Quantum Physics – with a Coin

Find a coin.

Go on, rummage in a pocket, purse or wallet and find something a reasonable size like a UK 2p or 10p coin, about 1 inch or 2.45cm in diameter. This is all you need to explain quantum physics to someone.

Yes I did just say quantum physics. Surely that’s only for geniuses you cry! Quantum physics is a subject that intrigues and is hopelessly misunderstood in equal measure. This little demonstration will really impress your friends and explain all the basics of quantum physics in simple language. Let me show you how.

I’m assuming you can toss a coin. Throw it up and catch it then slap it down on the back of one hand. Did you get heads or tails?

Quantum Physical States and Probability

The only outcomes possible in a coin toss are heads or tails. You can balance a coin on its rim if you are careful and have a flat table, but that outcome never occurs in a coin toss, due to the slapping-it-flat-on-the-back-of-your-hand action.  There is no way to get heads and tails at the same time as they are on opposite sides of the coin. So I’m going to go ahead and say that the result of a coin toss is one of two possible states, either heads or tails.

Toss the coin a few times and you’ll find out that the number of heads and number of tails usually balance out. You should have an unbiased coin. This would mean the chance of getting a head each time you toss is the same as the chance of a tail, 50:50 chance of either state.

What if we suspected one side had been weighted and so the coin was biased? Tossing the coin hundreds of times would give us a very reliable way of finding if it had been tampered with. The numbers of heads and tails should balance out. If 40% of the time the coin’s state was found to be heads and 60% tails we know it is biased towards tails.

Tossing the coin allows us to find out information about what states are possible and what is the chance of ending up with any one of those states.

Now we’ve established that, what state is the coin in before you catch it?

You might say “no state” but that would mean there was no head-ness or tail-ness there at all, nothing. That’s not quite right as the coin is there. You can see it spinning in the air. How do you describe that?

 

Superposition in Quantum Physics

Quantum physics has a neat word for describing the mixture of head-ness and tail-ness that a spinning coin has before you catch it. The word is superposition. Superimposing is a technique used in photography or film where one image is put on top of another. The final image is a composite of the two. Superposition is a bit like that.

The spinning coin is not devoid of states, we can’t say it has no heads or tails to it. Instead it is a constantly changing superposition of the two states. This superposition tells us nothing about what state this unique toss will end in. That depends on all sorts of things like how fast it is spinning, how high we throw it, when we catch it etc. It won’t help us work out the outcome of an individual throw.

The superposition does contain information about any bias in the coin. As it spins, a heavier side to the coin will spend more time at the bottom of the spin and the lighter side would spend more time at the top. There is some information there we could extract about how the pattern of heads and tails would look after 100s of throws, if only we had a way of measuring it.

 

Taking A Quantum Measurement

You already know how to measure the state of the coin. You catch it and slap it down on your hand. Look at the coin and there is your measurement.

But this involves permanently altering the condition of the coin. You are forcing it into one of two possible states. When I measure my height I don’t force a mixture of all possible heights into 5 foot 10 inches. There is no probability of getting anything other than 5’10”. This measurement of the coin is different to normal measurements. The act of measuring the system we are interested in (the spinning coin), fundamentally alters the system we are interested in. Bummer.

There is no way around this I’m afraid. To get information about the possible probabilities of either heads or tails we toss the coin 100s of times. Then we interfere with the spinning superposition each and every time, forcing it into a single state. Only by repeating this measurement over and over do we get enough data to work out a pattern.

This is true of quantum objects like electrons. It is called The Measurement Problem. Only in quantum physics does the act of measuring the system permanently change the system. Or to put it another way, extracting information from the superposition destroys it. This is called collapsing the wave function.

What is a Wave Function?

Waves bob you up and down in the sea or make use of your hand to signal your departure or arrival. In both cases something is oscillating between two positions over and over. Up and down on the sea and side to side with your hand.

Lots of natural phenomena can be described using the language of waves. The variation in light intensity due to day and night, seasonal mean temperature changes, hormone levels in menstruating women, anything which has a repeated variation across a range of values is wave-like.

Physicists use the mathematical language of waves to describe quantum states. The spinning coin has a repeated variation in a range of values, it flips from heads to tails and back again as it spins. We can use wavy maths to describe this variation. The mathematics of waves is even more helpful as it allows us to add waves on top of each other and work out the resulting wavy shape. Like different tides or ripples interfering with each other at a point on the sea.

The spinning coin has a changing superposition of the heads and tails states. The chance of measuring either state depends on which way up the coin is pointing when you catch it. As the coin rotates it is found in a 100% heads state only once each rotation and only for a very short time, likewise for the tails state. The the rotation moves one side of the coin slightly higher and the amount of “heads” reduces slightly and the amount of “tails” increases. Or more correctly the probability of getting heads reduces slightly and the probability of getting tails increases slightly. So the chance of ending up with heads or tails is continuously changing as the coin rotates. If you plotted the probability shape on a graph it would rise and fall and rise and fall just like a wave.

The wave function is the name given to a mathematical wave shape which describes this varying chance of getting a particular state in a measurement.

Collapsing the wave function forces a single state on the coin, in this case either of the extreme positions, giving a head or tail.

 

Now the Quantum Physics Bit!

All this talk of coins is preparing us for the big moment to tie all this in with teeny tiny quantum particles.

There is an experiment which shows exactly what we have been talking about with coins, but with electrons. It’s called the double slit experiment. It is the classic way of introducing people to the weirdness of the quantum world. Electrons behave like a wave superposition of states until you force a measurement on them and then they behave like a lump with a fixed state.

Instead of throwing electrons up and down and catching them with some clever laser trap equivalent of a coin toss (or something!), the electrons are thrown at a screen. The screen can detect the hits from the electrons and emit a tiny light burst. So a pattern builds up showing where the hits occur.

When you shine a wavy source, like a torch, on a screen you get a bright spot in the middle and it gradually dims as the light spreads out at the edges. If you fire a lot of blobs at a screen there is a big build up of bobs in the middle and fewer out to the sides. It is hard to tell one result from the other.

So the physicists put something in the way of the screen. A big sheet with two narrow slits in it.

quantum double slit experiment

Diagram of the double slit experiment from Wiki-Commons

Now you can tell the difference between the pattern produced by wavy things and the pattern produced by blobs. Waves overlap and produce a new wavy pattern as shown in the picture above. The blobby particles are simply split into two streams of blobs by the slits and produce two splats on the screen. No superimposing happens for them.

Electrons are supposed to be blobs not waves. They are particles. When a beam of electrons is fired at the slits they start to build up a pattern on the screen. The pattern is a wavy interference pattern!

quantum double slit interference pattern

Each dot represents the impact of an electron on the screen. Many hits build up to produce an overall wave interference pattern, even though electrons are particles. This is evidence of the wave-particle duality of electrons. Experiment performed by Dr Akira Tonomura in 1989 at Hitachi. Creative Commons ShareAlike licence.

Here we are looking at information contained in the wave function of the electrons. Only when hitting the screen are they being forced into a state. Then their position state is fixed to a definite value. Just like the coins spinning in the air contained information about the probability of heads or tails, so the electrons shooting towards the screen contain information about the probability of where they will show up in the interference pattern.

We can collapse the wave function earlier on and force the electrons into a position state much sooner if we measure them. We can put a sensor on the double slits and record which slit the electrons go through. This destroys the supposition of location states and forces the electron to be in the left or right slit. Like catching a coin destroys the supposition of heads or tails and forces the coin to be one or the other. Then the electrons behave like blobs and build up in two patches on the screen. The waviness of the electrons has been lost.

This experiment was astounding. To actually see the theoretical wave nature of the electrons supposition and then be able to collapse the wave function and bring their blob nature back again has boggled many a mind over the years. Tiny particles can be waves or can be blobs depending on how they are interacting with their surroundings. Some interactions collapse the wavy behaviour and force the electrons into a fixed state. What we understand as measurements always collapse the wavefunction because our measurements require a value, a fixed state to give a result.

Conclusion

Tossing a coin will never look the same again! Each time you catch a coin you can think about how every photon of light hitting your eyeball has just collapsed its wavefunction, every click of the TV remote, every interaction of microwaves with food in your kitchen is a quantum measurement happening in front of you.

Now we need to talk about Schrodinger’s Cat…

schrodinger's cat experiment

A thought experiment proposed by Erwin Schrodinger. Picture from https://www.nobelprize.org/educational/physics/quantised_world/

Don’t Teach from Definitions! Just Don’t.

frustrated student

I settled down to watch a TV programme about schools, “Living with the Brainy Bunch”. It’s not something I would normally do having worked in schools for 13 years, a bit too much of a bus man’s holiday. The premise of this show was, however, intriguing. Two failing students were going to spend time living with a top grade student and their family to see if this would improve their prospects. How very Pygmalion. I was genuinely interested to see what the outcome would be.

But then in the middle of the documentary I found myself shouting at the TV screen. A teacher in the background of one scene committed the cardinal sin of physics teaching. The title of the lesson and aim were up on the board and the first thing they did was say “this is Ohm’s Law” and wrote it down, V=IR. Noooooooooooooo!

 

What is Wrong with Definitions?

There is a wealth, a plentitude, an embarrassment of research which clearly shows that rote physics teaching achieves poorer results in the short, medium and long term compared with active learning. This article published in Nature in 2015 summarises developing thought on the subject.

The rote style of teaching is adopted by people rushed for time, overly reliant on the exam specification or who don’t know what good physics teaching looks like. It makes for lessons which are instantly forgettable and do nothing to develop the students’ understanding. And understanding not parrot-fashion learning is crucial. The bread and butter basics of physics teaching should be understanding and thinking skills.

Charles Tracy and Peter Main from the Institute of Physics wrote an article called “Defining physics”[1] and have suggested a rather long winded but none the less instructive way of thinking about what physics actually is. Peter Main outlines his definition of physics as

a way of thinking, a reductionist view of the world where phenomena can be understood in terms of a relatively small number of physical laws and limited only by the complexity of a system or phenomenon. [2]

He argues that defining physics by its content misses out the crucial ways of thinking that studying physics should develop (when done correctly). Why develop these ways of thinking? Because you can’t DO physics in any effective way at all without developing these ways of thinking. Tracy and Main include critical thinking, deep understanding, logical and experimental consistency, use and development of models, awareness of simplifications, the excising of prejudice in thought patterns and ability to go beyond “common sense” in their list of physics skills. None of these are being taught or practised when teaching is done by copying a definition in words and symbols and then applying it to examples.

