews in the postgraduate admissions system: we take it for granted that all applicants for PhD places will have good undergraduate degrees. What marks out an excellent candidate for a position as research student, however, is not the ability to pass exams but a mixture of creative flair and almost obsessive determination to surmount the difficult challenges involved in independent research. The correlation between these characteristics and degree results is by no means strong.
The problem for a UK University in adopting the Harvard approach is that credentialism is now running the system. Students apply to universities largely on the basis of their predicted A-level grades, lowering their sights if their predicted grades would not be expected to get them into a more “presitigious” department. But departments that take in students with low A-level scores also get marked down in the league tables for taking in “weaker” students. We’re all aware that A-levels are basically useless, but both sides are bound so tightly into the system that there seems to be no escape.
So what’s the answer? I don’t know if there is one, but I’d love to see what would happen if all universities abandoned A-levels and instead set their own entrance examinations and interviews. It would be a huge amount of work, but it would make a refreshing change if universities could gather useful information rather than relying on the uninformative guff produced by the national examination boards.
And here is Smith’s closing remark that rings very true to me for personal reasons,
There is a further dimension to the problem of credentialism. It encourages life’s winners to underestimate their good fortune and to over-rate the extent to which they deserve their success. Far from advancing talent over privilege, credentialism has strengthened the grip of people already at the top.
I’ve been trying to make myself useful over the last few days thinking about the new module I’m supposed to start teaching in October. I’m a bit daunted by it to be honest. The title is The Physics of Fields and Flows and it will be taken by students when they return to start their second year after the summer break. It’s twice the size of our usual modules, which means a lot of teaching and it’s all new for me, which means a lot of preparation.
The idea behind introducing this module was to teach a number of things together which previously had been taught in separate modules, specifically electromagnetism and vector calculus, or not at all, e.g. fluid mechanics. I’m not sure when or why classical fluid mechanics dropped out the syllabus, but I think it’s an essential part of a physics curriculum in its own right and also helps develop a physical understanding of the mathematics used to describe electric and magnetic fields. It’s one of the unhappy side-effects of modular teaching that it hides the important underlying connections between apparently disparate phenomena which are the essence of what physics is about.
Another thing I reckon we don’t do enough of these days is use lecture demonstrations. That’s harder to do these days because we tend to use pooled lecture theatres that don’t have the specialist equipment that they might have if they were dedicated to physics lectures only. Practical demonstrations are now usually given second-hand, by using video clips. That’s fine, but not as good as the real thing.
Anyway, it struck me that it would be quite easy to arrange a demonstration of the transition between laminar and turbulent flow using the simple and relatively inexpensive equipment shown in the rather beautiful image. Unfortunately, however, demonstrating this sort of thing isn’t allowed on University premises even for scientific purposes…Follow @telescoper
A very busy day today so I thought I’d just do a quick post to give you a chance to test your brains with some more order-of-magnitude physics problems. I like using these in classes because they get people thinking about the physics behind problems without getting too bogged down in or turned off by complicated mathematics. If there’s any information missing that you need to solve the problem, make an order-of-magnitude estimate!
Give order of magnitude answers to the following questions:
- What is the tension in a violin string?
- By how much would the temperature of the Earth increase if all its rotational energy were converted to heat?
- What fraction of the Earth’s water is in its atmosphere?
- How much brighter is sunlight than moonlight?
- What is the mass of water in a soap bubble?
There’s no prize involved, but feel free to post answers through the comments box. It would be helpful if you explained a bit about how you arrived at your answer!Follow @telescoper
I’ve had the same worry about finding myself in agreement with Michael Gove, at least on a few things; see here, for example. Anyway, this piece makes some very good points about the corruption of the GCSE system.
Originally posted on Protons for Breakfast Blog:
What do you do when someone with whom you basically disagree, says something sensible? Michael Gove has placed me in this situation three times now.
Firstly he abolished the Qualifications and Curriculum development Authority (QCDA). Secondly he pointed out at that school IT lessons are at best uninspiring. And now he has gone and acknowledged that our system of competitive exam boards has driven down GCSE standards.
I thought I’d do a quick post before I go out to pass on a story from the latest Times Higher. The news won’t come as a shock to anyone who actually works in a University, but it appears that the number of “managers” working in Higher Education is growing rapidly:
Data released by the Higher Education Statistics Agency reveal there were 15,795 managers in higher education in December 2010 – up by almost 40 per cent on the 11,305 employed in the 2003-04 academic year.
That was compared to the 19.2 per cent increase in academics since 2003-04. It means there is now a manager for every 9.2 academics compared with a ratio of one to 10.8 seven years earlier.
It’s tempting to take the usual easy shot at “managers”, but I’m not going to do that, at least not immediately, because I’m not at all sure precisely how they define a “manager” in the context of this survey. In my School we have a School Manager, who looks after budgets and runs the School Office which carries out a large number of complex administrative tasks related to research grants, undergraduate and postgraduate admissions, student records, and so on. People like this are indispensible because if we didn’t have them these tasks would have to be done by academics, which would be a distraction from their proper business of teaching and research, and which they would almost certainly do extremely badly. Managers who work alongside academic staff and understand the realities of University life are therefore a good thing to have. They actually help.
