Archive for teaching

Life at Level Five

Posted in Covid-19, Education, Maynooth, Politics with tags , , , on October 20, 2020 by telescoper

After refusing to do so two weeks ago, last night the Government decided to move all Ireland onto Level 5, the highest level of Covid-19 restrictions, for six weeks (although with some tweaks, e.g. the number of people allowed to weddings):

I think the previous refusal to implement tougher restrictions was a big mistake and has cost two weeks of exponential growth in new cases for no obvious benefit. I thought at the time that moving to Level 5 was inevitable giving the steep growth in numbers:

Here, for information is the latest plot of confirmed cases (as of last night):

The 7-day average of new cases is higher than it was at April’s peak, though thankfully the number of deaths is lower. Hospital (and specifically ICU admissions) are however, rising steadily.

We don’t know yet of any specific implications for teaching here at Maynooth University, though it will certainly mean even more teaching moves online. I think my own lectures will continue as Panopto webcasts in much the same way as before, except from my office rather than from a lecture theatre and without the handful of students who have so far been attending them in person. Next week (beginning 26th October) is our Study Week break which offers a bit of time to rearrange things. My first-year module has lectures on Mondays, Tuesdays and Wednesdays. Because the new restrictions kick in at midnight on Wednesday, that lecture will be the last one I do in a lecture theatre for a while. At least I got the best part of four weeks’ worth of lectures in that way.

More generally workers are required to work from home if they can with an exception for “essential services”. The general guidance given here includes:

11. The following services relating to professional, scientific and technical activities:

(a) the provision of engineering, technical testing activities and analysis (including the performance of physical, chemical and other analytical testing of materials and products);

(b) the provision of scientific research and development services;

(c) regulation, inspection and certification services, in accordance with law, of a particular sector by a body created by statute for that purpose.

and

16. The following services relating to education activities:

(a) primary and post primary school;

(b) higher and further education, insofar as onsite presence is required and such education activities cannot be held remotely.

This implies that the campus will not be closed like it was in March, so that this is not going to be a complete lockdown for either research or teaching. Moreover 16(b) does suggest that even laboratory-based teaching may carry on, but we await confirmation on that.

 

 

Teaching Improvisation

Posted in Biographical, Education, Maynooth with tags , , , on September 29, 2020 by telescoper

The sudden switch of all our teaching online on Friday has necessitated a certain amount of improvisation. I had intended to do my introductory session on Mechanics and Special Relativity to first-year students as a kind of interactive workshop using the blackboard in Physics Hall. When we were told to move everything online I thought I’d just do yesterday’s session from my office which has quite a good blackboard and a setup I had already tested. Unfortunately however an office refurbishment project I was assured would be finished before the start of teaching but which has barely started meant that yesterday there was constant hammering and drilling in the Department. That made it impossible to do an online lecture (or do anything else) in my office. I knew there would be nobody in Physics Hall, though, so I did the lecture there to an empty room.

The camera provided in that room is fixed to a monitor at once side of the theatre and is therefore useless for capturing the blackboard, so I used my laptop camera plus a handy litter bin to raise it up. It wasn’t great but was better than nothing.

You might ask why I don’t do this from home. The answer to that is that I haven’t yet got an internet connection in the new house, so I can do online activities from there.

You might also ask why a refurbishment job, which could have been completed at any point during the summer when the building was empty, has only just started now we’ve started teaching again. If I had an answer I would tell you. I think the six people whose offices are currently unusable would like to know too, though at least they can work from home. It’s tough enough trying to keep everything together these days without this.

Fortunately today a colleague in the Department of Psychology found me a quiet place to work. It’s a small windowless cubicle normally used for experiments. At least it’s quiet. I think the next step will be a padded cell somewhere.

On the Exploitation of Postgraduates

Posted in Education, Maynooth with tags , , , on September 27, 2020 by telescoper

Thinking through the implications of Friday’s announcement for teaching I saw the following advice sent out to students from Maynooth University

For the next few weeks most lectures will move online. You will be invited on-campus for practical classes, tutorials and for the teaching which requires a lot of interaction.