Teaching from definitions is teaching content only, and in the most dry and uninteresting way. You remove all thinking for the students and present a fait accompli. Effectively you are conveying this message “some other smart people came up with this, I’m not going to tell you how, just shut up and learn it OK?”. You do this and you are a disgrace to the profession.

Telling a student an answer, e.g. plug it in V=IR, and you enable them to solve a single set of simple problems. Explain to them how and why V=IR came about and they have an understanding that will enable them to solve many problems. Allow them to discover the relationship for themselves and work out how to use it and you’re a bloody genius. This is what we should all be doing in our classrooms.

 

Teaching from Definitions and the Impact on Girls

Teaching from definitions is stated by female students as one of the things which turns them off physics. This was an interesting outcome from the research “Girls in the Physics Classroom”[3].  From that publication note this particular quote:

Physics makes greater use of precise technical language and symbolic representation than the other science disciplines – probably than all other school subjects apart from mathematics. Most physics teachers are steeped in the use of, and sometimes the abuse of, this type of language. For example, it is not uncommon to hear “V = IR” used to denote Ohm’s law. For many pupils – boys and girls – this use of language and symbols is mystifying and it reinforces the impression that the subject does not connect with their world. Teachers who “talk equations” at an early stage in physics education risk alienating many students – girls in particular – from the subject.

The author goes on to say how pupils at KS4 begin to heavily link maths to physics but not because they are frequently using maths in analysing data or solving problems. No they get used to being presented with equations out of a useful context.

“It’s all about remembering equations. I can work out the resistance of a wire but I don’t know what it means.”

 

Girls especially found that this was a problem because they felt unable to “ask questions about a word or equation” and so felt that their understanding was stalled. Teachers who only introduced equations once the underlying concepts were well established were able to keep girls’ interest for longer.

It is important to understand that the reluctance of girls to engage with technical shorthand language is not a result of their reduced understanding. Indeed the author stresses that when questioned by the researchers the girls had an equal understanding to their male peers. Historically girls outperform boys in GCSE science including physics. In 2016-2017 169,455 girls achieved A*-C in maths and science GCSE compared to 163,256 boys [4].

The difficulty appears to be cultural. Boys are cultured to use technical language and be rewarded with peer status and the approval of older authority figures when they do. Think about how boys discuss football stats or the specifications of their mobile phones, cars, computers. They spend years developing a confidence with numerical shorthand and technical language in competitive communications with their peers. Girls are socialised to use more expressive and empathetic language. I can’t tell you how weirdly you are treated as a young woman if you try having a conversation about the amount of memory, processing speed and other specifications of a tablet, laptop or phone. Bafflement not at the content of the conversation but at my motivations, awkward silences and “what is wrong with you?” are all responses I have had when trying to talk geek to other girls.

When a teacher uses technical language and algebraic shorthand in a physics class they are unwittingly displaying a bias in favour of one gender. The use of a snappy V=IR shorthand feels instantly familiar to boys. Girls aren’t familiar with this way of speaking and seem uncomfortable with using it, holding back their replies. Then a boy shoves up his hand or calls out and gives a terse one word reply, the teacher accepts it and the lesson moves on. But you have lost the interest of the girls. Overtime this communication bias leads them to give up on answering questions in class. They feel less able to access the lesson and join in the teacher-pupil conversation.

The advice from the report was as follows:

Teachers, both male and female, in the most successful schools made more sparing use of technical language, used terminology in context and avoided algebraic shorthand. They used everyday language wherever possible and, where terminology was needed, it was carefully defined and pupils’ understanding was checked…

 

…The guiding principle was to establish ideas and concepts before the use of terminology or equations.

Once understanding is established the teachers introduced the terminology and rigorously policed its correct use. No sloppy reference to “electricity” when “current” is the word required.

It can’t be overstated how much the use of language effects students studying science. Too much technical jargon and it feels more like a foreign language lesson than something relevant to real life. As one girl in the report says:

“If physics is relevant then we ought to be able to talk about it using normal language. I used not to ask questions because I didn’t know how to put them – I didn’t have the right words. [Teacher X] doesn’t mind this and encourages us to have a go. If we use the wrong words [Teacher X] doesn’t correct us or make us feel embarrassed.”

We need to make our lessons as inclusive and easy to comprehend as possible. That doesn’t mean leaving out technical scientific terms. It does mean developing the understanding first through direct experience of the phenomena and its applications then slowly building in the correct language and algebraic shorthand once this is established.

 

The Importance of Discussion, Analogy and Relevance

Before students can develop a facility with technical language they need to have a handle on the topic. This means discussions about the uses and phenomena associated with the topic. How discussion is done in a classroom can vary. Little or no discussion takes place in rote lessons. The teacher asking a closed question “what is ….” and getting a terse response is not discussion.

To aid context and understanding students need time to explore what they know about a topic amongst themselves. Small group discussions work well when combined with the requirement to produce a group response or an answer on a small white board. Questions like “What is it about electricity that makes it so useful to us?”; “What happens when we turn a light switch off?”; “Why do we have to have a system of pylons and cables around the country?”; and “Why can’t we store electricity?” are so much more useful than “what is the definition of current?” [3].

This discussions and group responses can all occur using ordinary language. Then the teacher can lead the whole group in the development of these ideas. “Why can’t we store electricity?” is bound to lead to a discussion of the role of a battery in a circuit. From this charge separation, electric fields and the transfer of energy through the movement of charges in a wire can all be demonstrated and explained.

Mental images of what is going on are very useful, particularly in some topics. Electricity is notoriously lacking in direct visual input, and so requires a suitable analogy. All students benefit from this but teachers need to be careful they don’t use out of date or again biased examples. As one female student says “I’m not interested in how Beckham bends a ball or what the acceleration of a Ferrari is – why should I be?”. An even better approach is to see if students can devise their own analogies. All of this aids understanding and model building before any equation needs to be introduced.

I would leave equations until after the students have done an experiment or seen a demonstration where the relationship of interest is clearly shown. It is so much easier to infer and remember a result from data you have collected yourself. Set up a simple circuit with a resistor. Take some readings, plot a graph, draw a gradient. Then introduce Ohm’s Law.

Lastly, understanding is aided when physics is contextualised. It is a mistake to assume all students want modern, real world examples when asking for relevance. What is relevant can vary from person to person. It is enough to say that a topic is relevant because it helps explain X, Y or Z. Or maybe it connects with some wider moral or philosophical issues (origin of the Universe), some ethical argument (use of nuclear power), even a conspiracy theorist’s misunderstandings (climate change). They may well want to hear about applications of this topic in their daily lives but they also like to know about applications beyond their limited experiences. Sometimes it is relevant because it is the pathway to a desired career goal, relevant in a pragmatic way. If you wish to study architecture, physics can be relevant even if not everything is about the construction of buildings.

 

The Death of Definitions

I started out by saying teaching from definitions is a method used by rushed teachers, those reliant on the specification and those who don’t understand how best to teach.

What if you are rushed for time? The curriculum demands increase year on year and sometimes cramming triple science GCSE into a double science timetable requires corners to be cut. So cut the definitions. Teach circuits with circuits even if you have to demonstrate rather than do a class practical. Get students to take the readings with you, volunteers can write the data up on the class board. They can still work out the relationships you need individually and they will learn as they do.

People are often told “don’t teach to the specification” I think this doesn’t go far enough. Some people actually teach the specification. There is nothing wrong with using this document to guide your lessons but you don’t get students to work through 3-4 points from the spec each lesson. It is a check list to ensure you cover each point, not an instruction manual. Teaching from specification or textbooks indicates lack of confidence.

The best remedy to lack of confidence in physics teaching is to find out how to teach the subject from an expert. Buy a good book, enrole on a CPD course or get support from physics specialists in your school or online, for example TalkPhysics.

Or you could keep reading the articles on here, The Physics Teacher.

 

References

[1] Main, P. C. and Tracy, C. M. (2013) “Defining physics.” Physics World, 26(4), 17–18

[2] Main, P.C. “Thinking Like a Physicist: Design Criteria for a Physics Curriculum”  Schools Science Review March 2014, 95(352)

[3] “Girls in the Physics Classroom” 2006,

[4] https://www.gov.uk/government/statistics/revised-gcse-and-equivalent-results-in-england-2016-to-2017 viewed 14/7/2018

Work Done in Physics

work done example - cable car

Work done is a boring topic. It is the very definition of a boring topic, even the name of this physics concept is dull. The word “work” doesn’t exactly make you jump up with excitement in the same way as “explosion” or “play” might, does it?

The definition of work done also seems very arbitrary, force x distance. Why? Why should we care about something defined as force x distance? Then you are expected to rote learn that work done is measured in joules, the unit of energy, but it’s not an energy store because it’s work done. Got that? This is just confusing to the average student.

Often work done is taught along with a demonstration of something being lifted up like the ski lift in the picture. Maybe the class sets out to find the work done by a person climbing stairs by firstly weighing the person then finding the height of the staircase. You are informed that motion in a horizontal direction doesn’t get included, no work done walking across the room. This contradicts the common experience of getting out of breath when walking quickly. Surely I’m doing work? The term work done also crops up in electrical circuits too where there are no stairs. None of it ties together very well. Ask for help from a teacher and the reply is usually, “that is the definition of work”!

There is an way to think about work done which makes a whole lot more sense! Imagine for a moment that we are stepping into a chapter of the brilliant series Horrible Histories, I would like to take you back to the Industrial Revolution.

 

Pit Ponies and Barges.

Back in ye olden days when there were no motors or even steam engines, heavy things were moved by teams of people or horses. Horses were used in mines to haul carts full of ore and coal, and to pull things up from the mine to the surface. Barge horses were used to pull canal barges laden with goods along canal ways.

winching children into a mine shaft

Two children are lowered down the mine-shaft to the coal- face by a woman working a winch Date: 1842 Source: ‘The Condition & Treatment of the Children employed in the Mines & Collieries of the United Kingdom’, page 7

And yes just like in Horrible Histories, young children were hand cranked down dark mine shafts to chip away at coal and mineral ores in polluted air with nothing more than a candle for company. Makes double maths look slightly more appealing.

 

winding horse whim

A sepia photograph of a winding-horse whim from Wheal Geevor Tin Mine copyright of Geevor Tin Mine and Pendeen Community Heritage, permission given for education use.

 

canal barge horse

A working canal barge with horse pulling the barge along, approx 1900

Then came the invention of steam engines and machinery to automate this process. It was important for the new industrial engineers to be able to explain their machines in a language that the mine owners could understand. They used the term “horse power”. This is the machine equivalent of the work that could be done by an average horse. Horses being more useful than small children.

