SciBlogs

Archive August 2011

Exams that you can talk in Marcus Wilson Aug 30

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I had a very interesting day yesterday in Auckland, at a NZ Engineering Educator’s forum.  Here, there were representatives from across the tertiary sector looking at ways of improving the way that Engineering is done at universities and polytechnics.

The main speaker was Keith Willey, from the University of Technology, Sydney. He gave some great insights into the way that feedback works and how students can use each other to learn (peer learning). He’s done a lot of work trying to get these strategies to work really well. He showed a few video clips from his classrooms – the most obvious thing that struck me was just how noisy it was. 

Keith talked a bit about a few strategies he’s used – e.g. multiple choice scratch-cards to give the students really instant feedback, but I’ll share the most totally outrageous one – allowing students to talk to each other during tests and exams.

It needs a bit of qualifying – students are allowed to talk to each other (but not write anything down) in the first fifteen minutes of the exam. The point is that the exam then becomes a learning experience in its own right – not just a summative exercise. Students can discuss strategies for tackling particular problems before doing them, and learn from each other. 

That, of course, is the point. The idea of an engineering degree is that a student who completes it has ‘learned’ – has acquired knowledge, skills, abilities etc that are suited for engineering. The role of the teaching staff is to provide them with, and to help them  take, opportunities to learn.  And an exam is one of those opportunities.

Very, very interesting. It would take some nerve to implement it here.

The proton and neutron: same and different Marcus Wilson Aug 26

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Lately, I’ve been doing a bit of reading about the use of group theory in particle physics. I need to do this because I’m meant to be teaching it in the next few weeks. Now, the education research says I can still teach something without being an expert in it -  I just need to be able to inspire my students to learn it themselves. That’s re-assuring, because I am certainly no expert in particle physics. Of all the area of physics, it’s the one I’ve always had most trouble grasping. Perhaps it’s because you can’t neatly summarize it with one equation – I’m not sure.

Anyway, one thing I am sure about is that finding a textbook on group theory in physics (and particle physics in particular) that is accessible to mortals like me is a bit of a mission. The books I’ve looked at in our library, and there are lots of them, tend to give the impression that the whole thing is insanely complicated. After a fair bit of reading, I’m beginning to get the hang of some of it, but it is really nasty stuff.

As I’ve already said, group theory is about looking at symmetries. In particle physics, we can see lots of symmetries of various forms, so groups sit naturally here. An example (probably the simplest one) is the symmetry between the neutron and the proton. These two particles make up the nucleus of an atom. At school we’re told that the proton has a positive charge, a neutron has no charge, and that the two have near-identical masses. In fact, it’s not just (nearly)  the same  mass that the proton and neutron share – they are pretty-well identical, except for their charge.

This leads to the question of whether, in some fundamental way, the proton and neutron are actually  different manifestations of the same thing. Heisenberg developed this idea with his ‘isospin’ theory. It turns out that there’s a clever mathematical way of describing isospin, using what’s known as the SU(2) group. This group contains the underlying physics – when we look at its symmetries the neutron and proton states naturally ‘drop-out’, in the same way that  (some of) the gaits of a quadruped ‘drop-out’ of the analysis of the symmetries of a rectangle.

But it gets better than that. Not only does this group describe neutrons and protons it describes other, not so well known particles – the pions, as a neat mathematical combination of two nucleons. (By nucleon we mean a neutron or proton).  The whole physics of the way that neutrons and protons interact through exchange of pions is encapsulated in the SU(2) group. Really neat!

Unfortunately, the realm of particle physics is rather bigger than neutrons, protons and pions, and so our SU(2) group doesn’t get us terribly far. But it makes a start, and certainly helps us (by which I mean me) to see why particle physicists like to bleat on about symmetry groups.

 

 

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Crop circles Marcus Wilson Aug 24

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There’s a great article in Physics World on crop circles. Not a discussion about man-made / weather-made / UFO-made  – any sensible interpretation would be man-made – but just HOW do you make such intricate and vast patterns so quickly and leave almost no traces behind. Some of the patterns that crop-up (sorry) in crop fields can be fractals, reproduced to an astonishing level of detail.

