Energy – the most poorly-taught concept in all of science?
Posted by: ozymandias1 on: July 27, 2011
It is important to realize that in physics today, we have no knowledge what energy is.
Richard Feynman
Sometimes when I’m teaching I have been known to go off on a tangent which may be only marginally related to what we’re doing in class; other times I manage to restrain myself and may just allude to the tangential concept in passing.
But then there are times when these tangents are actually necessary, and by leaving them out I am doing the students an injustice. Ususally I try to include this information in the students’ notes also but sometimes I just don’t get around to it. Energy is just such an example.
Georgina (this is where I’m supposed to say that Georgina is not her real name, but as far as I’m aware it actually is) is one of the top students in my fifth year class this year and I used to think that she was a bit of a ‘slogger’ – liked to work hard and liked to know that there was always a ‘correct’ answer. In fact I wasn’t even sure if she would adapt to my style of teaching, where I tend to ask questions and not always provide the answers. But Georgina showed what she was really make of when we were revising the chapter on Energy.
“I know this sounds like a silly question”, she said, “and I know we’re finished the topic now, and it’s not that I can’t do the problems and exam questions because I can, it’s just that I don’t seem to get what energy actually is“
I realised that there was more to this student than I first thought.
You see nobody gets energy; in fact by pretending that it’s all straightforward we actually do the students a disservice. Not only are we ignoring the wonder associatied with the idea, we are also denying them the opportunity to engage with the concept at any level beyond the superficial.
Bottom line – nobody gets energy because there’s nothing ‘to get’. Energy is not tangible (alghough it is ‘an indirectly observed quantity’ if you want to sound clever), you can’t hold it in your hand, you can’t weigh it on an electronic balance, you can’t see it, touch it, smell it etc. Yet when the universe was first created there was a certain amount of this put in to the mix (actually now that I think about it the mix itself was energy (with perhaps just a little dash of time)), and it’s all still there today. Its form can change, but the energy itself can’t ever disappear – no sirree bob.
It could be argued that it is in fact merely an accountant’s trick which enables him to ensure that all actions balance.
Consider the following analogy which I like to use.
If a child asks you ‘what is money?’ you could take a few coins out of your pocket and show them to the child and say ‘this in money’. Now fast forward a couple of decades; all transactions are now done electronically/online and all coins and paper money are no longer legal tender. Now how do you explain what money is?
Well it’s a means of payment for goods and services, right? Somebody sells you an orange and you agree to transfer into their account a set amount of this ‘money’. And now that the shopkeeper has this money in his account he can use it to buy something else. So it’s a bit like a transferrable IOU.
Now energy is a bit like this, but there is only a certain amount of IOU’s in the universe and this was set when the universe first came into being (I’m not sure if we know how much energy is in the universe – presumably we do?), although to complicate matters since the early part of the last century (thank you Albert) we now know that all matter (‘stuff’) is basically energy in another form.
Anyone still with me?
Now the point of all of this is to highlight once again that there is no reference to this concept on either the Junior Cert or Leaving Cert syllabus. It could be argued that this is because it would be too difficult, but the obvious response to this is that nobody understands Energy as it is currently presented anyway. Students merely learn off the definitions and formulae and if they think about it at all will probably just assume that it’s just another example of Physics being ‘too hard’ to understand.
So what’s the actual point in asking students to learn the definition in the first place?
In fact I’d imagine many students who can give the appropriate definition for Energy (“Energy is a form of Work”) couldn’t follow up by explaining what Work is (it’s a mathematical product of force and displacement to give the simplified version).
At Junior Cert level students are expected to be able to show how light and sound are forms of energy – again most students should be able to give the correct demonstration but if you ask them how this demonstration verifies that it is is form of energy few will be able to give a convincing answer. In fact while Energy is the single greatest unifying concept in all of science, even that idea alone is not worthy of mention in the sylllabus; as a consequence Energy is seen as just another chapter to be learned off, with (once again) no emphasis on how it ties together everything else.
Now if teaching Junior Cert Science and coming from a Biology or Chemistry background what are the chances of your students developing an appreciation of this all-encompassing concept? – were you ever told about it?
I thought I’d find something on YouTube to illustrate this, but I couldn’t find anything.
What is it about this idea that we want to avoid?
Below are some quotes from other more prominent commentators on this elusive concept:
When Feynman wrote,
“It is important to realize that in physics today, we have no knowledge of what energy is,” he was recognizing that although we
have expressions for various forms of energy from (kinetic, heat, electrical, light, sound etc) we seem to have no idea of what the all-encompassing notion
of “energy” is.