Do you notice how the term work done slipped into that sentence? What work was being done here? In each example a heavy object is being pulled some distance by a horse. Pulling is an example of a force. The depth of the mine shaft, the length of the tow path, these are distances.

Now the definition of the work being done by the horse makes a bit more sense. The horse has to do some physical work to move an object a distance along or up. The horse has to pull, so there is definitely a force involved. In the mine the pull is upwards to overcome the downwards pull of gravity. On the towpath the pull is forwards, but what is the horse pulling against? Not gravity this time. The horse pulls against the water as it drags the canal barge forwards.

So the work being done by the horse is the result of the force it has to use to move the object and the distance it has to be moved.

A machine like a steam engine would need to be as good as, or better than, the work that could be done by a horse. That would make the steam engine attractive to potential buyers.

 

Defining Work Done

The term work was first adopted in the 1820s. There is a reference by the French mathematician GaspardGustave Coriolis in “Calculation of the Effect of Machines, or Considerations on the Use of Engines and their Evaluation“. He used it in the sense of a “weight lifted through a height”, from  the use of early steam engines to lift buckets of water out of flooded ore mines.

A “weight lifted through a height”, was also the way Sadi Carnot defined work in his famous paper Reflections on the Motive Power of Fire in 1824. Carnot said:

We use here motive power (work) to express the useful effect that a motor is capable of producing. This effect can always be likened to the elevation of a weight to a certain height. It has, as we know, as a measure, the product of the weight multiplied by the height to which it is raised.

Now hopefully you can see how work done = force x distance was a really useful quantity to a Victorian engineer.

A horse hauls 500kg up a 20m mine shaft. What is the work done by the horse on the load? (take g = 10 m/s^2)

 

A barge horse is pulling a barge with an effective mass of 8000 lb along a river for 1km. 1kg = 2.2lbs. Covert the weight to kgs and calculate the work done by the horse on the barge.

 

A steam engine can do the work of 4 horses. One horse can move 600kg a distance of 3km in 1 hour. How much work can each horse do? How much work does the engine do in 1 hour? What is the power (joules per second) of the steam engine?

When something moves it has kinetic energy. By doing work the horse is getting some heavy object to move. No movement and no work has been done. If the thing doesn’t budge, even though the horse might be straining all its muscles, in the strict physics sense no work has been done.

Giving these heavy barges and piles of coal some kinetic energy is what the horse is for. The horse’s store of chemical energy in its muscles slowly runs down while the heavy barge’s kinetic energy store slowly fills up. There has been a transfer of energy from one to the other through the action of the force. Work done is an energy transfer process. It is not a store of energy but a way of showing energy in flux. It is an amount of energy going from something that exerts a force to make something else move. This is why it is measured in Joules. It is the amount of energy being reduced in the horse to make the kinetic energy of the barge increase.

Amount of energy reduced in horse = amount of energy gained by barge = work done by pulling.

The work-energy principle basically sums up what this red equation says. An increase in the kinetic energy of an object is caused by an equal amount of work done on the object by the force acting on the object.

Work done fits nicely into our ideas about the conservation of energy. It allows us to explain why energy isn’t lost or destroyed by the horse when we get something moving. The changes in energy are a measure of the work being done to move the thing.

 

Generalising the Concept of Work Done

Physicists are practical people. If they come up with a new idea then they are going to look for different ways to use it. This makes life easier as you then have fewer laws of physics to learn. In fact some physicists devote their lives to finding the fewest number of rules you can have to describe the interactions of all things.

Theory of everything cartoon

Calamities of Nature cartoon Strip from 2012

Work done gets taught to school students because it is one of those concepts which has lots of practical applications. It can be used in many different areas of physics. Any time a force is acting on something and it moves you can say work is being done.

Hopefully you can see how work done by a horse depends on a force (due to the horse pulling on a weight) and a distance. To make this more general we can remove the horse altogether. Imagine a force acting on something that moves that thing some distance. We don’t need to worry about the actual object doing the pull (or push). We only need to think about the force involved and the distance moved. When the force only pulls in one direction we only include movements that are in that direction in our calculation of work done.

How about a tractor beam from the Death Star pulling on the Millennium Falcon? Or a magnet pulling the cover of a bag shut. Or a strong wind propelling a windsurfer. Or the negative end of a battery pushing away negative electrons in a wire?

A force of 50 newtons acts to move an object 2.5m. What is the work done by the force on the object?

From this more general way of thinking we can jump across to other areas of physics. The only thing that changes is how we come up with the value of the force. In the case of ponies and mines we use weight, a force equal to the mass x the pull of Earth’s gravity. In a different situation the force could be due to electromagnetism, gas pressure, radiation pressure, pretty much anything that can exert a force and cause a movement.

 

Electrical Work Done

Electrical work done, or electrical work for short, is the work done by an electric field on a charged particle which causes the particle to move.

The electrical field in a circuit is produced by the battery. Inside the battery charges separate out towards a positive terminal and a negative terminal. This separation of charge results in an electric field between the positive and negative charges, just like the magnetic field between the north and south poles of a magnet. The electrical field fills the space between the two terminals. To make use of this electric field hold it in a loop of conductive wire. This is a circuit.

This electrical field does work on the free electrons in the conductive metal wire. The electrons move as a result and this average drift of the electrons along the wire is what we call current.

Electrical work done = force from electric field x distance charge moves

In this way chemical energy that was stored inside the battery is reduced and the kinetic energy of the electrons in the wire is increased as work is done on them through the action of the field. This is how batteries run out. Eventually the battery exhausts the chemicals inside it and not enough charges can be separated out to maintain a strong enough electrical field to exert a force on electrons in the wire.

An electric field due to a battery exerts a force of 6×10^-18 newtons on an electron in a 30cm wire. There are 2.5×10^28 free electrons in the wire, what is the total work done to move all these electrons through the wire?

 

Thermodynamic Work Done

There was a famous experiment done by the British scientist James Joule which links the work done by a weight moving through a height, to the heat energy gained by some water. It is regarded as one of the starting points of a whole branch of physics, thermodynamics. Thermo for heat energy and dynamics for how heat is exchanged between systems and their surroundings.

James Joule heat engine

The apparatus used by Joule in his famous experiment

The apparatus is ingenious. By rotating the paddle and transferring energy to the water through friction, Joule was planning to measure the heat energy gained by the water. I always find this astonishing. When I first learnt physics, I had no idea agitating water would heat it up! I always thought of stirring things to cool them down but that is a different process (evaporation) altogether.

Joule figured out that linking the rotating axis of the paddle to a string and pulley system  meant he could lift a weight up at the same time as rotating the paddle. He slowly wound the weight up high, let the system settle and then released the weight. As it dropped, it rapidly turned the paddle and the thermometer reading went up. He was relating an increase in temperature to the work done moving a mass.

Work done to lift weight = energy needed to rotate paddle = energy gained by water

Joule used this to define the mechanical equivalent of heat. Now any change in temperature of a system could be given a number relating it to work done. Work could be done to a system or by a system. This was fantastically useful in the time of steam engines, with their hot boiler tanks, pressurised gases pushing mechanical parts around causing motion.

When we use the word “system” in physics we mean whatever object or objects are being affected. It could be a boiler filled with water turning into steam. The entire thing, container, liquid and gas would be the system. Energy would be supplied to the system through a fire heating the boiler. It would be transferred out of the system through heat loss and the steam escaping to push a turbine or piston.

Work done in thermodynamics is the energy transferred by a hot system to its surroundings. The amount of work done by this system is found from the effect it has on its surroundings. So if a system of hot gas expands and pushes on a piston the work done is defined by the movement of the piston caused by an expansion of the gas.

heat transferred into a system = work done on surroundings + heat left in the system 

Concluding Work Done

Work is such a useful and big concept. We have barely scratched the surface here. The main points to take away are

  • Work done is a way of transferring energy from one store to another.
  • As a sort of energy in flux, it is also measured in Joules.
  • Work always gets things moving, its results in an increase in kinetic energy of something.
  • It doesn’t matter what sort of force is acting, so long as it makes something move.
  • The movement can be as general as the pressure of a gas pushing on its surroundings.
  • All calculations of work done reduce to force acting x distance moved.

 

Answers to Questions

A horse hauls 500kg up a 20m mine shaft. What is the work done by the horse on the load? (take g = 10 m/s^2)

Work done = force x distance, force in this case is a weight of 500x10N = 5000N using the relationship weight = mass x g. 

Thus work done = 5000N x 20m = 100,000J

A barge horse is pulling barge with an effective mass of 8000 lb along a river for 1km. 1kg = 2.2lbs. Covert the weight to kgs and calculate the work done by the horse on the barge.

The effective mass is how heavy it feels to the horse to pull barge probably weighing tonnes along in water. The horse isn’t actually lifting the barge up so this isn’t the actual mass of the barge.

Force of barge in N = effective mass in kg x g = 8000 x 2.2 x 10 = 176,000

Work done = force (N) x distance (m) = 8000x 2.2 x 10 x 1000 = 1.76 x 10^8J

A steam engine can do the work of 4 horses. One horse can move 600kg a distance of 3km in 1 hour. How much work can each horse do? How much work does the engine do in 1 hour? What is the power (joules per second) of the steam engine?

One horse can do 600 x 10 x 3000 = 18,000,000J of work.

The engine does 4 x work of one horse = 4 x 18,000,000J = 72,000,000J in one hour

power = energy (J) / time (s) = 72,000,000 / (60×60) = 2000W

A force of 50 newtons acts to move an object 2.5m. What is the work done by the force on the object?

work done = force x distance = 50N x 2.5m = 125J

An electric field due to a battery exerts a force of 6×10^-18 newtons on an electron in a 30cm wire. There are 2.5×10^28 free electrons in the wire, what is the total work done to move all these electrons through the wire?

work done = force on one electron x length of wire x number of electrons

work done = 6×10^-18 x 0.3 x 2.5x 10^28 = 4.5 x 10^10 J

 

A Personal Study Plan – Personal Training for Your Brain

study

Last year I qualified as a personal trainer. It was a six week full-time course in a top gym. We spent a few hours each day doing physical activity but also spent lots time learning about the psychology of motivation and getting clients to stick to plans. After all motivating your clients is part of the trainer’s job. Motivating your students is part of your job as a teacher or tutor. Motivating yourself is a huge part of physical training or academic study. You need your own personal best-ever study plan.

 

Here I am posing with my fellow trainers after we finished the course.

There are big similarities between training your body for sports and training your mind for exams. You have a goal in mind, some strengths and weaknesses, various actions you can take to get stronger or faster in key areas, a timescale over which you need to train and set hours a week you dedicate to training. It makes sense that all the information out there about how to train your body can be carried over to form a great study plan to train your brain.

