How accessible is physics?

[Twiglet]

SInce we kicked off a few threads with A level maths & physics problems, a couple of people passed comments about "schoolboy" problems in a rather depreciating way, so I looked up a couple of articles (uk based) to see just how many schoolboys (and girls) would have much of answering the problems Jim & I were posing.

The source docs I found are:

http://www.buckingham.ac.uk/news/pressr ... ics-2.html
http://www.aps.org/publications/apsnews ... udents.cfm

Most worryingly, from the Bucks uni study:

"Only just over 3.8 per cent of 16-year-olds took A-level physics in 2004 compared with about 6 per cent in 1990."

So in short, even with the basic problems we've been playing with, only a pretty small number of people (1 in 15 to 1-20) would have much hope of answering or understanding the solutions to those questions.

We live in a world which relies very strongly on technology created through the understanding of science, but it seems that understanding science is a low priority for most students. Even back in 1990 in the uk, the percentage of students taking physics to A level was small, much less the number pursuing it to university. Physics and maths are perceived as "hard subjects",

What are the reasons people find science hard? I have a few ideas. I think that in the 1990s physicists were in very high demand in technology and industry sectors, and remain so in professions like accountancy, so given teachers salaries and the state of education, you'd really have to love to be a teacher as a graduate physicist.

The other reason is that it's very hard to bullshit physics. In social sciences, you can know nearly nothing, and come out with a D or C just by being articulate. In physics and maths, if you don't know anything, you can flunk out with zip. By the same token, if you know your stuff, you can ace out with 90+%, something which is very hard to do in arts and social sciences.

Still "schoolboy physics" shouldn't be frowned upon. Only about 3.6% of the uk population can perform schoolboy physics, and a much smaller fraction than that can do it well, and an even smaller fraction go on to take their skills any further.

Rambling aside, how accessible do you find physics? What do you think scientists could do to make science more accessible? What aspects of science are you most curious about?

[Animavore]

Well Stephen Hawkin manages it in a wheelchair so it must be fairly accessible.

[Clinton Huxley]

Well Stephen Hawkin manages it in a wheelchair so it must be fairly accessible.

They used the power of physics to build a ramp.

Me, I love physics. Unfortunately, my brain refuses to do complicated sums. Might as well try to get a cow to cross a tightrope.

[Trolldor]

I quite enjoy reading about physics, but whatever talent I had for math stops where basic maths does. I can rocket through simple division, multiplication etc. etc. but algebra I start to get hazy and beyond that I'm gone.

[Animavore]

Me too
I can understand things worded with illustrative examples, even relativity and quantum mechanics (seems easy but I know people who get it so wrong) , but the maths are lost on me.

[Clinton Huxley]

What a sorry bunch of numerical numbskulls we are.

[Xamonas Chegwé]

As a trained maths teacher and a (once and future) private tutor in maths, I have a few strong views about the teaching of maths in British schools. Physics is heavily maths based - if you can't do maths, you can't do physics - so these points have a knock-on on the teaching of physics as well.

1. Mathematics, more than any other, is a subject that builds from the bottom up. Unless the foundation is strong, you cannot build upon it. A child that does not understand the concept of addition, cannot understand multiplication. A child that does not understand the concept of an angle, cannot understand trigonometry. A child that does not understand the concepts of the triangle, angles, right-angles, square-numbers, algebra, rearranging equations and square-roots cannot understand Pythagoras' theorem no matter how well it is taught!
2. Mathematics, due to its concepts building on each other, is also a subject where a child that lags behind for whatever reason (truancy, sickness, lack of attention in a single key lesson, Mandy in the row in front developing breasts) can rapidly become discouraged and develop the view that they 'can't do it'!
3. Maths is seen as 'hard' and 'boring'. This is a direct result of the previous point.

These are the problems. the next step is to look at what causes these problems.

1. As has already been pointed out, you cannot hide in maths. Your answers are either right or wrong. There have been attempts in recent history to 'amend' this by awarding points for 'trying to use the correct method' - frankly, this is bollocks designed to up the exam results without actually teaching the subject!
2. Large class sizes are far more of a problem in maths than they are in other subjects. In a History, English, French, etc. lesson, a large class fulll of mixed ability pupils can all learn something. In maths, only those children that have the minimum required understanding of the prerequisites for the lesson's subject will learn anything at all! The rest might as well not be there - they will gain nothing, they will reinforce their convictions that they 'can't do it', they will disrupt the other students out of boredom and frustration and, most importantly, they will make the lesson hell for the teacher!
3. The majority of primary teachers are women with degrees in art subjects. I have nothing against women with degrees in art subjects - many of them are fucking hornyextremely competent. the trouble is that they themselves come from the group of children that found maths arcane, difficult and boring while they were at school - that is why they took arts degrees instead of the far more lucrative scientific disciplines! They have been through a short period of training as part of their PGCE course in 'how to teach maths' but they do not love the subject, they do not find it interesting or exciting, and they do not have the depth of understanding of maths to answer the questions that even a 7 or 8 year old child might ask. I know this. I spent 6 weeks in a primary school as part of my Bachelor of Education and I saw teachers that could only pass on, by rote, the methods that they had been taught at school themselves, without having a clue how to explain the theory behind 'carrying the one' to a curious kid that asks, 'why?'