I can’t see significant numbers of students travelling to campus for a tutorial when they have no other teaching sessions but thinking about this yesterday I was struck by the decision that tutorials should go ahead while lectures shouldn’t. Tutorials are largely given by postgraduate students and it seems extremely unfair to me that they should be required to run the risk and incur the expense of travelling to campus in order to carry out in-person teaching, when full-time staff can minimize their chances of infection by staying at home and teaching remotely.

I’ll therefore be instructing all postgraduate tutors in my Department that they are not expected to run their tutorials on campus.

Yesterday I moaned about university staff being taken for granted but the situation is even worse for postgraduate tutors, who make an invaluable and essential contribution to teaching but are often treated horrendously badly by universities.

Take for example the scandalous situation at NUI Galway, where postgraduate students are being required to undertake 120 hours of unpaid teaching duties per year. The University’s justification for this is the following

Contributing to teaching is an integral part of the training of a research Master’s or PhD student. Teaching assists you in the acquisition of generic and transferable skills, and is an important element in the formation of a research graduate.

This may well be true but it does not constitute an argument why such work should be unpaid. I would argue that an even more “important element in the formation of a research graduate” is learning not to allow oneself to be exploited.

One of the very few things I can say I achieved in my time at Sussex was to abolish the use so-called Graduate Teaching Assistantships in the School of Mathematical and Physical Sciences that required postgraduates to do unpaid teaching and make all such work voluntary and paid.

I am well aware of the reason why Galway is trying this on – it’s the chronic underfunding of Ireland‚Äôs universities and colleges exacerbated by rampant managerialism – but that’s no excuse for institutionalised exploitation. I wholeheartedly support the postgraduates at Galway refusing to carry out unpaid teaching duties and hope the University will withdraw this unjustified and iniquitous policy.

A Semester of Covid-19

Posted in Biographical, Covid-19, Education, Maynooth, Music with tags , , , , , , , on September 12, 2020 by telescoper

It’s the Twelfth of September so it’s now precisely six months to the day since schools and colleges in Ireland were closed because of the Covid-19 pandemic. The initial announcement on 12th March was that the closure would be until 29th March. Little did we know then that six months later campus would still be closed to students.

Here is how the pandemic has progressed in Ireland since March:

On 12th March, 70 new cases of Covid-19 were announced in Ireland; yesterday there were 211. The current 7-day average in Ireland is over 180 new cases per day and is climbing steadily. Things are similar, if not worse, elsewhere in Europe. as countries struggle to contain the pandemic while simultaneously attempting to reopen their economies. We are heading towards a very difficult autumn, with a large second peak of infection definitely on the cards. Who knows how this will turn out?

The word ‘semester’ is derived from the Latin for ‘six months’ but the term now applies almost exclusively to half a university teaching year, usually more like four months.

I’m looking ahead to the next teaching semester at Maynooth University, which starts in two weeks. The last time I gave a face-to-face lecture was on the morning of March 12th (a Thursday). Going home that evening I was engulfed by morbid thoughts and wondered if I would ever see the students again. Now we’re making plans for their return to (limited) on-campus teaching. Outline teaching plans have now been published, so returning students will have an idea how things will go. These will be refined as we get a better idea of student numbers. Given the continued increase in Covid-19 cases there is a significant chance of another campus closure at some point which will necessitate going online again but, at least to begin with, our students in Theoretical Physics will be getting 50% or more of the in-person teaching they would have got in a normal year.

Yesterday third-level institutions made their first round of CAO offers. Maynooth’s can be found here. Our offer for MH206 Theoretical Physics & Mathematics is, like many courses around the country, up a bit at 510 points reflecting the increase in high grades in this year’s Leaving Certificate.