With this in mind, here is my Personal Trainer guide to study.

So Why are You Here? What is Your Study Plan Goal?

One of the first things a trainer needs to find out from a potential client is what they are hoping for. So what are your academic goals? Are you clear on that? Do you want to score over 80% in your final exams,  to get B,B,C and secure that university place, a level 5 in your maths GCSE to get accepted at sixth form? These are the sorts of concrete goals that you can structure a study training plan around. Wanting to please your parents or do better than your cousins is not a particularly good goal, we’ll discuss intrinsic versus extrinsic motivation later. These latter two goals also lack definite measures of success. Exactly how well do you have to do to “please your parents”?

Once a goal is identified, trainers try to match what they specialise in and what can realistically be achieved with what the client wants. This often involves a discussion about setting realistic expectations.

A 50 year old couch potato who last did exercise at secondary school will not be able to run a marathon in six months no matter how hard they want to. Likewise a D grade 18 year old who has no study routine and has bluffed their way through their A Level course is not going to get a A after six weeks private tutoring. You need realistic expectations.

What are realistic expectations for study? I was once employed to improve the performance of the physics A Level students in a school. The Year 12 students were underperforming according to their expected grades and they needed some help. In 12 months I brought up their grades by an average of 1.5 grades per student. One student went from an E to a B, one from an E to a C and so on. The two hardest working students stayed as they had been. So with one whole year of intensive help an underperforming student can pull up their grade to equal to or just above their expected grade. That is realistic.

If you have never been an A grade student and your teacher predicts you a C grade then you will most likely get a C grade. A B grade may be possible with a lot of extra coaching and work on your part, week in week out. You will not get an A*. Learning, much like training is a cumulative process. You don’t become a top gymnast or deadlift twice your bodyweight overnight, you need to have spent years doing the ground work. Logically we all know this when applied to physical skills but somehow people think it doesn’t apply to study: it does.

So step one of developing your study training plan is to set yourself a realistic goal with a realistic timescale.

 

How Much Time do You Have?

Now you have an idea of the client’s goal, as a trainer you must think about how much time the client has to devote to achieving it. People who work long, very involved hours, like a doctor or teacher, and have a long commute and family commitments cannot spend 2 hours a day training. You’ll be lucky if they have two hours a week.

Someone with a less demanding job, who works locally and is single, no kids could spend 2 hours a day training if they wanted to.

How about you? Full-time attendance at school is 8.30-3.30pm on average. You get 45 minutes lunch break and an evening free to do what you want. You aren’t finishing at 5pm with a 50 minute commute on top. Do you have a part-time job? This will take out some time. What about hobbies? I used to do 3 hours of dance a week all through primary and secondary school. It took 30 minutes to walk to the dance studio. All these sorts of things add up.

Work out exactly how many hours you could physically do between the end of school and your normal bedtime and then take off some hours for rest and relaxation. The remainder is the time you could realistically devote to studying, if you wanted to.

 

Are There Obstacles to Your Study Plan?

Believe it or not overcoming obstacles is an important part of a personal trainer’s job. We find out if the client has significant financial, emotional, practical problems that could interfere with their training plan. It is really important you think about this when preparing a study plan, not just to help write the plan but so that you can go easier on yourself. I wish I had known more about this as a young person. I had a horrendous list of obstacles to my studying which I only slowly became aware of as I got older. Here was my list (it looks bad, I’m warning you),

  • My family were financially hard up
  • My father had a drink problem, violent temper and mental health problems
  • There was no history of higher education in my family
  • I developed severe clinical depression at 16 and tried to kill myself
  • The antidepressants I was given affected my motivation and memory
  • I was bordering on anorexic and couldn’t sleep properly
  • Years of abuse had left me with PTSD
  • I spent most days numbed out in a state of dissociation
  • I had no access to books or tutors outside of school
  • My parents had very low expectations
  • I was in the early stages of developing an incurable autoimmune disease
  • No one in my school knew any of this

I told you it was bad. For years I beat myself up because I didn’t achieve my predicted grades at A Level; I got a A and 3Bs instead of 4As. I feel stupid typing this because as a woman in her 40s looking back on this I am bloody amazed I got anything at all. So yeah, there can be all kinds of significant obstacles to you being able to study effectively. Money, abuse, racism, disability, lack of role models, low family expectations, lack or resources, no room for you to work in, noise in the house, babysitting responsibilities, illness, medication, mental health problems, relationship problems, eating disorders, local economics, unemployment of a parent, etc, etc. Go and look up Adverse Childhood Experiences (ACEs), white privilege, male privilege, straight privilege and educate yourself in the ways our society can personally and structurally disadvantage some people.

That doesn’t mean give up! It doesn’t mean loose hope and throw in the towel. I was the first person in my family to graduate university which I did with a first class honours degree despite having been rushed to hospital three times over four years with complications to the autoimmune disease I developed.

But it does mean be realistic about what obstacles you face, because then you can find ways to tackle them and get on with your goal.

 

Making a Personal Study Plan

You know what you want, how much time you have a week until your goal needs to be achieved and you have a handle on what might get in the way. Great! Now you are all set to plan away.

Do you know what a Gantt chart is? It’s a project management plan used by engineers. Here’s an example:

Example of a Gantt chart – BBC Bitesize Revision

You need to construct a week by week plan like this which says what you are going to train that week (maybe practise rearranging equations) and when you will do it. Here is a marathon training plan:

Example personal training plan for a marathon – ActiveEdge Fitness and Sports Performance

Do you see how they are similar? Personal training plans assume that you have a dedicated time slot, Tuesday and Friday afternoons for example, and then describe what exercises or practises you will do each week for a few weeks, 6-12 weeks usually. Then progress gets checked and the next block of weeks have harder or different exercises. Do this. Choose your dedicated time slot. Work out the intermediate steps topic-by-topic towards your chosen goal.

Use your teachers to help you if you are finding it hard to figure out what the steps should be. Textbooks are set out in a way that puts the basic concepts first then slowly builds on them. Use a textbook to help you breakdown a subject into smaller pieces. Start with the basics first. Be realistic and don’t timetable 6 hours a week if you have difficulty doing 30 minutes homework a night. Just like training your body, you have to build up to longer times. Start with 10 minutes a day if that is more then you are doing now. Add 5 minutes more a week. Soon you are doing 30 minutes a day every day and that is fantastic!

 

Checking Your Progress Along the Way

Maybe you want to get better at answering GCSE electrical circuits questions. How will you know if your plan is actually working? You need to measure yourself against your personal best like an athlete would.

Choose a set of past paper questions from a website (here or here for example). Test how much you score at the start of your chosen time block, let’s say a fortnight long. Then study this subject. Retest yourself on a new set of questions two weeks later and see how you have improved. Mark schemes are available on the two websites I linked to. This is how a trainer would work with a client but with barbells and squats not questions on resistors in series.

Work out what % of questions you are getting correct. Now you have actual measurements and you can follow your progress. You could even plot them on a graph and stick it on your wall (motivation, right there) with a horizontal line at the level you want to reach so you can see yourself get closer and closer. Maybe your goal is a B grade and 60% correct is a B, so draw your line there.

 

Reward Yourself for Progress

This is so important. Studying for exams is hard, emotionally draining work. It involves a daily struggle with self-belief and disappointment and setbacks when you just can’t get a particular topic right. You must reward yourself along the way. Little treats can make a big difference. You can reward a treat for reaching a certain number of hours studied, reaching a certain mark, finishing a particular topic. How you set a mini-goal or checkpoint is up to you.

A CBT (cognitive behavioural therapy) practitioner I worked with once had a sliding scale of rewards that matched an increasingly demand scale of goals. Start with an easy step on your study plan and reward yourself with a little treat. For each harder step, increase the quality of the treat. Have something really special saved for achieving your final goal.

Here are some examples of ways you can reward yourself.

Little treats:

  • 30 mins of favourite computer game
  • chocolate bar
  • watch favourite movie
  • new bath bomb and 1 hour in the bath listening to music
  • football down the park with your friends

Medium treats

  • trip to the cinema
  • buy the new top you’ve had your eye on
  • download a new album
  • weekend trip into town with friends

Big treats (may require adult agreement)

  • big night out with friends
  • sleepover with best mate
  • shopping trip with bank of mum and dad
  • few days away on a mini-break
  • new phone/game console/”desirable gadget of choice”
  • driving lessons

OK so you get the idea. When you meet a target, go ahead and treat yourself, it really boosts motivation.

 

Overcoming Obstacles

You remember my horrible list of obstacles to studying which sort of f***ed up my GCSEs and A Levels. Yes, we need to talk a bit more about how to overcome stuff like that.

Pick an obstacle to your study plan that you could have some success with (getting my father to change was not something I could have had success with). For examples; not having access to textbooks. Now think about how this could be overcome. Brainstorm it. I could have asked my teacher to borrow one over the weekend or asked the school librarian for a copy, if they didn’t have one I could have requested they buy it in. Maybe I could have borrowed a friend’s over the weekend. I could have looked in local charity shops. These days you can find textbooks on line. I’m not advocating stealing copyrighted content (maybe a little bit). If you are a poor student from a disadvantaged background, downloading a pirated PDF of your school textbook is hardly the worst thing you could do IMHO. Ahem, moving on.

Maybe you babysit younger siblings until your mum gets home from work. Explain to them what you are doing. Show them your study plan. You’d be surprised how this can work, small children do respond to sincere emotions. Or bribe them with sweets. If they sit and watch My Little Pony for 30 minutes without disturbing you eating Haribo then you get 30 minutes of study done. Make sure you give them the little packets though, not the big family sized ones.

Not all your obstacles will be surmountable. As a young woman going into a male dominated area of science, I couldn’t overcome decades of structural sexism. I could and did read all about women who made successful careers in science and I educated myself about the ways sexism showed up and how to tackle it by reading books by famous feminists. I enlightened myself and underwent a huge shift in how I saw the world. These books and the ideas inside gave me language to describe, understand and vitally, to separate myself from the circumstances I was experiencing. It wasn’t me. It was society. If you are Black, LGBT, disabled or female the emancipation of your mind is a crucial step to overcoming internalised oppression. Get woke.

 

Setbacks and Disappointments

I am training for a pole showcase in October. I am going on stage in front of an audience in a small theatre and performing a routine for 3 minutes. Right now my goals are shoulder mounts and a secure extended butterfly. This is an extended butterfly:

The Extended Butterfly Pose

Seriously, I am trying to do that. I can do the splits, that’s not the problem. The issue is my bottom hand, or rather elbow as mine are hypermobile and flex way past 180 degrees. I have to keep the arm straight and not lock my elbow out to ensure the line of force is straight through the joint. This means I have to use far more muscle strength than someone with normal elbows. It is hard. Some days I can do it, some days I can’t and I get so frustrated I feel like crying.