There’s some evidence that the crop-circle makers are really very scientifically based and have moved beyond the rope, peg and stomping board and are armed with magnetrons and other secret techniques by which they carry out their art.

Read the article and see what you think. I love the bit about a couple of the makers being motivated to produce ever more detailed patterns in an attempt to ridicule the scientists who clung to a natural (e.g. whirlwind) view of their formation.

And why are there so few crop circles in NZ?  Are we working our students too hard that they don’t have time to get involved in this stuff?

Momentum conservation Marcus Wilson Aug 23

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It’s mid-semester break here at Waikato so I have time to breathe and get back to things other than teaching, such as seeing what the PhD students are up to. Yay.

But, here’s a comment about what I was talking about last week with the first year students: conservation of momentum.

If you look in first-year textbooks with regard to conservation of momentum in two dimensions, they tend to be full of examples about colliding billiard balls and car crashes. The former is a rather tedious example of an elastic collision (one in which kinetic energy is conserved) – the latter a nasty example of an inelastic-ish collision (in which the projectiles stick together after collision).  But there are a lot of more interesting examples to be found, and it’s always nice when I see a textbook that uses them.

For example, why not talk about the Large Hadron Collider, rather than billiard balls. The LHC collides protons together, and momentum is conserved. True, the products of the collision can be many and varied (maybe even a Higgs Boson – who knows?), and we’ll have to use special relativity to analyze them properly, but momentum will be conserved. It’s a nice topical example – far more inspiring than billiard balls and car crashes.

Here’s another example from the realm of the small – Compton scattering. This happens when a gamma ray or X-ray scatters elastically from an electron. The electron recoils, takes away energy from the gamma ray, which then changes its wavelength. Arthur Compton worked out that there was  a relationship between the observed change in wavelength of the wave and the angle through which the wave is scattered, and this could be explained by a single interaction between the gamma wave and the electron.  To do this he used momentum and energy conservation (it’s an elastic collision) – with the complication that it has to be done relativistically. In fact, Compton Scattering can be considered an experimental proof of special relativity and quantum mechanics – the experimental results tie in with the relativistic predictions. We get our third-year students to do this experiment, and it generally works very well. One can even extract the mass of the electron from the results.

Arthur Compton received a Nobel Prize in 1927 for what can be viewed as applying momentum conservation to a simple collision. I think it’s well worth talking about in first-year physics – students might struggle with the relativity bit, but the concepts are absolutely easy, and the result is really significant.

Better than car crashes for sure.

 

Turning into physicists… Marcus Wilson Aug 18

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There were a couple of moments in the first-year lab yesterday that made me want to despair:

The first one:

Student: My magnetic field doesn’t change when I increase the current

Me, seeing what the problem is: How do you connect an ammeter in a circuit?

Student: In series. Um…oh, hang on…we’ve done parallel, haven’t we?

The second one:

Student: We’ve switched it on, but nothing’s happening. 

Me, seeing that the red ‘on’ light isn’t on: Is it plugged in?

At this point I could have despaired – how can we possibly teach students who can’t plug something in or put an ammeter in series with what they want to measure.  But, I haven’t, because I also teach in the third year labs, where things often are at the other extreme – e.g. students suggesting ways of improving the experiment – and sometimes actually going and doing it. Last week, we were working with a ferrofluid (a magnetic fluid – pretty cool stuff) and a pair of them, while waiting for their experiment to settle, decided that a good way to fill the time would be to build the biggest electromagnet they could out of what they could find in the lab and see how the fluid responded to it.  I think that shows some initiative, some real understanding of physics (since they went on to build the thing) and actual ability to do experimental work for themselves.  The result was a little bit messy but quite interesting.

So we have students who perhaps can’t plug in an ammeter properly in year 1 turning into real physicists by the end of year 3, so that’s no cause for despair, really.

 

Four legs good Marcus Wilson Aug 16

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Those of you who own a four-legs will have noticed that they usually exhibit a range of different gaits depending on the occasion. Taking Mizuna our cat as an example – he walks (back-left, front-left, back-right, front-right, each leg a quarter of a cycle behind the previous), he trots (back-left and front-right together – then back-right and front-left together, each movement half a cycle behind the previous), he runs (back-left, back-right, front-left, front-right, or alternatively back-right, back-left, front-right, front-left).  Mostly he sleeps, but that’s not a gait.