The various forms of energy (½mv2, mgh, ½kx2, qV,mcT, ½I2, ½CV2, etc.) are abstractions not directly observable.
2007 American Association of Physics Teachers
Feynman’s quote in context:
There is a fact, or if you wish, a law governing all natural phenomena that are known to date. There is no known exception to this law – it is exact so far as we know. The law is called the conservation of energy. It states that there is a certain quantity, which we call “energy,” that does not change in the manifold changes that nature undergoes. That is a most abstract idea, because it is a mathematical principle; it says there is a numerical quantity which does not change when something happens. It is not a description of a mechanism, or anything concrete; it is a strange fact that when we calculate some number and when we finish watching nature go through her tricks and calculate the number again, it is the same. It is important to realize that
in physics today, we have no knowledge of what energy “is.” We do not have a picture that energy comes in little blobs of a definite amount. It is not that way. It is an abstract thing in that it does not tell us the mechanism or the reason for the various formulas.
The Feynman Lectures on Physics Vol I, p 4-1
Good luck to all exam students
Posted by: ozymandias1 on: June 15, 2011
Something to take with you into your Science exam tomorrow – the quotes are from Einstein:
Not everything that can be counted counts, and not everything that counts can be counted.
Imagination is more important than knowledge.
Do not worry about your difficulties in Mathematics. I can assure you mine are still greater.
These exams are all about how good you are at learning stuff ‘off by heart’. Now no society in this day and age needs students who are good at learning stuff by heart so why do we do it – why don’t we spend time teaching students how to think for themselves?
Because that’s a lot harder to assess. So let’s teach something that we can assess and not worry too much about how useful that actually is. ‘That seem a little silly? Consider the following story:
A cop walking his beat one night finds a drunk on his knees, searching for something on the street.
The cop asks the drunk, “What are you doing?”
“Looking for my car keys,” says the drunk.
The cop asks, “Where did you lose your keys?”
“I don’t know,” the man answers.
The cop, a bit perplexed, asks, “Then, why are you looking here if you don’t know where you lost your keys?”
The drunk replies “Because the light is better here, under the streetlight.”
The following is a question on a physics exam at the University of Copenhagen:
“Describe how to determine the height of a skyscraper with a barometer.”
One student replied: “You tie a long piece of string to the neck of the barometer, then lower the barometer from the roof of the skyscraper to the ground. The length of the string plus the length of the barometer will equal the height of the building.”
This highly original answer so incensed the examiner that he failed the student who immediately appealed on the grounds that his answer was indisputably correct.
The university appointed an independent arbiter to decide the case.
The arbiter ruled that the answer was indeed correct, but did not display any noticeable knowledge of physics. It was decided to call the student in and allow him six minutes in which to provide a verbal answer which showed at least a minimal familiarity with the basic principles of physics.
For five minutes the student sat in silence, forehead creased in thought. The arbiter reminded him that time was running out, to which the student replied that he had several extremely relevant answers, but couldn’t make up his mind which to
use.
On being advised to hurry up the student replied:
“First, you could take the barometer up to the roof of the skyscraper, drop it over the edge, and measure the time it takes to reach the ground. The height of the building can then be worked out from this formula I have worked out for you on my text paper here.”
Then the student added, “But, Sir, I wouldn’t recommend it. Bad luck on the barometer.”
“Another alternative”, offered the student, “is this: If the sun is shining you could measure the height of the barometer,then set it on end and measure the length of its shadow. Then you measure the length of the skyscraper’s shadow, and thereafter it is a simple matter of proportional geometry to work out the height of the skyscraper. On the paper is the formula for that as well.”
“But, Sir, if you wanted to be highly scientific about it, you could tie a short piece of string to the barometer and swing it like a pendulum, first at ground level and then on the roof of the skyscraper. The height is worked out by the difference in a gravitational formula, which I have determined here this time on a long sheet of paper with a very long and complicated calculation.”
“Or, Sir, here’s another way, and not a bad one at all. If the skyscraper has an outside emergency staircase, it would be easier to walk up it and mark off the height of the skyscraper in barometer lengths, then add them up.”
“But if you merely wanted to be very boring and very orthodox about the answer you seem to seek, of course, you could use the barometer to measure the air pressure on the roof, and on the ground, and then convert the difference in millibars into feet to give the height of the building.”
“But since we are constantly being exhorted to exercise independence of mind and apply scientific methods, undoubtedly the best way would be to knock on the janitor’s door and say to him ‘If you would like a nice new barometer, I will give you
this one if you tell me the height of this skyscraper’.”