Shit happens. My strength can vary because I have had a disrupted night (six year old had a nightmare at 2am), because I was stressed (running two businesses and applying for jobs) or maybe I skipped lunch and don’t have enough energy. Day to day fluctuations occur and just because I have not got it down today doesn’t mean I can’t get it sorted by the end of October. I keep practising the intermediate moves and use my pole instructor each lesson to help me practice.

You will find you can’t make the progress you want. Sometimes you will spend weeks struggling with the same topic and make no obvious progress. This is normal. It is to be expected. Here is one of my favourite cartoons for these moments:

Just keep going. Stick with your study plan. Every step you take in the right direction is one more than the person who gave up.

 

I hope you can see the benefits of devising your own personal study plan and tackling your revision like you would training for a competition. You need a goal, a timescale, dedicated segments of your week, in-between steps to aim for and rewards along the way. I can’t guarantee you spectacular results but you will do much better than you otherwise would have done. This is so much better than nothing. As the sign on my gym wall states; you are lapping everyone still sat on their arse. Good Luck.

 

 

Memory and Recall – Top Revision Tips

Mind like a sieve? Can’t get those last few facts to stick? Are you daunted by the sheer volume of information you need to learn? Do not despair. Memory, like any other cognitive skill, can be developed and strengthened. There has been a lot of research done on the most effective ways to recall information. I’m sure your teachers will have shared this information with you. But are you actually taking their advice?

Let’s clear up one important obstacle to memorising things before we start. You don’t know better than your teachers, educational psychologists or neuroscientists. If they have told you to use certain techniques that are known to work well THEN USE THEM.

Unless you happen to be one of the tiny percentage of the population who was blessed with photographic memory, you will have to adopt some strategies to encourage your brain to load up and regurgitate the facts you need to pass your exams. Just accept that and stop fighting it.

The Science of Forgetting

Memory is a three step process; information has to be encoded, stored and retrieved. The information could be about past events; we remember a favourite book or an exciting holiday. But is also future directed in that we have to remember to take our dog for a walk or to go to a doctor’s appointment.

Memorising things doesn’t take place in isolation. Your memories are placed inside a framework built from your prior knowledge and understanding. If you always take your dog for a walk after dinner every evening it becomes a habit and is harder to forget. If you rarely visit the doctor and someone else made the appointment for you it will be easier to forget. You need to encode your memories within your existing framework.

Memorising gibberish is much harder than memorising things that make sense because your brain is less able to put the nonsensical things into the wider framework of your understanding. Nonsense can’t be placed alongside similar facts and your mind will find it harder to accept it.

Memorising things for school exams is more difficult if you don’t understanding the topic because it feels like you are cramming gibberish into your head.

Hermann Ebbinghaus did a study of how well people would retain gibberish in 1885. The results are not good for anyone who thinks forces and motion is just gobbledygook. Ebbinghaus memorised different made up words such as “WID”, “ZOF and “KAF”. He tested himself over and over again after longer and longer times had passed to see how much he could remember. Being a scientist, he plotted the results in a graph, which is now referred to as Ebbinghaus’ forgetting curve.

 

It’s an exponential decay curve. You can recall 100% of gibberish immediately after cramming it, but then the amount you remember drops very rapidly. If you revise a subject you don’t understand well the night before an exam, only about 30% will still be in your head at 9AM the following morning.

We need to find a way to beat this dramatic drop in fact retention. Fortunately scientists nowadays have a much better understanding of how to do this than they did in 1885. It is all to do with remodelling neurons and synapses. The stronger the synaptic links the easier it is to store and retrieve information. It all boils down to encoding memories in your neurons.

 

The Science of Memory

Eric Kandel, a neuroscientist at Columbia University in New York shared the 2000 Nobel Prize for Physiology or Medicine for his work on how memories are made in the brain. Prof. Kandel has shown that short-term memories, like cramming for an exam when you aren’t sure of the facts, involve relatively quick and simple chemical changes in the brain. These changes occur at the synapse which are the nodes that link neurons together. These simple chemical changes don’t last long, they are a bit like a plastic cup, use it once then throw it away.

Fortunately Prof. Kandel also found out how to build a memory that lasts much longer. For this to occur the whole structure around the synapses have to change to be more efficient. New proteins have to be made and neurotransmitters must work more efficiently to connect the small groups of neurons involved in making a particular memory.

The more often a particular bundle of neurons is triggered, the more efficiently they communicate with each other and therefore the easier it is to recall something. Repeated use of a neutron bundle will lead to the remodelling that is necessary for long term memories. Once the remodelling has occurred the change is pretty much permanent, or consolidated in psychology-speak.

 

How to Stay Ahead of the Forgetting Curve

By putting these bits of information together and you can see how we beat the drastic drop in recall from cramming facts into our heads. You need four crucial things; time (you cannot do this overnight), understanding (you remember things which fit into a sensible framework), repetition (the more often a bundle of neurons is activated, the greater priority your brain gives to remodelling it) and sufficient stimulation (the variety of ways in which a  group of neurons is activated will also encourage remodelling into a more efficient and long-term structure). Your brain adapts to the specific demand you place on it by strengthening certain synaptic links. Its like the SAID principle in sports training.

Let’s look at each of these in turn.

Time

You can top up the amount you can recall by regularly reviewing what you want to remember. This second graph shows what happens if you look back over your work at regular intervals. 

At first glance this seems to be a great thing! But then you realise its not just the components of a circuit you have to remember, but all the energy stores, the parts of an atom, the life cycle of a star, and then there’s biology, chemistry, French, maths…It’s not too long before you realise topping up alone will take up every hour of the day unless something else kicks in to help. Something else does, you can relax.

The amount you can remember steadily increases and holds at a higher position. You are not Dory from Finding Nemo, you don’t go back to zero each time. The rate at which you forget the facts gradually slows down as your brain starts to expend energy remodelling these neurons. You are using them a lot so your brain figures they must be important.

Look at that green line! By topping up your knowledge at regular intervals you can keep the amount of data remembered at an impressively high level. This means revision starts the second your lesson finishes and is a process which should be on going throughout the year. If you haven’t looked back over your notes since you wrote them you are going to need a month to six weeks before your exam to get retention up to >80%. Did anyone say revision plan? That’s what they are for.

 

Understanding

You cannot recall things which make no sense to you, your brain is very reluctant to waste energy trying to fit nonsense into your head. Understanding the material you are trying to memorise is the cornerstone of your revision, it must come first. This is VITAL. You cannot correctly encode a memory from a poorly understood concept.

How do you improve your understanding? Firstly identify what it is you don’t get. Is it how the wire conducts electricity, you don’t get the concept of current? What the heck is potential difference? No idea how to carry the amount of gravitational potential energy from a fall over to a calculation of kinetic energy? Using your specification will help you identify your weaker areas of understanding.

Now see if you can solve this problem by reading through a textbook or reliable science webpage. Often reading about the same topic from several different directions can make something click. You need to find the explanation that sits most comfortably within the framework of your brain and what you need to do that may be different to your friend or different to your teacher’s style.

Try asking another teacher within the science department, they may have a way of explaining it which makes sense. Try asking an older student or relative who has done this subject at a higher level. Hire a tutor, maybe just for one or two sessions to work through problematic topics. Watch videos on You Tube of animations or demonstration of the science bits you don’t understand yet. All these resources are available to you to track down a suitable explanation. You do have to do the leg work though because it will not be delivered to you on a silver plate.

 

Repetition

This is pretty self explanatory, you have to revise each topic more than once. As little as 10 minutes a day is sufficient to start the remodelling process. Working too long on one thing will actually tire you out and stop your brain working efficiently. Take lots of breaks, maybe every 20 minutes, and chunk things up into pieces. Once you have spent a week revising 10 minutes a day you can start to leave longer intervals between revision periods on this particular topic. Revision timetables or plans allow you to divide your course content over a sensible timescale (a few months) and ensure you can cover all the material you need.

 

Sufficient Stimulation

This is the final important stage to memorising effectively. It is easy to do this well but frequently ignored by students who believe they have found the one and only method which works for them and refuse to ever try anything else. That is silly. Even if you aren’t a “diagram” person, your brain will pay way more attention to a subject you have tried to draw a diagram of BECAUSE you don’t normally do that.

The path of least resistance in studying is the path of least progress. Remember that!

Multisensory learning is most effective. This means you have to stimulate several senses and try various modes of retaining information to get the brain to wake up and take notice. Read, highlight, annotate and then transform into something else. A picture, comic strip, timeline, diagram, mind-map, memory prompt card, summary table, story, recording on a dictaphone perhaps even deliver a presentation to your bemused cat. Try 3-4 different ways to encode facts you are struggling with. Link things together. I remembered the key code to get into a secured door by realising it was in the form of a date and looking up to see what happened on that day in history. It was a famous historic battle. I never forgot the door code after that.

 

Multisensory Examples

Using Sound

  • Write lyrics to a song you know that summarise the key facts.
  • Revise to the sound of a song you like and only use that song when revising that topic, then hum the song (quietly) in the exam room. You will remember more.
  • Recite things out loud to a rhythm: “kinetic energy is half mass times speed squared” ki-ne-tic (pause) en-er-gy (pause) is half-mass-times-speed-squared.
  • Read your prompt cards out loud.
  • Get someone to quiz you and answer verbally.

Using Images

  • Pinterest a topic.
  • Create a mood-board to summarise something including drawing or printing out images that fit and sticking them on.
  • Build up a mind map using colour codes for specific topics.
  • Make charts and posters and pin them up in your living space.
  • Use little cartoon images on prompt cards or notes.
  • Use colour when writing your notes to highlight, underline or write out specific things. All definition can be blue, all equations red etc.

Using Actions

  • use hand movements to shape out what you are revising. A clenched fist for a nucleus, the other hand pointing to knuckles as protons and neutrons.
  • Walk around as you read or recite your notes.
  • Writing is an action, moving your hand across the page encodes movement memories.
  • Use plasticine to build little models, while you recall collisions and transfer of momentum for example.
  • Try acting out experiments or demonstrations from your course.
  • Check out Dance Your PhD to see how far you can take designing your own movements to go with a topic.

 

For more information on memorising techniques you can look up the following articles. Now go forth and revise.