We won’t know the final numbers for at another week or more but based on the traffic on Twitter yesterday Maynooth in general seems to be very popular:

Outline teaching plans are available for new students but these will not be finalised until Orientation Week is over and students have registered for their modules, which will not be until Thursday 24th September, just a few days before teaching starts. The weekend of 26th/27th looks like being a very busy one!

Returning to the original theme of the post I have to admit that I haven’t set foot outside Maynooth once in the last six months. I haven’t minded that too much, actually, but one thing I have missed is my weekly trip to the National Concert Hall in Dublin. Last night saw the start of a new season of concerts by the RTE National Symphony Orchestra at the NCH. There is no live audience for these so it’s not the same as being there in person, but watching and listening on the live stream is the next best thing.

Last night’s programme was a very nice one, of music by Mendelssohn Mozart and Beethoven, that not only provided a welcome tonic to the end of a busy week but also provided a great example of how to adapt. I’m glad they’re back and am looking forward to the rest of the season.

Time, Money and Guidance in Higher Education

Posted in Covid-19, Education, Maynooth with tags , , , , on July 27, 2020 by telescoper

There was a welcome announcement last week of a package of supports for further and higher education institutions and students in Ireland to cover costs incurred by third level institutions during the Covid-19 pandemic and enable further and higher education students to return to college this September.

There wasn’t much sign of any help at all coming under the previous Government, so this is perhaps a sign that the new Department of Further and Higher Education, Research, Innovation and Science might be a force to be reckoned with in the new administration.

If this funding is to achieve its aim, however, it will have to reach its targets very quickly. The new academic year is to commence at the end of September, which is just two months away. The slice that is intended to go directly to students to help them buy laptops or tablets can probably be spent quite quickly, but the money intended for colleges and universities to buy equipment will take much longer to filter through.

Speaking for myself, as Head of a Department of Theoretical Physics I’d say we desperately need better video equipment for both live and recorded material. At present we have no lecture capture facilities at all in any lecture theatres. We also need graphics tablets to help lecturers show mathematical working via remote means. There is likely to be a big rush for this sort of thing between now and September, and no guarantee we will have it in time for the start of lectures.

You might well ask `why don’t you buy this stuff now?’. The answer is simple: I haven’t got the money!

Things are even tougher for schools. Here there is another big support package on the way, this time of ‚ā¨350 million to allow them to open at the end of August. Getting kids back to school is obviously important not only for their education but also to allow their parents to return to work. However, the time available to prepare all the things necessary is just a month, even shorter than it is at third level.

Among the funds being made available is ‚ā¨75 million for `building works’. I’m sure that investment is very welcome, but can it do anything between now and the end of August? It’s actually rather difficult to spend money that quickly if due process is followed. Just look at how the UK government has squandered tens of millions on phony contracts, such as the ¬£12 million it blew on a Covid-19 tracing app that never worked.

On top of that 1000 new schoolteachers are going to be provided. Will they be recruited in time?

Another announcement to appear last week contained guidance for further and higher education on returning to on-site activity in 2020. This guidance has been interpreted in the media in a rather unhelpful way, causing many of my colleagues to go into a panic. This, for example, from the Irish Times:

Physical distancing rules of two metres will apply on college campuses from September in a move which will severely limit the ability of universities to hold lectures and graduation ceremonies.

A strict requirement of 2 metre distancing at all times would indeed severely reduce the capacity of lecture theatres, but if you look at the guidance it is considerably more nuanced than this. The real problem with this guidance is that it is so vague. We can only hope we get something a bit more concrete soon so we can plan for September. Alternatively we could just wing it. All of it. At the moment this seems the only viable strategy.

Leaving Late

Posted in Covid-19, Education, Maynooth with tags , , on July 18, 2020 by telescoper

The time of Covid-19 was already an “interesting” time to be an academic in Ireland but yesterday it got more interesting still, as news emerged that this year’s (estimated) Leaving Certificate results will not be published until 7th September, which is three weeks later than usual. The first round of CAO offers will be made on 11th September. All this is about three weeks later than the usual cycle of examinations and results.