It’s a wonderful story, and when told is usually attributed to the Danish physicist Neils Bohr, but like all great stories is almost definitely apocryphal.
Good luck in the exam 
Junior Cert Science revision: the experiments
Posted by: ozymandias1 on: June 12, 2011
- In: JC Science
- 5 Comments
With the Junior Cert Science exam just around the corner this resource will come too late for most, but for what it’s worth I am highlighting it here anyway. With over 45 experiments needing to be written up for Coursework A the sheer volume can be quite intimidating, particularly for those of us who are struggling with the subject in the first place.
That’s why I’ve put together a very short summary of all the experiments on the revision page of thephysicsteacher. Each set (Physics, Chemistry and Biology) can fit onto one double-sided page (well almost – need to work on reducting Physics) and if students are looking for a more indepth description they can go to the original notes, which also contain every question which has ever appeared on an exam paper (at Higher and Ordinary level) along the accompanying solutions.
Hope it’s of use to some of you out there.
And remember – real Science bears little or no resemblance to the rubbish you have to learn for this exam, so try not to be put off by the subject.
Military sponsoring Science: let’s just keep that out of our textbooks shall we?
Posted by: ozymandias1 on: June 12, 2011
I like to use the following cartoon as an introduction to discussing what science is about.
As for the answer to how science really works – I simply tell students I don’t know, and I’m not sure anybody does.
I’m not even sure we could agree on on a definition of what Science is.
However I think we can agree that military aims has (right from the very beginning) been a strong factor in the advancement of science (but no I can’t quantify the word ‘strong’). Consider the following:
America’s budget crisis is prompting tough discussions about its defence spending, which, at nearly $700 billion, is bigger than that of the next 17 countries combined.
Link
A more important concept that needs to be recognised is why textbooks coveniently ignore this dark side and persist in painting a picture of science that is at odds with reality (disinterested quest for knowledge, great scientists of the past were pargons of virtue and all that lark).
Actually why the history of science was first portrayed in this idealised light is a fascinating study, but possibly for another day.
This school picture obviously contradicts what we know now. We as teachers should be demanding a more accurate portrayal of our subject (a human endeavour, warts and all) and not to acknowledge this is to do our students a disservice.
We are beginning to row back at least from presenting science as a font of absolute knowledge and I think that’s where the ‘How Science Works’ theme kicks in, but there is still the murky patronage, both past and present, which needs to be acknowledged.
Junior Cert Science – Graphs and the phrase ‘directly proportional’
Posted by: ozymandias1 on: June 1, 2011
Usually there is at least one graph to draw on the Junior Cert Science paper, and if it’s in the Physics section then chances are it will be a straight line graph (the main exception is Cooling Curves). There’s nothing on the syllabus (that I’m aware of) that states that students are expected to know the significance of a straight line graph. In fact here’s a piece of research for you – next time you’re in class ask your students why we’re expected to bother with graphs in the first place. My bet is that very few will be able to give a convincing answer.
One reason we ‘bother’ with graphs is to establish a relationship between two variables; to use the correct jargon we want to see if the variables are ‘directly proportional’ to each other. Now that term ‘directly proportional’ is very important. In means in effect that the two variables are increasing at the same rate. For example if you are on a bicycle travelling at a steady speed of 10 m/s, then for every second that you cycle you will have travelled 10 m (d’oh), and if you travel for twice as long you will cover twice as much ground. If you travel for four and a half times as long, you will cover four and a half times the distance.
So again, the time and the distance covered are increasing at the same rate – they are directly proportional to each other.
The graph is our way of verifying this – it turns out that when you plot all the given data and you end up with a straight line which passes through (0,0) then we can state that the two variables are directly proportional to each other.
So why am I telling you all this now?
Because in the exam you may be asked to draw a graph and then say what the relationship is between the two variables. And if you don’t use the phrase ‘directly proportional’ in your answer then you probably won’t get full marks.
Now as I mentioned I have never seen this phrase highlighted in a Junior Cert textbook so you may well have heard it here first.
Now to help you I have compiled all the graph questions that have ever been asked at Junior Cert into one word document. You can find it on the revision page of thephysicsteacher here (it’s no.3 – Graphs). It also contains all the solutions to the questions, plus a list of do’s and don’ts.
Make sure you check it out before going into the exam. And if you’re reading this as a teacher please remember when photocopying to copy back-to-back and reduce two pages onto one. In doing so you reduce the amount of pages by a factor of 4.
Good luck!
Applied Maths Resources II
Posted by: ozymandias1 on: May 11, 2011
To go with the previous post on Applied Maths papers there is an accompanying set of notes on each topic here.