 

Further Resources

Ed Cooke is a memory competition winner and has written several articles in The Telegraph about how to develop memory techniques.

https://www.telegraph.co.uk/education/educationadvice/9900341/Revision-techniques-how-to-build-a-memory-palace.html

https://www.telegraph.co.uk/education/educationadvice/9888492/Revision-techniques-how-to-learn-complex-concepts.html

https://www.telegraph.co.uk/education/educationadvice/9826494/Revision-techniques-How-to-learn-boring-facts.html

 

Several universities have revision guides online to aid students

https://intranet.birmingham.ac.uk/as/libraryservices/library/skills/asc/documents/public/Short-Guide-Memory-Techniques.pdf

https://cdn.southampton.ac.uk/assets/imported/transforms/content-block/UsefulDownloads_Download/3F82D0A1F6F34D62AC4DDBFF3A4BAFDE/Memory%20revision%20and%20exam%20techniques%202014.pdf

 

Some articles from the Times Educational Supplement and Guardian on revision

https://www.tes.com/revision-tips/fail-safe-memory-recall-techniques-exam-students

https://www.theguardian.com/education/2016/may/07/the-way-youre-revising-may-let-you-down-in-exams-and-heres-why

 

Teaching Resources on Revision – mostly free

https://www.tes.com/teaching-resources/blog/revision-tips-and-techniques-gcse-students

Make the Most of Your Specification – Top Revision Tips

It is good practice for teachers to share the content of the examination course with their students. Each year the exam boards print the content of the exams you are taking. This content specifies precisely what you are expected to learn, hence they are called the specification. Here in the UK the main exam boards are AQA, OCR and Edexcel.

If you aren’t sure which exam board your exams are with the first thing to do is ask your teacher. The exam boards also publish textbooks and revision guides to help you with learning and revising the course content.

Getting Hold of Your Specification

If by some oversight your teacher hasn’t given you a photocopy of your specification, don’t worry! They are all freely available on the internet for anyone to look at. Past papers, markschemes and examiners’ reports are also available.

Here are links to the major exam boards’ different GCSE and A Level physics specifications.

AQA GCSE

AQA AS/A Level Physics

Edexcel

GCSE Combined Science and Physics  – use the tabs to find the single GCSE physics specification

AS/ALevel Physics

OCR GCSE

OCR AS/ALevel

The specifications are large PDF documents over 100 pages long. Most of it is irrelevant to you. Tedious details of how each exam paper is arranged and assessed fill many, many pages. Go to the index and find “subject content”, this is the bit you want. In a combined science GCSE there will be separate biology, chemistry and physics sections. Most specifications have useful internal links which allow you to jump straight to the physics content from the index.

Be careful, the page number in the index rarely (if ever) coincides with the page numbers on the PDF reader you use to look at it. The document may say physics is between pages 59-74, but if you type those pages into the printer dialogue box and hit print the wrong pages will print out. Select the correct pages from the sidebar thumbnails and print the selected pages. I print the pages back to back and two per sheet to save paper. It’ll look something like this:

 

Understanding Your Specification

Let’s assume you have printed your own copy or been given a copy of your course content. You will find it is conveniently divided into sections by topic. AQA Trilogy which is the example given above, has all the physics content in chapter 6 of the specification and individual topics are numbered 6.1, 6.2, and so on.

Generally speaking, these topics aren’t taught in the exact order that they appear in the specification. This is not a teaching plan. Your teacher can divide up this course content however they like. So don’t be surprised if you were taught topic 6.4 before 6.1.

Your exam questions can be on anything in the first column. The second column lists key experiments, science skills or maths and ICT skills. It gives details about how to use equations and the sorts of data/graphs and typical experiments. Ignore the codes like WS 1.2, 4.3 etc.

At the end of the physics chapter is a short summary of the key ideas that cover the whole subject. This is surprisingly helpful and condenses the content down to overarching principles which you should always have in mind when tackling questions.

Using Your Specification

There are so many ways you can use a specification! I could spend a whole morning showing what you can do with this document. Here are my 5 top revision tips for making the most of a specification.

1 – Definitions and Equations

Go through section by section and write out the definitions the examiner provides you with. For example “A system is an object or group of objects”. There will be definitions for all major physical quantities like current, pressure, momentum etc and for qualities such as insulator, conductor, solid, liquid, gas etc.

Examiners often set one mark questions which ask “What is the definition of X?” and you need to be able to correctly write a short sentence which answers that. Writing out definitions is a good way to get used to concisely answering these questions.

Quantities are often stated as relationships between other quantities, e.g. current is the rate at which charge flows past a point in a circuit and is measured in Amps. These relationships lead naturally to equations; current = charge/time or I = Q/t. The specification includes all of these.

At GCSE all the formula are given in a data sheet which you can refer to in the exam. However they DO NOT give you the units that these quantities are measured in. You have to remember that current is Amps (A), charge is Coulombs (C) and time is seconds (s). The specification lists all the quantities, their units and symbols. Grab a highlighter pen and highlight every equation in your chosen colour. Then you can make a quick and easy list to test yourself make sure you have learnt all the units correctly.

2 – Examples and Scenarios

The specification gives the examples that are asked about on the exam paper. In the pages shown above the section on energy starts with a bullet point list. These are the common situations where a student should be able to describe energy changes.

When revising the topic you can use these examples to check that you can indeed describe the energy changes in an object moving upwards or a vehicle slowing down.

Here it is useful to use the specification to test yourself. Get some paper or a notebook and write out the answer to each example as if it were a question.

3 – Key Facts to Learn

Each section includes the key facts that students need to use to solve problems and answer questions.

There are three parts to this subsection, the last two clearly relate to possible exam questions. Show the directions of the force, current and magnetic field using Fleming’s left-hand rule. List that factors that affect the size of the force. Can you do this? Anything that starts “students should be able to…” is obviously something you can be asked.

Note how they don’t actually give you those factors that affect the force or describe Fleming’s left-hand rule. This isn’t a textbook, it’s a what you should know guide. You’ll need to look these things up in your notes, a textbook or on a reliable science website.

So what do we do with the first paragraph? These parts of the specification are key key pieces of understanding which you should be able to reproduce in answers asking for an explanation. For example “Explain what happens to a current carrying wire in a magnetic field  – 3 marks” could be answered by the first paragraph. You should be able to write these ideas in your own words.

4 – Ticking Off Your Revision as You Go

I encourage students to systematically read through their specification and tick off every sentence, equation and definition that they are sure of. Then go back and put a star or double line next to the bits they need to go over because they don’t remember it or aren’t sure. Using a pencil is helpful because you can rub out stars and tick off bits as you work through each section.

Ticking off the content as you go allows you to be systematic and cover every section completely. The specification is better than your notes from class as notes often have missing bits. You can’t always rely upon class notes to have covered every single point. Many times teachers demonstrate or talk through something but don’t have time to write up formal notes on all of it. It would take far too long and writing notes isn’t the point of a lesson anyway. That’s not taking into account the times you were absent, day dreaming or mucking about! The specification is the bible of your course and is the go-to document for checking your have covered everything.

 

5 – Understanding is the Key to Remembering

There is no point remembering incorrect facts and your brain won’t retain information that you can’t make sense of. Use your specification to find the gaps in your understanding then spend your time targeting those gaps. Everything else will fall into place around them. There is no point revising things you understand and remember already. You must find and work on the gaps.

Then use your class notes, reliable webpages and textbooks to study and understand the sections you have identified that need work. Create your own notes, labelled diagrams or mind maps of topics you have identified as weaker. Just reading a page of text will not miraculously make you understand and recall it. You have to do something with the material to make it stick.

Take a list of bits you just don’t understand yet to your teacher or tutor and see if they can break down the topic and explain it. Sometimes all you need is to hear the explanation put in a slightly different way for it to click.

Go and Do This Now!

How incredibly helpful is this document? It lists everything you need to know in concise and manageable chunks which let you learn key facts and check off every single item as you go. You can find which bits you don’t understand and there are all kinds of ways you can colour, highlight and annotate the sections to flag up bits you need to work on or remember.

Coloured pens, stickers, highlighters and post-its are your friends when it comes to revision.  That’s why I chose the picture at the top of the page. Make good use of your specification and you will feel so much more confident and prepared. I remember getting hold of my A Level chemistry specification a month before the exam (the teacher was reluctant to hand it over) and it made such a difference. Go and use it now.

Teaching Radioactivity – A simple demonstration of alpha, beta and gamma

This is one of my all time favourite fun classroom activities. You would not normally equate teaching radioactivity to a roomful of bemused Year 10 students as fun but prepare to be amazed by this simple way to demonstrate the sizes, penetrating power and ionising properties of alpha, beta and gamma radiation.

 

Equipment Needed

One large exercise ball, 50-70cm in diameter pre-inflated

A pea shooter with peas/pellets or a potato gun with potato

A low power laser pointer, the sort used for presentations

This is best done in a large area like a sports hall or even outside weather permitting.

toy pea shooter with pellets

Safety Considerations

You may wish to give out goggles to protect eyes from the pea shooter.

The laser pointer/light beam should be directed towards peoples bodies about waist-chest high and not at faces. It would take 10 whole seconds of unblinking gaze at a typical classroom laser to damage your eyesight. There is a lot of hysteria around the use of low power laser pointers designed for presentations which is entirely unwarranted. The greatest risk of eye damage comes from the pea shooter.

 

How to do it

Choose, and I do mean choose as without fail the most disruptive student in the class will volunteer for this, three students to be the radiation.

The other students line up in 2-3 rows. If you have a class of 30 that would be 3 rows of 9 with the 3 students being radiation stood separately. To be really fancy you could even stagger the rows so students in the row behind are in the gaps of the row in front.

Now each radiation is going to irradiate this block of students who are modelling a material, e.g human skin.

The alpha (exercise ball) student should roll their particle towards the “material” and it will move fairly slowly and bounce off of the top layer of students. Let the alpha radiation have a few attempts to “ionise” the material. When “ionised” the student in the material should raise their hand. This allows everyone to see where the radiation is affecting the material.

Next the pea shooting/potato gun beta student irradiates the rows with their beta particles which are much smaller and faster, and can penetrate a bit further. Again students should raise their hand if hit by the peas and ionised. Let the student try 3-4 times to hit someone.

Finally the laser pointer student can shine their gamma rays through the material and onto the rear wall, penetrating a long way but ionising no where near as much. A straight beam from a laser pointer will skim one student at most.

It is important that the radiation is randomly directed and not aimed at the rows of students as real radiation doesn’t have a conscious intent to interact with matter. This is a limitation to the model which can be discussed at the end. I considered blindfolding the radiation students to increase the random nature of their interaction with the matter students but few teenagers are comfortable being blindfolded in front of the rest of their classmates and generally become too self conscious.