Here at Maynooth University the start of the academic year has been delayed by one week to September 28th, so the three week delay in Leaving Cert means we have to speed the processes up of getting everything in place for new students to start by two weeks. That is going to be a challenge, and even if we manage it we will only find out very late in the day how many students we have to accommodate in first-year lectures.

The current plan for teaching next semester at Maynooth University is that all modules will be allocated the same timetable slots and rooms as last year. However, most lecture rooms have had their capacity reduced by more than half. Lecturers need to know how many students they have in order to decide how to use the available lecture slots and how to strike a balance between live and online delivery.

To give an example, I had about 90 students in my first-year module last year for which I had three lectures per week in Physics Hall, which has a normal capacity of 90. Next year the capacity of this room is likely to be around 30 with social distancing so. if I have the same numbers as last year, I will have to split the class into three groups and have one weekly session with each group. The material not covered live will be put online. I’m planning on that basis now, but if I find we have more students in Year 1 than last year I’ll have to have a Plan B. I won’t know that until just before teaching starts.

And then there is the possibility that teaching will actually start later for first-year students, requiring the lecture content to be revised. That’s not the current plan at Maynooth University, but a lot can happen between now and September…

We do indeed live in interesting times.

Of course I’m not the only one to be facing such challenges. Mine is a relatively small class by first-year standards and other bigger courses will experience far more serious difficulties.

If any prospective student is getting worried reading this, I can promise you that we will be doing the best we can to provide the best education we can in whatever circumstances we find ourselves in this September. Please bear in mind that workloads on academic staff (including Heads of Department!) are going to be very heavy after a summer in which very few will have been able to take any holidays at all. So please bear with us. We didn’t want any of this any more than you did, but we just have to make the best of it.

Challenges Past and Future

Posted in Covid-19, Education, Maynooth with tags , , , , , , on June 19, 2020 by telescoper

Yesterday afternoon we held our Departmental Examination Board in Theoretical Physics (via Microsoft Teams*) which all went remarkably well in the circumstances.

The most challenging thing to happen yesterday afternoon was that a bloke came to cut back the bushes outside my office with a very large and noisy hedge trimmer. I thought I was going to have to contend with that all afternoon but it seems he had done most of it the day before and only came back yesterday to finish off. He left before the Exam Board started.

The next stage of our Exams process is for all the Departmental results to be collated for those students on joint programmes before the final University Board takes place about ten days from now. After that students will get their results.

That doesn’t quite finish examination matters for 2019/20 however because some students will need to take repeat examinations in August. These will be a week later than usual as a knock-on effect of the extra week we were given to mark and correct the May exams. We anticipate that at least some of the repeats will be the traditional `in person’ on campus style, but some may be online timed assessments like the ones we held in May. That depends a bit on how the Covid-19 pandemic pans out in Ireland over the next few weeks (and of course how many students actually take repeats, as social distancing generates a capacity issue for the examination halls).

At the moment we are optimistic because the number of new cases of Covid-19 is low and stable. That coulld change, of course, if the virus starts to spread again so we have to have contingency plans.

Even more uncertain is what will happen in September, although I have been very annoyed by some reports in the media that seem to have been actively trying to put students off coming to University next academic year on the grounds that there won’t be any lectures. We certainly plan to offer as much face-to-face teaching as possible and I think other third-level institutions in Ireland will do likewise. There will of course have to be a backup if there is another lockdown, which may mean switching back to remote teaching at relatively short notice, but at least we’ve done that once already so know much better now what works and what doesn’t. Nevertheless I would encourage all potential students not to believe everything they read in the media nor be deterred from attending university by rumours from sources who don’t know what they are talking about.

Earlier this week I was starting to think about how we might build the required flexibility into our teaching for next year and two main things struck me.