There are two other forms of motion he employs occasionally. There’s the bound (back legs together, front legs together) which is his gait-of-choice for high-speed ascent of the stairs (he trots on the way down) and the highly amusing pronk, in which he bounces on all four legs simultaneously – this is reserved for moments of great excitement such as being fed. Yes, pronk is a real word!

We bipeds, on the other hand, are rather short of choices when it comes to motion. We can walk (left, right…) or we can jump (legs together) and that is it. I don’t count symmetry-breaking gaits here, such as the hop or the skip – they are a bit unusual, just like the quadruped’s canter – and I count ‘run’ as being the same as walk, in that our two legs still move in anti-phase to each other.

The increased range of gaits available to the quadruped can be naively attributed to them having more legs, but perhaps a better description would be that they have increased symmetry. We bipeds have a single mirror plane, left-to-right when it comes to legs, but quadrupeds, with legs arranged in a rectangle, can be thought of as having a front-to-back mirror plane as well. (Yes, I know they don’t really have a mirror plane here, but the legs approximately have.)

Group theory is a mathematical encapsulation of symmetry. We can use it in physics to simplify problems. A typical example is finding the modes of vibration of a molecule with a particular symmetry. It’s often presented as rather abstract mathematics but when applied to physics it becomes beautifully and simply powerful. For example, our pronk, trot, bound, and another gait, the pace (left legs together, right legs together – not sure if any animal does this one), drop out of the analysis for a rectangular arrangement of legs. (The walk and run/gallop are a bit more subtle). Applied to the biped, we simply obtain the walk and the jump. The more symmetry you have, the greater the range of gaits you have.

In the limit of lots of symmetry indeed (the millipede, which approximately has complete translational symmetry along its length) there are a huge number of gait options. We can then start describing these in terms of waves, and, in particular, by wavelengths and frequencies of the action rippling down the body. This then has analogies with other physical systems, such as vibrational modes in solids (phonons), where different frequencies of sound wave travel at different velocities through the solid. Group theory isn’t just abstract, as many textbooks would make out, it really is quite practical and fun.

So, next time you come across a four-legs, or a six-legs, have a careful look at how it moves.

P.S. I’ve drawn a bit from my memory of an Ian Stewart book here, though I can’t quite remember which one. I’m not sure I still own it.

 

The dangers of reflective blogging Marcus Wilson Aug 14

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Friday morning saw me doing my usual Friday-morning-thing, namely work on my PGCert Tertiary Teaching portfolios. (I’ve put in a recurring appointment in my calendar every Friday morning for this semester so I actually get down to doing this task.) As part of this, I’ve been pulling together relevant blog entries on my teaching experiences.

A dangerous move, because I’ve started reading them again. Some of them are full of good intentions that haven’t quite materialized. Here’s a quick example. Back in April this year, I wrote about the book ‘Assessment for Learning’ by Paul Black et al. I highlighted the discovery that giving a (secondary) student a summative mark with a piece of work (e.g. 8 out of 10) completely negates any formative comments you write on the work – i.e. you may as well not have bothered writing any comments. However, if you don’t put a mark on the work, the students will take note of your comments and improve. I then said "Worth a shot in one of my papers…"

I now recall that I intended to do this with my experimental physics class. (For this class, it’s a fairly easy thing to do because I spend a lot of time with them in the laboratory, and the course is completely under my control – I don’t have to fit in with what another lecturer is doing.) So my intention was not to give the students marks on their work, but rather give them feedback and discuss with them where they can improve. However, my intention has not turned into reality. It’s halfway there, in that I give them comments, discuss the work with them, and then ask them to give themselves a mark (Phil Race style, www.phil-race.co.uk, see also here), but after they do that I end up giving them a mark (which usually is pretty close to their mark.) Not quite what I had in mind earlier.  There is next year.

Of course, at some point, I would need to get ‘summative’, because the students need to get a grade for every course they do. But there are probably plenty of options for doing that.