The problem I have is that, as it seems to me, much of the growth in numbers of “managers” does not involve people in this sort of job at all. The greater part of the increase is in centralised administrative divisions or, as they’re called in Cardiff, “Directorates”. In fact Cardiff is nowhere near as bad in this respect as some other universities I’ve either worked in or heard about from colleagues, but it is an issue even here.
The problem we find with such folk is that they are so remote that they seem to have no idea what people working in academic Schools and Departments actually do. For one thing they seem to think we just loaf around all day waiting for the chance to fill in some new forms or attend a some allegedly vitally important meeting at short notice (usually in teaching term, and usually mid-morning when lectures are in progress). In fact, there isn’t a day of the week when I don’t have teaching of some sort going on in teaching term. That’s not unusual for an academic in my Schoo, so it’s extremely difficult to attend such events at the drop of a hat without jeopardising teaching. The frequent requests to do so mean that I’d be surprised, in fact, if most of these managers actually knew when teaching term was. Meetings scheduled outside term of course eat into research time, but given that managers think “doing research” means “having a holiday”, you might be surprised we don’t have more meetings during the student vacations. Of course the real reason for this is that they don’t want us to attend (see below).
Another result of the increase in administrative staff is a plethora of badly thought out “initiatives”, similar initiatives even arising from several directorates simulaneously as managers compete with each other to weigh down academics with forms to fill in. The worst of these involve idiotic schemes in which Schools have to prepare lengthy documents to bid for minuscule amount of money from the central University coffers, the cost in staff time of administering such procedures far exceeding the financial or other benefits they can possibly deliver.
Worse, these central units are sometimes so badly run that they mess up the basic administrative tasks that they should be carrying out. Schools are thus forced to duplicate the work that should be done by someone else to make sure that it’s done properly. The idea that centralised administration leads to greater efficiency rarely works in practice. In contrast to the staff in individual Schools, most of whom actually care deeply about what they do because they work directly with the people involved, to the administrators are sometimes – not always, by any means, but definitely sometimes – too remote to care.
So in the end I am going to take a cheap shot at creeping managerialism, but only insofar as it relates to the invasion of universities by people who have no understanding of the core activities of a higher education institution, but who think they have the right to dictate to people who do. Instead of meaningful cooperation with academics, we have phoney “consultations”: meetings usually scheduled in such a way that academics can’t attend (see above) or documents requiring a response with absurdly short deadlines. This kind of management does not lead to a more “professional” institution, it just leads to alienation. In short, these people don’t help at all, they’re a positive hindrance.
Over the last decade, the burden of red tape has steadily increased for all kinds of institutions, but only the NHS vies with Universities in taking the fetish of managerialism to absurd levels. Academics will soon have to take courses in management-speak before they can be employed at a University as the influx of business types continues to accelerate.
The greatest irony of all this is that in the UK universities (with some notable exceptions) are generally regarded by the wider world as examples of international excellence, whereas British businesses (again with some notable exceptions) are seen by those abroad to epitomize incompetence and failure….Follow @telescoper
I’ve been annoyed ever since I woke up this morning because there was an item on the 7am news that irked me. A person called Claire Tomalin was quoted as saying, among other things, that
Children are not being educated to have prolonged attention spans and you have to be prepared to read steadily for a Dickens novel and I think that’s a pity.
She goes on to lay most of the blame for this shortcoming on television, as such people tend to do.
It’s a facile argument. For one thing most of Dickens’ novels were originally published in short installments, so reading them that way seems quite a sensible approach to me, and one that should probably be encouraged not criticized. There’s no getting away either from the fact that some of Dickens’ output is very heavy going indeed. Dare I say that not all Dickens is particularly good? Not liking Dickens is a matter of taste, not a mental defect caused by watching Big Brother.
And another thing: what fraction of children in Dickens’ time could read at all? Much lower than today, I suspect.
Claire Tomalin’s comment is not just a lazy generalization, it’s also yet another easy shot at the younger generations who have to put up with this sort of gibe from middle-aged grouches over and over again.
Examination results usually provoke similar outbursts, related to “dumbing down”. I actually do think that, at least in some subjects, examinations are much easier than they were “in my day”, but I don’t think that’s a reason to criticize the examinees. It’s more a fault with the examiners, who have decided that the young can’t cope with difficult challenges. That’s an insult in its own right. I maintain my view that education, especially higher education, is not about making things easy. It’s about showing students that they can do things that are hard. Most importantly, though, dumbing down examinations is not the same as dumbing down people.
It’s not just young schoolkids that attract such ill-informed invective. I come across it quite regularly with respect to the (alleged) lack of skills possessed by the young adults (usually 18-22) we teach as undergraduates, some of it even from colleagues.