The first is that while we have more-or-less been forced into making various kinds of video material available to students, this is something that I feel we should have been doing already. I’ve long felt that the more types of teaching we incorporate and the wider range of learning materials we provide the better the chance that students find something that works for them. Even if we do have a full programme of lectures next year, it is my intention to continue to provide, e.g., recorded video explainers as well because they might augment the battery of resources available to the student.

Some time ago I had to make some policies about `reasonable adjustments’ for some disabled students learning physics. In the course of providing extra resources for this small group I suddenly thought that it would be far better, and far more inclusive, simply to make these resources available to everyone. Likewise, we’ve been forced to adjust to providing material remotely but we should be thinking about how to keep the best things about what we’ve done over the last few months and embedding them in the curriculum for the (hopefully Coronavirus-free) future and not regard them all as temporary special measures.

The other thing that struck me is in the same vein, but a little more speculative. Over the last many years I have noticed that students use printed textbooks less and less for learning. Part of that may be because we in a digital age and they prefer to use online resources. The switch to remote learning has however revealed that there are some students who are disadvantaged by not having a good internet connection. I just wonder whether this might lead to a resurgence in the use of textbooks. I’ll certainly be making a strong recommendation to the new first-year students in Theoretical Physics that they should get hold of the recommended text, which I have previously regarded as an optional extra.

*At one point I got muddled up between Teams and Zoom and called it Tombs. It was a grave error, but it can only be a matter of time before Microsoft Tombs actually arrives…

100 Years of Feynman

Posted in Cute Problems, Education with tags , , , , , , on May 11, 2018 by telescoper

Today marks the centenary of the birth of Noble Prize-winning physicist, science communicator and bongo player Richard Feyman. It’s great to see so many articles about him today, so I was wondering how to do my own quick tribute before I head to London for the Royal Astronomical Society Annual General Meeting this afternoon.

With university exams coming up¬†it seemed a good idea to celebrate Richard Feynman’s legacy by combining todays 100th anniversary with some tips (inspired by Feynman) 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.

Richard-Feynman-cornellI began with Richard Feynman’s formula (the geezer in the above picture) for solving physics problems:

  1. Write down the problem.
  2. Think very hard.
  3. 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 key point is to write down the information given in the question and then try to think how it might be connected to the answer. To start with, define appropriate symbols and draw relevant diagrams. Also write down what you’re expected to prove or calculate and what physics might relate that to the information given.

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. The process of problem solving is not always linear. Sometimes it helps to work back a little from the answer you are expected to prove before you can return to the beginning and find a way forward.

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.

  1. Read the question! Some students give solutions to problems other than that which is 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.
  2. Remember to explain your reasoning when doing a mathematical solution. Sometimes it is very difficult to understand what students are trying to do from the maths alone, which makes it difficult to give partial credit if they are trying to the right thing but just make, e.g., a sign error.
  3.  Finish your solution appropriately by stating the answer clearly (and, where relevant, in correct units). Do not let your solution fizzle out Рmake sure the marker knows you have reached the end and that you have done what was requested. In other words, finish with a flourish!

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!

 

Cosmology: The Professor’s Old Clothes

Posted in Education, The Universe and Stuff with tags , , , , , , , on January 19, 2018 by telescoper

After spending¬† a big chunk of yesterday afternoon chatting the cosmic microwave background, yesterday evening I remembered a time when I was trying to explain some of the related concepts to an audience of undergraduate students. As a lecturer you find from time to time that various analogies come to mind that you think will help students understand the physical concepts underpinning what’s going on, and¬†that you hope will complement the way they are developed in a more mathematical language. Sometimes these seem to work well during the lecture, but only afterwards do you find out they didn’t really serve their intended purpose. Sadly it also¬† sometimes turns out that they can also confuse rather than enlighten…

For instance, the two key ideas behind the production of the cosmic microwave background are recombination and the consequent decoupling of matter and radiation. In the early stages of the Big Bang there was a hot plasma consisting mainly of protons and electrons in an intense radiation field. Since it  was extremely hot back then  the plasma was more-or-less  fully ionized, which is to say that the equilibrium for the formation of neutral hydrogen atoms via

p+e^{-} \rightarrow H+ \gamma

lay firmly to the left hand side. The free electrons scatter radiation very efficiently via Compton  scattering