 

Black, P., Harrison, C., Lee, C., Marshall, B. & Wiliam, D. (2003) Assessment for Learning. Maidenhead, U.K.: Open University Press.

 

 

Friction: Stick or Slip? Marcus Wilson Aug 12

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Going back to my last entry on the sliding car, it’s worth commenting a bit more on the nature of friction here. When a car goes round a corner, what prevents it from sliding is the friction between the tyres and the road. Tyres are unsurprisingly designed to be able to give a high frictional force when in contact with the road. If you’ve got access to a car tyre that’s not  attached to a car, try putting it up vertically (as when mounted on a car) and pushing it sideways across the road. Not at all easy, which is quite reassuring, really.

Friction is a complicated beast. We usually separate discussion into ‘kinetic’ friction and ‘static’ friction. Kinetic friction is what happens when an object is moving; static when the object is stationary. Kinetic friction can often be described nicely by ‘the coefficient of kinetic friction’; in this case the frictional force (which of course acts against the direction of movement) is given by the coefficient of kinetic friction times the normal force that the surface exerts on the object. From Newton’s second law, the normal force exerted on an object on a flat surface will equal the object’s weight (but that’s not true on an inclined surface) and so the heavier an object is, the greater the frictional force on it when it’s sliding. That should pretty well tie in with your personal experience, I’m sure. Pushing that filing cabinet is so much easier when you take the files out first.

The coefficient of friction itself depends on the nature of the two surfaces – so rubber on asphalt has a pretty high coefficient of friction, but steel on ice (ice-skate style) is extremely low.

Things are similar but slightly more complicated when an object doesn’t move. We use a coefficient of static friction now, but this time we have to say that the frictional force is less than or equal to the coefficient of static friction times the normal force. (If that force isn’t sufficient to hold the object in place, it will start sliding.) So, the larger the coefficient of static friction is, the steeper the ramp you need before an object starts sliding down it.

Now, things often get interesting with friction because the coefficient of kinetic friction can be considerably less that the coefficient of static friction. What this means is that an object can be hard to get moving, but, once it is moving, sliding it becomes much easier. An example is shifting furniture around our new house by pushing it across the carpet. The difficult bit is to get the chest of draws to move to start with – but once it is moving, maintaining its movement isn’t so tricky.

A great example of the interplay between kinetic and static friction is with bowing a violin string. The string moves in a ‘slip-stick’ manner. It will stick to the bow, and move with the bow, until the restoring force on it is large enough to get it to move across the bow (the ‘slip’) which it will then do very easily, returns towards its original position and overshoots (like simple harmonic motion). Restoring forces then bring down the velocity of the string, and, once the velocity of the string is reduced, it sticks again and the cycle continues. A nice little animation and comprehensive explanation can be found here.

 

NZ Scholarship physics Marcus Wilson Aug 10

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I’ve recently had a look at the 2010 New Zealand Scholarship Physics exam, for the first time. (This is the exam taken by the top final year school students in physics – the best performers get rewarded with scholarships that will help them financially at university).

The scholarship exams are hard. There’s no denying that. For physics, this has often been seen in the way that several concepts can be mixed up in one question. To do well, the students have to be good at identifying what is going on, physically, in a particular situation, and pulling together their knowledge over different areas of physics to make sense of it. The famous ‘equation-spotting’ method (see what information you are given, see what you are told to find, and find an equation from the list given that contains all those quantities in it) does not work at scholarship level. There’s an infamous example from a few years back (the ‘phugoid oscillator’ – go look up what those are if you’re interested) that needed five different equations just to answer one part of the question.

However, in the 2010 scholarship exam I think there was a subtle shift in the type of question asked. Instead of having questions where the student had to identify and pull together the concepts, the questions seemed more focused on individual concepts, but having the student drill down to the core of that concept to see how well they really understood it.

At this point, a big disclaimer is in order: I DO NOT SET SCHOLARSHIP EXAMS; I DO NOT MARK THEM, AND HAVE NOTHING WHATSOEVER TO DO WITH THEIR IMPLEMENTATION; I HAVE NO INSIDER-KNOWLEDGE TO GIVE YOU; what I write here is MY interpretation. I might be completely mistaken.