I was thinking the other day what a boon it is for a middle-aged fogey – and obvious potential grouch – like myself to have the pleasure of actually talking to so many younger people at work, and listening to what they have to say. That way I’ve come to my own conclusions about what they’re really like. You know, like you do with people. Most folk of my age don’t have jobs that bring them into contact with younger folk, so they have to rely on articles in the Daily Telegraph to tell them what to think. That, sadly, even goes for those lecturers who have fixed ideas about the inferiority of “students nowadays”.
I think I’ve been very lucky, especially over the last few years, to have had the opportunity to work with a wide range of students as, e.g., project supervisor or tutor. Interactions like this provide a constant reminder not to generalize about the generations. There is of course a range of ability and commitment, but there was in my day too. The majority still work hard, learn quickly, and are friendly and courteous. There’s also no doubt in my mind that the best students nowadays are as good as they have ever been, if not better.
It’s the oldies who are the problem.Follow @telescoper
I came across the phrase Impostor Syndrome the other day. As a phrase it was quite new to me, but the state of mind it describes is far from unfamiliar. Digging around to find out a bit more I chanced upon an article written by renowned MIT astrophysicist Ed Bertschinger who explains it thus:
Impostor Syndrome is the feeling of not deserving to be in the position you are, and of being afraid that advisors, instructors, or peers will come to realize that you are not as capable as you may seem. The effect can be harmful when it selectively reinforces negative messages and causes people to try less hard because they are convinced they are incompetent when they are not.
That someone as intelligent and capable as Ed Bertschinger could confess to having such feelings will surely help others counter the negative effects these self-doubts might have on their careers. In the piece he reveals figures that show that Impostor Syndrome is pretty commonplace in academia, though more prevalent among females than males. Sarah Kendrew has blogged about this from the perspective of a younger researcher.
Impostor Syndrome has certainly accompanied me all the way through my academic career. It started as early as the 11+ examination to get into the Royal Grammar School. I was quite a backward child when I was very young – I didn’t learn to speak until I was three – and assumed that taking the examination would be a waste of time and I would go to the local comprehensive along the rest of the kids. In fact, I passed, and got a scholarship without which I couldn’t have gone, but was convinced that I only got in because of some form of adminstrative error. During my first term at RGS I was overwhelmed by feelings of inferiority and struggled at almost every subject. I kept at it though and surprised both myself and my teachers by doing rather well in the examinations.
It was all very similar when I went to Cambridge. Nobody from my family had ever gone to university before, never mind Cambridge, and I assumed I’d fluked the entrance examination there as well. I took it for granted that everyone else was cleverer and better prepared than me, but I gradually realised that wasn’t true. Some were, of course, but I found that if I worked hard I could do OK. I admit I was a bit erratic as student, but I always thought it was better to be good at some things than average at everything. In parenthesis I’d say that I think the Cambridge style of examinations was kinder to people like me than the way things are done in most places now, in that it didn’t involve a straight average over papers.
The same pattern emerged when I began graduate studies at Sussex. I felt woefully unprepared to work in cosmology, especially since many of my supervisor’s other DPhil students had completed the fiendish Part III Maths at Cambridge before starting their postgraduate degree. I was fortunate in being given a problem that suited me – and I should say received excellent guidance and advice from my supervisor, John Barrow. Despite going through some frustrating periods when I thought I wasn’t going to get anywhere with my research, I completed in less than three years.
Thereafter I got postdoc position, an SERC Advanced Fellowship, a permanent position at Queen Mary, and then a Chair (at Nottingham) by the time I was 35. Looking back on all these successes the only thing I can attribute them to is outrageously good fortune. There are many cleverer people with far stronger technical skills than me who either took much longer to get a permanent job or who haven’t yet managed to do so. At times I marvel at my own good luck, at others I feel guilty about others who are clearly better than me but haven’t been so fortunate. I guess they probably resent people like me, but it’s best not to think of that.
If you compare yourself with others,
you may become vain or bitter,
for always there will be greater and lesser persons than yourself.
The bad thing about having feeling that you’re an impostor all the time is the constant fear that you’ll be found out and be subjected to all sorts of humiliation and, worse, that you’ll find someone relies on you for something that you’re unable to deliver. The latter is especially stress-inducing if you work a lot in collaborations.
However, there is a good side too. I think a bit of self-doubt actually makes one a better person, in that knowing your own weaknesses helps appreciate better the qualities that others possess and instils a desire to help nurture the talents of people around you, especially the younger ones.
When students ask me for advice about scientific careers I usually say the usual things: work hard, choose your problems wisely, make connections, believe in yourself. If I were being completely honest, however, I’d say that I really believe that the most important thing is to be lucky.
Ps. The wikipedia page on Impostor Syndrome also includes a reference to its converse, Dunning-Kruger Effect in which “incompetent people find it impossible to believe in their own incompetence”. I wonder if this might be even more prevalent in academia?Follow @telescoper