Many of these are 30 – 40 pages long so don’t print unless you have to; when I distribute these to students I use the photocopier to photocopy two pages onto one (A3 – A4) and also to go double-sided. This reduces the number of pages by a factor of 4.
Each topic has its own contents page at the beginning which breaks the chapter up into sub-topics. Each sub-topic then has an introduction and some exam questions with worked solutions (or at least most do – it’s still a work in progress). There is then a guide to answering the individual questions (which also includes the answers), although I think this only goes from 2010 to 1995. Every question from 2010 to 1970 is included in the booklet with similar-type questions arranged together.
If you’re a teacher feel free to copy any or all of this to suit your own purposes; life, as always, is simply too short for anything else.
There is also a 1 page guide to approaching the exam itself on the same page.
Hope it’s useful.
Applied Maths Resources
Posted by: ozymandias1 on: May 4, 2011
A bit late in the year perhaps, but for anyone out there studying (or teaching) Applied Maths it might be worth noting that I have uploaded a full set of exam questions in the Exam Material section of the website. These go from 2010 all the way back to 1970. I scanned them in from some old papers I had filed away and then converted them to Microsoft Word so that they can be easily incorporated into other documents (more on that later).
It was an interesting exercise in that up until that point I thought that Applied Maths was one of the very few subjects which required more than simply learning off past questions, but it turns out that if you are prepared to cover the full gamut of questions then almost every question you will see in the 2011 or 2012 paper will be very close in apperance to at least one question which has appeared in the past.
Because I have converted into Microsoft Word there is sure to be the odd typo along the way, which is why on the same page you can have access to the original papers which I scanned in and uploaded (these only go back to 1976 because the quality of the 1975 – 1970 papers was simply too poor to read after scanning).
In the meantime I am working on a set of solutions for all these – some of which have already been provided by a colleague so it’s a case of trying to fill in the gaps but when I have them I intend to stick them up on the same page – stay tuned, but don’t hold your breath!
Sure to be of use to someone – try to avoid printing these if you can.
And good luck with the study.
Quantum Theory – why do we ignore the mystery?
Posted by: ozymandias1 on: April 16, 2011
Isn’t it crazy that one of the most wonderful concepts in Physics – the dual nature of light – doesn’t get a better deal from the leaving cert physics syllabus?
Students are expected to know how to demonstrate that light is a wave, and also to be able to recall Einstein’s interpretation of the Photoelectric effect (which proved that light is a particle) but then there is nothing else about what is one of the greatest mysteries in Physics – how can light be both particle and wave?
Quantum Theory is one of the most popular concepts in popular science books, yet we leave it out altogether.
Isn’t there a responsibility on us as teachers to make our voices heard? Or is it the case that we don’t really care?
The following is a video taken during the Solvay Institute of 1927 – it helps to give some feel for the characters involved (see the Quantum Physics page of thephysicsteacher.ie for a link to this and other related videos).
This is one of my favourite videos on quantum theory – it emphasises the wonder, and that’s always a cool trick when introducing any new physics concept to students.
Did you know Galileo had a facebook page?
Posted by: ozymandias1 on: April 16, 2011
Hattip to my colleague Mark Campion for finding this little beauty:
Nuclear Physics Resouces
Posted by: ozymandias1 on: March 19, 2011
For anyone out there interested in educating themselves on all things nuclear. I teach this as two seperate chapters for Leaving Cert Physics. I would like to think that by studying the notes on the two chapters plus watching the associated links you would actually be in a position to answer any leaving cert questions on the topic.
You can download the word documents for the two chapters here (they’re chapters 30 and 31) and the links for the associated videos are beside them but I’ll put them here for convenience:
The Atom and Radioactivity
Fission,Fusion and NuclearEnergy
The nice thing (I think) is that the word documents contain every exam question that has ever appeared on that topic (broken into individual short questions) plus the solution to each question.
At least I think that’s cool.
It means not only can you put yourself in a postion to understand what’s happening in Japan at the moment but it should feel nice to know that you can do leaving cert Physics!
After all, it’s not rocket science (is it?)
Apart from that, the following video serves as a reasonably good source of information although it is by no means comprehensive and doesn’t list the potential dangers, which is what most people want to know.
Finally, a useful timeline of events is available from Mr Reid’s blog here
Normally we cover this topic towards the end of sixth year but this is the perfect time to introduce the concepts to fifth years; I wonder how many teachers chose not to alter their lesson plan because that’s just not the order in which it’s meant to be taught?
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