So, here’s an example, straight off the exam (which you can access from www.nzqa.govt.nz – just do a search on ‘scholarship physics’).

"A television safety advertisement features a car taking corners at dangerously high speeds. The danger is symbolised by land-mines appearing scattered around the corners. As the vehicle approaches a corner, the voice-over says ‘There is more force taking you off the road and less force keeping you on it.’ The car skids across the road and rolls over an embankment. Discuss the accuracy of the voice-over statement, with reference to centripetal force and friction."

First of all, what a lousy presentation of physics. Why didn’t I blog about that when the advert was showing? Anyway, in terms of the question, it gets to the heart of what happens with circular motion. The student really needs to show they have grasped what goes on when a car travels round a curve, that there is centripetal force on the car towards the centre of the circle, and that this force is provided by friction between the tyres and the road.  A common misconception is that centripetal force is somehow generated by an object moving in a circle – that it is an ‘extra’ force in addition to all the other forces acting on it. It isn’t an extra force – it is simply the resultant of summing all the forces acting on the car. The car is accelerating towards the centre of the circle, therefore the net force on it must be towards the centre.

So…the statement is wrong on both counts. First of all, there is no force ‘taking you off the road’. Secondly the force keeping you on it actually goes up at high speed – it’s the frictional force between the tyres and road. But take the corner at too high a speed and the frictional force is no longer adequate to keep you on it – and you go sliding. 

If you don’t really UNDERSTAND centripetal force and circular motion, you don’t have the slightest chance of answering this question. By understand, I don’t mean being able to say F = m v^2 / r, but I mean knowing physically what causes something to move in a circle. Our centripetal force equation is easy to write, but not so easy to grasp.

 

 

Teaching: Theory or practice? Marcus Wilson Aug 07

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I’ve just finished reading a nice little article by Linda Leach, of Massey University, on the engagement (or lack thereof) of tertiary teachers with education theory.  She’s interviewed f tertiary teachers and has identified a number of ways that teachers understand ‘theory’.

First, it’s very clear that ‘theory’ means different things to different people, and with the article comes a plea for educators to be more precise about what they mean when they use the word. She’s considered four different broad interpretations of the word: 1. As the obverse of practice, 2. As a Generalizing or explanatory model, 3. As a body of explanation, and 4. As scientific theory.

What’s clear is that many teachers take the view that theory is the opposite of practice. Since, in teaching, it is clearly the practice that matters (since it’s what the students experience) this leads to the conclusion that  theory is irrelevant and there is no benefit in engaging with it. Leach says "Few of [those] who avoid theory seem to understand theory as either personal or practical"

The fallacy is the implicit assumption that theory and practice are unconnected. (I mean, you don’t have experimental physicists and theoretical physicists working in complete isolation from each other, so why expect that with teaching?) What you believe about student learning will influence the way you teach, whether you formally acknowledge it or not. That’s become clear for me as I think about my teaching practice. I have my own ‘beliefs’, or my own models, call them ‘theories’, of how students learn, and these influence how I teach. Formally looking at teaching ‘theory’, though the Postgraduate Certificate of Education, has helped me to identify what my beliefs and philosophies really are, and how these have changed since I’ve been teaching.

For example, In Pratt’s terminology (1998) I take a ‘Development Perspective’ of teaching – that is, challenging a student’s way of thinking about physics – having him or her try to interpret what they are seeing, reading, etc., and build a model of physical understanding that works. That in turn influences the way I set assignments, for example, and how I organize and run lecture and lab sessions.  But this isn’t where I started from – in the beginning I was much more towards the ‘Transmissive Perspective’ – where I held the body of knowledge and it was my job to pass that to the students. A different belief / theory about teaching and learning, which was accompanied by different practice. Identifying what my internal biases are as a teacher (what theories I hold to) is an important step towards improving my practice.

Theory does influence practice, whether you recognize it or not. So it’s a good idea to have at least a glance at it, from time to time.

 

Leach, L. (2011). Tertiary teachers and theory avoidance. New Zealand Journal of Teachers’ work. 8(1), 78-89.

Pratt, D. D. (1998). Five perspectives on teaching in adult and higher education. Florida: Krieger.

 

 

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