Learning Points

Alpha radiation = exercise ball – large, slow, very ionising, not penetrating

Beta radiation = peas from shooter – smaller, faster and moderately ionising and penetrating

Gamma radiation = laser beam – very fast (speed of light), very penetrating, not very ionising

The sizes and speeds of alpha, beta and gamma radiation are readily apparent from this demonstration. Alpha particles are around 8000 times heavier than an electron and consist of two protons and two neutrons bound by nuclear forces. Gamma is part of the electromagnetic spectrum and is represented as a light beam to show this.

The penetration of the radiation is modelled by the number of layers of students that can be touched by the radiation. The large exercise ball as an alpha particle will bounce around the front row but no deeper. The peas can shoot in further but only go a certain distance as they have a limited speed as a projectile. The laser/light beam will reach the opposite wall.

Ionising power is represented by the number of students being touched by each radiation hit. The slower larger exercise ball will hit at least 2 students each roll. Each hit can be seen as knocking out an electron and ionising the atom. The pea shooter will hit maybe one student each time. The laser pointer randomly aimed may hit one or two people in total.

At the end of the demonstration activity each student should complete a chart summarising the relative mass, speeds, penetrating and ionising effect of the three types of radiation. It helps to summarise the properties of each type as you go along. This can be done socratically by prompting the students with questions – how far did this “radiation” penetrate? How many atoms could it ionise? Why do you think that was? etc.

Limitations to the Model

As with all classroom models this demonstration has various limitations and it is instructive for the students to consider how this model isn’t like real atoms interacting with radiation.

The main points are that real atoms have much more empty space in them and many more electrons.

The alpha particle is deflected by repulsion of like charges not by physically hitting a large, solid atom as this model suggests.

The shell model of electrons taught to 14-16 year olds isn’t well modelled by this demonstration as we have nothing to represent the orbiting electrons. No indication is made as to the nature of the bonding between the atoms in this “material” either.

Conclusion

Students have always responded very well to this activity. It works well for less able students who find book-learning challenging as they vividly remember what happens in the demonstration and you can refer back to how “Jo was hit with the exercise ball, do you remember?” and they always do.

More able students enjoy getting out of the classroom and doing something a bit silly and are able to find the flaws in the model and extrapolate the scenario more easily than less able students who may need to be led to the learning outcomes in smaller more structured steps.

Try it out and let me know what you think.

Tackling Long Answer Questions – Top Revision Tips

In the UK the new A Level and GCSE exams include 4-6 mark questions which require an in-depth written answer several paragraphs long.

These long answer questions come in certain types and test the higher level thinking skills of interpretation and explanation (creating a logical explanation for a scenario), synthesis (pulling ideas from different areas together) and evaluation (weighing up options or outcomes). They also award a mark for clear written English and a well structured argument.

Long answer question can put the fear of God into many students who never seem able to break the 3/6 mark barrier and achieve the higher marks.

Thinking Skills in Long Answer Questions

Some questions on exam papers are easy, 1 mark for recalling the charge of an electron for example. These questions usually come with a certain prompt or command word which indicates you have to remember a fact but not actually do anything with it. “State the definition of electric current” is a typical, “name”, “give”, “what is…” etc are all command words for rote recall questions.

Long answer questions are different. Usually they give quite a lot of information before stating what you must do with it. They are setting the scene and every word used to set that scene is important. Examiners spend hours getting the phrasing of exam questions just so. If they have told you about the efficiency of a power station in the introduction to the question, you HAVE TO mention that in your answer.

The skills you need to answer these questions go beyond just including the larger amount of information these questions give you. Here is a famous pyramid called Bloom’s Taxonomy. Benjamin Bloom was an American educational psychologist who chaired a group which first devised this taxonomy (or classification) of command words into groups according to the level of brain power needed to complete each task.

Long answer questions are targeting the top three layers; analysing, evaluating and creating. These skills involve selecting the most important information, working out which order to put it into, identifying the key bit of physics the question is about, linking in related principles that may not be explicitly stated in the question and offering a solution to the problem solved. What makes this hard is holding all these aspects in mind at the same time.

Let’s look at an example:

6 mark A Level physics question – OCR exam board

  • Identifying the most important information: They tell you up front it is about the Big Bang. They mention the CMB radiation, they give you wavelengths.
  • Key bits of physics: the origin of the CMB, probably need to relate this to wavelengths somehow, the idea of the expanding universe, OK that’s Hubble’s Law, then wavelengths from galaxies which must mean cosmological redshift tying in with Hubble’s Law. OK sorted.
  • What order to put them in: “Explain” command word, 2-3 marks for explaining the role of CMB in Big Bang theory. Go on to discuss how present day Universe must still be expanding and how we could show this, 1-2 marks, relate data from the table to this. Have to use an equation relating wavelength at rest and in galaxy to redshift or recessional velocity. Need to use data they have given me, 2 marks for working out the redshifts. “Comment” command word, finish off with remark about how the data is relevant.
How to Tackle Long Answer Questions

The main strategy is not to read the question and immediately start writing, DON’T DO IT!

Here is a printable infographic which breaks down how to tackle these questions.

Step 2: Annotate the question is identifying the most important information

Step 3: Jot down ideas is recognising the key bits of physics to use

Step 4: Sequence your ideas is working out what order to put them in

 

Types of Question

Now we know how to go about answering these questions let’s consider certain types of question that crop up.

1) Experimental Design

Describe how you would compare … in a laboratory. Billy Bob wants to determine Planks Constant using LEDs, outline an experimental method which would….

The main things to include are apparatus, preferably a labelled diagram, brief method stating what you change, what you measure and what needs to be controlled. Give the range over which you take readings using the equipment you chose. Mention how many repeat readings you take. State two (or more) measurements will be plotted and what data processing you may need to do to find the desired result. This could be a simple as saying we divide voltage by current to find resistance, or you plot an I-V graph and work out the gradient. But you must say what you intend to do. Experimental method does not mean JUST apparatus and method. You must talk about range of data, reliability and data processing as well.

6 mark experimental question, A Level Physics – OCR exam board

The marks for this question were awarded as follows:

Equipment used safely (E)

  1. Wire fixed at one end with load added to wire
  2. Suitable scale with suitable marker on wire
  3. Micrometer screw-gauge or digital/vernier callipers for measuring diameter of wire
  4. Referencing to safety concerning wire snapping

Measurements Taken (M)

  1. Original length from fixed end to marker on wire
  2. Diameter of wire
  3. Measure of load
  4. New length of wire when load increased

Calculation of Young modulus (C)

  1. Find extension (for each load) or strain (for each load)
  2. Determine cross-sectional areas or stress
  3. Plot graph of load-extension or graph of stress-strain
  4. Young modulus = gradient x original length/area or Young modulus = gradient
  5. Calculate Young modulus from single set of measurements of load, extension, area and length.

Reliability of results (R)

  1. Measure diameter in 3 or more places and take average
  2. Put on initial load to tension wire and take up ‘slack’ before measuring original length
  3. Take measurements of extension while unloading to check elastic limit has not been exceeded
  4. Use log wire (to give measurable extension). Scale or ruler parallel to wire

To get 5-6 marks you had to include all points E1, 2, 3 and 4 for equipment, all points M1, 2, 3 and 4 for measurements and for the calculations you were expected to show C1, C2, C3 and C4.

Each specification says which experimental methods students should be familiar with and you can practise these questions by ticking off each experiment in turn and writing your own diagram, method, data collection and calculation notes.

 

2) Big Physics

We have seen an example in the previous section. Big Physics is particle accelerators, the Big Bang, life cycle of stars, fission and fusion, MRI scanners etc. These questions ask for descriptive explanations of the phenomena. Quite a lot of which is recall from lesson notes and reading. However exam questions increasingly throw in a data or a graph to make the answer more specific to a situation.

These are best revised for by practise writing the “story” of a particle through a mass spectrometer, the “story” of the interstellar dust cloud which becomes a blue giant or whatever.

 

3) Analysis of a given scenario

These questions are the trickiest in my opinion as they throw a piece of data or a novel set up at you and you have to think on your feet a bit more. These questions are often designed to identify the A* students as they are the ones who score 5-6 marks most easily on these.

Here are two example, one GCSE and one A Level

6 Mark GCSE Physics – AQA exam board

6 Mark A Level Physics – OCR Exam Board

These question include apparatus and/or graphs and tables. You must refer to the data in the graph or table. Describing the overall trend in words, identifying relevant data points on the graphs and using the numbers given on the axes i.e. quantifying the data will all score points.

In the first example the axes are not numbered so you would have to point out key features or trends. Most particles have an average speed much lower than the fastest particles forming a large hump or maxima on the graph, and that small number of particles have very high speeds forming a tail. You should fully describe the graph in other words. Do not say “the graph goes up at first and then it goes down”. The fact that a small number of particles have a slow speed is irrelevant to the question about evaporation (why?) and so you wouldn’t need to include a comment on that as it is not important information.

The second question outlines a device which student won’t be familiar with but they will have seen similar circuits before. The important information includes the stated range of temperatures and this should be linked back to values on the top graph because the graph has gridlines and numbered axes meaning you will be expected to read values from it.

The circuit is a potential divider (a fixed and a varying resistor in series) with two resistances and two voltages necessary to use the potential divider equation. Explaining how it works now becomes a more general question on explaining how a potential divider works.

Using the data to work out the voltage across the thermistor will be the route to take to score the second half of the marks.

Tackling an analysis long answer question involves more of the identifying the key physics step than some of the others. You have to be able to look at the question from a distance and spot the topic area they are asking about, recall the main points and then go back in to the detail and apply that to the scenario. You always get marks for spotting the topic area and identifying the key features/equations to use.

 

4) Pros and Cons

These style questions are often a straightforward comparison of two outcomes, for example should nuclear power replace fossil fuel power stations? Or they ask you to consider the wider impact of a certain choice given data and context in the question, for example is converting to an electric car a worthwhile choice?

6 mark GCSE Physics Question

This particular question about Europa came with some additional data showing where it is (a moon around Jupiter) and how far away it is compared to the Earth’s Moon.

These questions are best tackled as a list of pros and cons, 3 reasons with an explanation for each side and an overall judgement on the best outcome. The specific reasons you choose for or against will of course be led by the important information you have identified from the question and any key physics ideas (distance, speed and time, energy costs etc) that you know relate to the topic.

 

Conclusion

Following these tips and thinking about what type of question you have been handed will enable you to get the most out of your answer. Every question style can be tackled using the 1-6 Step method shown in the infographic, this is the basic cake, tailoring your important information and key physics topic facts to the question style is the icing on the top.