\gamma +e^{-} \rightarrow \gamma + e^{-}

thus establishing thermal equilibrium between the matter and the radiation field. In effect, the plasma is opaque so that the radiation field acquires an accurate black-body spectrum (as observed). As long as the rate of collisions between electrons and photons remains large the radiation temperature adjusts to that of the matter and equilibrium is preserved because matter and radiation are in good thermal contact.

 

Image credit: James N. Imamura of University of Oregon.

Eventually, however, the temperature falls to a point at which electrons begin to bind with protons to form hydrogen atoms. When this happens the efficiency of scattering falls dramatically and as a consequence the matter and radiation temperatures are no longer coupled together, i.e. decoupling occurs; collisions can longer keep everything in thermal equilibrium. The matter in the Universe then becomes transparent, and the radiation field propagates freely as a kind of relic of the time that it was last in thermal equilibrium. We see that radiation now, heavily redshifted, as the cosmic microwave background.

So far, so good, but I’ve always thought that everyday analogies are useful to explain physics like this so I thought of the following.

When people are young and energetic, they interact very extensively with everyone around them and that process allows them to keep in touch with all the latest trends in clothing, music, books, and so on. As you get older you don’t get about so much , and may even get married (which is just like recombination, not only that it involves the joining together of previously independent entities, but also in the sense that it dramatically¬† reduces their cross-section for interaction with the outside world).¬† As time goes on changing trends begin to pass you buy and eventually you become a relic, surrounded by records and books you acquired in the past when you were less introverted, and wearing clothes that went out of fashion years ago.

I’ve used this analogy in the past and students generally find it quite amusing even if it has modest explanatory value. I wasn’t best pleased, however, when a few years ago I set an examination question which asked the students to explain the processes of recombination and decoupling. One answer said

Decoupling explains the state of Prof. Coles’s clothes.

Anyhow, I’m sure there’s more than one reader out there who has had a similar experience with an analogy that wasn’t perhaps as instructive as hoped or which came back to bite you. Feel free to share through the comments box…

How to Solve Physics Problems

Posted in Cute Problems, Education with tags , , , , , , on September 18, 2015 by telescoper

It’s Friday afternoon at the end of Induction Week here at the University of Sussex. By way of preparation for lectures proper – which start next Monday – I gave a lecture today to all the new students in Physics during which I gave 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.

Richard-Feynman-cornellI began with Richard Feynman’s formula (the geezer in the above picture) for solving physics problems:

  1. Write down the problem.
  2. Think very hard.
  3. 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 key point is to write down the information given in the question and then try to think how it might be connected to the answer. To start with, define appropriate symbols and draw relevant diagrams. Also write down what you’re expected to prove or calculate and what physics might relate that to the information given.

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. The process of problem solving is not always linear. Sometimes it helps to work back a little from the answer you are expected to prove before you can return to the beginning and find a way forward.

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.

  1. Read the question! Some students give solutions to problems other than that which is 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.
  2. Remember to explain your reasoning when doing a mathematical solution. Sometimes it is very difficult to understand what students are trying to do from the maths alone, which makes it difficult to give partial credit if they are trying to the right thing but just make, e.g., a sign error.
  3.  Finish your solution appropriately by stating the answer clearly (and, where relevant, in correct units). Do not let your solution fizzle out Рmake sure the marker knows you have reached the end and that you have done what was requested. In other words, finish with a flourish!

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.

To illustrate the advice I’ve given I used this problem, which I leave as an exercise to the reader. It is a slightly amended version the first physics problem I was set as tutorial work when I began my undergraduate studies way back in 1982. I think it illustrates very well the points I have made above, and it doesn’t require any complicated mathematics – not even calculus! See how you get on…

problem