Hubble’s Law – Using Historical Data 1

When teaching physics I think there is a lot of reliance upon writing down a law, Hubble’s Law for example, on the blackboard at the start of a lesson. Then without much or indeed any explanation as to how this result came about, students are left to to work out some example problems or do a couple of experiments using this result.  They are expected to accept without question the “Law of Physics” we have given them. This doesn’t encourage critical thinking and this approach is one of the reasons so many students are turned off physics as a subject.

Chalk and talk teaching is unhelpful and frankly boring. A better way to teach is to supply information and allow the students to discover the results for themselves. Not only is this more interesting, but by doing the work themselves the students learn more effectively and this method mimics the actual scientific process of discovery and deduction. Now I appreciate we don’t have access to large telescopes and apparatus, I’m not suggesting we reproduce the entire experiment! We can make use of historical data to enable students to reproduce important results for themselves. I’m going to write a few posts which show how the data from various famous experiments can be used when teaching physics.

Teaching Hubble’s Law

 

Hubble’s Law describes the expansion of spacetime

Hubble’s Law is an example of a topic which can be taught this way. Usually it is taught by stating the relationship between distance and recessional velocity (Hubble’s Law V=Hr) and this equation is used to deduce the age of the universe etc. Some discussion is made of the interpretation of the recessional velocity – students are expected to understand that spacetime itself is expanding between the observer on Earth and the distant galaxy not that all galaxies are flying away from us.

So turn the lesson around and start with the data. Hubble’s original research paper is short and the data produces a nice line graph. Students can be given the data and be tasked with reproducing his graph of results. They can then construct their own interpretation of what the linear relationship implies. It is good practice to get students to label their graphs with a sentence or two describing the data for example: “a graph to show the relationship between recessional velocity of galaxies and the distance to those galaxies”. Teasing out precisely what relationship; linear, inversely proportional or whatever, can follow.  Students can find a value for the Hubble constant from the gradient of their line of best fit. Comparing this to present day values shows the considerable advances in our measurements of redshifts and distances.

A little bit of algebraic manipulation draws out the units for the Hubble constant as being per unit of time. Time from what? is the key question to ask. What is the start time and what is the end time to find the difference in times that go with the difference in distance to give us a velocity? Change in distance/change in time = velocity. Every time I have taught this one student at least realises that 1/Ho is the time since the galaxies started to move apart and is therefor an estimate for the age of the Universe. You don’t have to tell them, they can work it out! This starts all sorts of discussion about how appropriate this estimate of the age of the Universe is. It is a great way to introduce the earlier, hotter, radiation dominated phase of the Universe where the rate of expansion was slightly different and then further back to Inflation and the Hot Big Bang Theory.

Active learning, the idea that students are working out the relationships not being passive recipients of them as Laws of Physics, has been shown time and time again to produce better learning outcomes. Students understand the topics better and recall more of the information correctly when assessed.

Here is a worksheet which allows more able GCSE 14-16 year olds or AS/A2 16-18 year olds to plot Hubble’s data. A scientific calculator is required and this activity wouldn’t be suitable for students who struggle with large numbers or data processing.

I have also attached Hubble’s paper “A Relation Between Distance and Radial Velocity Among Extra Galactic Nebulae” from 1929.

Equipment needed: graph paper, rulers, pencils and scientific calculators or log tables.

A RELATION BETWEEN DISTANCE AND RADIAL VELOCITY AMONG EXTRA-GALACTIC NEBULAE by Edwin Hubble

Hubble’s Law worksheet

Phases of the Moon for Young Children

Recently I went in to my daughter’s primary school and spent the afternoon running an activity for the 60 children aged 6-7 in her year group. They had been studying the Solar System and I’m happy to offer my services as an expert of all things astrophysics. I ended up delivering a lesson which introduced the key science skills of observation, spotting patterns and making a prediction as part of the topic of the phases of the moon.

Misconceptions and Remedies

There are many common misconceptions regarding the Moon which children arrive with at secondary school. It never ceases to surprise me how many 11 year olds don’t think the Moon is ever visible by day, despite the fact that they have all seen it! This is easily fixed with a few reminders of times they have seen the Moon outside, often it is actually in the sky during the lesson, or photos can be shown with the moon in daylight.

They have no grasp of the relative sizes, distances or position of the Moon with respect to the Earth. I have often spent a lesson with tennis balls and plasticine blobs getting the students to make scale models with the Moon 30 times the Earth’s diameter away. I always discuss how the photos we commonly see of the Earth-Moon as a pair are doctored to bring the Moon much closer – this really does need explaining to students.

Typical Earth-Moon image:

Actual Earth Moon separation:

Students without fail believe the Moon orbits the Earth’s equator. In fact the Earth is tilted by 23 degrees to the ecliptic and the Moon is a further 5 degrees above that. Reminding students of the Earth’s own tilt is often enough to get them to realise the Moon must alternate its position above and below the equator. They also benefit from discussion about the locations where solar eclipses occur to further realise the Moon can’t stay over the midline of the Earth. This nicely introduces the idea of the ecliptic plane of the Solar System and the various orbital tilts that planets have. The idea of planetary alignment and paranormal events is quite common in science fiction and fantasy shows on TV, conjunctions are never perfectly aligned however and you can explain why.

So there are some significant gaps in the children’s understanding of our Earthly relationship to our nearest neighbour in space. In an attempt to get the children thinking about what they could see of our Moon with their own eyes, I planned a Phases of the Moon lesson.

Lesson Plan – Outline

AIM: to introduce the names for the phases of the Moon and to recognise the shapes associated with the names. To observe the shape of Moon over the course of a week and predict what it would look like the following week. More able students will be able to offer an explanation in terms of the shadow face/illuminated face of the moon and our position with respect to those two hemispheres.

TIMING: 45 minutes

5 minutes: Elicitation and questions

20 minutes: Copy and name the moon phases, practise naming the phases

10 minutes: Observe the “moon” in pairs

10 minutes: Discuss conclusions and explain observation task

LOCATION: A room large enough for 30 children to sit and with space to walk around the illuminated ball (see below). Curtains or blinds will be needed to darken the room.

APPARATUS: One large inflatable gym ball, roughly 60cm in diameter, with a stool to sit it on; a bright torch positioned to shine straight onto the ball from the side; some A4 pictures of the Moon printed from NASA’s website and therefor publicly useable (all NASA pictures are usable for educational purposes). A worksheet and pencil each.

ORGANISATION/BEHAVIOUR MANAGEMENT: The children need to sit and write on their sheets for part of the lesson. They sat on the floor or a bench in 3 rows. Ideally I would give them clip boards to use next time. When pairs of children are observing the ball the remainder of the class needs to be kept busy. During this time one teacher practised the shapes and names with them again which worked well.

Lesson Plan – Activity Details

ACTIVITIES:

  1. Elicitation and questions: Firstly students are seated facing the front and asked what they know about the Moon. Do they know what it is made from? How can we see it? Does it always look the same? Why do you think that? How do people on Earth find out about the Moon?
  2. Introduce vocabulary: Following this the students are given a pencil and worksheet, the teacher holds up a picture of the Moon and asks for the name for its shape (full moon, gibbous moon, half moon, crescent moon, new moon). Some students will know some of the names. They copy the word down and sketch a picture of the moon in that phase. Repeat until all 5 are done.
  3. Memorise shapes: The students put down their pencils and worksheets and try to make the moon phase shapes with their arms or bodies (depending on how much space you have). The teacher leads by saying a phase and the children have to find a way to make themselves resemble the shape.
  4. Observe the shadow face/illuminated face: in pairs, the students come and look for the dividing line between the bright face and the shadow face of the gym ball “moon”. They look from the front, side and behind and link the shape of the bright surface that they can see to the shape of the Moon at different times of the month.
  5. Observation experiment: The rear side of the worksheet has a chart where the children can write the day or the week, whether they could see the moon (due to cloud cover), was it visible at day or night and what shape it had. They go away and complete this during the week – realistically in children aged 6-7 most will do 3 or 4 observations out of a possible 7.
  6. Make a prediction: The final task on the worksheet is to make a prediction about what shape the Moon will have in a few days time. The students are using the pattern they have seen in their observations and linking it to the order of the phases introduced in the class activity.

 

FOLLOW UP: It was left to the class teacher to follow up this activity throughout the week with reminders and a discussion on their results the following week. The vocabulary of the phases of the moon can be easily incorporated into their continued work on the Solar System topic; in written work describing a trip to the moon, in art work, as part of maths learning about shape (sphere, hemisphere, crescent etc) and fractions (whole, half, quarter).

Evaluation

So how do I think it went? I have never taught science to such a young group of children before and on the whole they were interested and well behaved.

The worksheet seems to be pitched at the right level, most students could read it and understood what to do however some students needed to be shown where to draw the picture and where to write the word. Some students took a little longer to write than others and there was discussion about how best to show shadow and a New Moon which was interesting, eventually they solved these issues for themselves.

The A4 pictures of the moon phases were large enough to be seen be everyone as I sat in front of the group.

They enjoyed standing up and making moon shapes with their arms over their heads, a big circle for a full moon, D shape for half moon, banana shape for a crescent and so on. If I had thought this through a bit more I could have taken them to the centre of the hall (we were in the main school hall) and made a bit more of this.

Some children really wanted to touch the ball and trace the line between the shadow and bright side, so if I repeated the lesson I would take some plasticine or a coil of rope for the ball to sit in so it didn’t wobble around so much on the stool.

The one thing I felt needed improving was the time when I showed the illuminated big ball to the pairs of students. Those waiting in their seats were not occupied enough. Partly this was due to were I had had to position the ball, the sun was very bright through the windows that afternoon and the corner of the hall was the only suitable dark enough spot even with the curtains pulled. That meant far fewer students than I had anticipated could walk around the ball at a time, I had planned for 8-10 students to walk and view both sides, front and back at the same time. One class teacher stepped in and led the group in practicing the shapes and tested them on the words while their classmates took turns to look at the ball. The other teacher didn’t and the students eventually became restless.

I would prepare a word search or pairing/matching game for this period of the lesson if I did it again to reinforce the vocabulary while they waited.

With one group we had a good discussion about how scientists find things out which led nicely onto the homework observation task. We ran out of time with the other group which meant the task was explained with less context. This bothered me but the students didn’t seem to mind. The students very much enjoyed asking questions about how scientists work, one asked me if scientists have rows with each other about who is right, which of course they do very politely via academic publications.

Additional Resources

moonphasepictures – Word document of A4 lack and white Moon phase photos

Phases of the Moon – students’ worksheet

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