And finally, if not the solutions, at least a few suggestions as to how things might be improved.

1. Specialist maths teachers at primary level. In the UK, children have a single teacher, for all subjects, from starting school until attending secondary school at the age of 11. This doesn't work! What happens is this: If you are lucky and get one of the few primary teachers that understands, can communicate and, most importantly, loves maths, you will leave for secondary school with a massive advantage in that department. (This is not just speculation - I have been told by maths teachers in secondary school that every kid that came from Mrs Blahblah's class in Thingummy Primary School is streets ahead of everyone else in the class - this is true of the 11/12 year olds - a couple of years of mixing with the can't do it - won't do it majority soon beats that out of them!)
   My suggestion is to have a single teacher that takes the class for around 50% of the time, with separate classes for maths and science, held by specialist teachers. This is not such a bizarre concept for a primary school - there are already specialist teachers for music and physical education - I am not knocking the benefits of either of these subjects but aren't maths and science worthy of similar status? The perception is that specialist music and sports teachers are required because not every teacher has the ability to play an instrument, or the physical fitness levels necessary for keeping up with a pack of hyperactive 10 year olds - but the simple fact is that 'any old teacher' does not have the mental skills necessary to impart mathematics and science to kids and to pass on their own love of the subject to the next generation.
2. Far smaller classes for maths and science subjects. This to be combined with much more streaming of abilities. It is somehow seen as 'elitist' to insist upon the separation of able and less able children - bollocks! It is common sense! Struggling children are not 'helped along' by being included in a class with more able peers - they are made to feel even more stupid and inadequate! Mixed classes resolve DOWN to the lowest common denominator - I have taught in mixed classes - I have seen it in action. A class full of less able kids at approximately the same level can all be given the same work and CAN help each other to understand it.
3. Employ 1-on-1 tutors within schools that can assist struggling pupils with their maths. As little as 20 minutes a week of personal tuition can be enough to bring a child that can't keep up with things back into the mainstream. Again, I have been a tutor, I have seen what a difference it can make. A teacher in front of a class of 30 has no time to make sure that every one of the class understands even the most basic prerequisites for that day's lesson. A trained tutor can quickly spot the gaps in a child's knowledge and fill them. Tutors can also assist the teachers to maintain the differential between streamed ability groups, moving children up or down as required and drawing attention to particular issues with specific kids.

[Xamonas Chegwé]

Yeah, I know, tl:dr.

[Twiglet]

I wonder to what extent it's possible to "get" physics without having a decent grounding in the maths.

I know there have been moves over the last 20 years in the uk and Australia towards teaching physics "conceptually", which often seems an excuse for avoiding needing to teach formulae by wrote.

I strongly agree with all XC's post about how maths teaching could be improved, and the reasons why people fall behind, but I'd like to elaborate on the maths thing because it's come up many times in this section.

Paul Dirac, one of the greatest mathematicians to have lived, said something along the lines of "I understand what an equation means when I know what the solution looks like without having to solve the equation".

When science is being taught, conceptual teach has value IMO, but I think that it's very hard to "get a feel" for what kind of solutions will be produced without performing calculations a few times and examining the results. A good basic example of this is mental arithmetic vs calculator use. Kids who are never taught mental arithmetic know what buttons to push, but they are much less likely to know when their answer looks ridiculous.

i.e. 12x12= ?? 1464 (obtained by calculating 12x122 - a typo on a calcultor) looks obviously ridiculous to someone who knows their times tables by wrote.
Similarly anyone who has plotted a few graphs of y=mx+c knows to expect a straight line graph, and when they have done a few, they know what the graph looks like without having to calculate the intersects.

Teaching concepts by analogy can be very powerful without maths..like (electric) voltage, current and resistance... by comparing the situation to a waterfall... voltage is the height of the waterfall, resistance is width of it and current is the amount of water that flows down it. That's an easy picture for kids to "get". What they may not get is where both analogies start to break down (not that they need to at a schoolyard level).

So conceptual teaching is good, but it has it's limits. They've been very apparant in the relativity threads. Humans are good at understanding analogies which mirror our experience, but when the physics points to something very counter-intuitive, as relativity does in saying that the speed of light constitutes an absolute limit, it's very hard to give analogies. To grasp it,. one needs, as Dirac suggests, to have an idea of what kind of solutions it will produce. If someone gets too hung up on analogies, they end up chasing their own tail without actually coming close to grasping what the theory means or predicts.

Quantum physics suffers from this even more than relativity, yet without quantum theory, we would still be on valve based computers and performing eye surgery with scalpels..not to mention all the other areas where the application of quantum theory has resulted in the design of amazing life changing new technologies. Silicon based semiconductors and lasers are always the first things which come to mind for me in discussing quantum theory. Of course, you don't have to understand quantum theory to appreciate whats arisen from it, but do many people even know whats arisen from it?

I guess that's another point. How many people have any practical use for relativity or quantum physics in the course of their daily lives unless they work in academia or R&D somewhere? If something seems hard, and you can earn a lot more money studying somethine else comparatively easy, then why bother except perhaps for the challenge or curiosity?

Back in the period after WW2 there was huge kudos associated with studying science. The classic "smart person" was a "rocket scientist" or a "nuclear physicist". Does that cache still exist? Has it gone to ground since the end of the cold war?

I guess also scientists aren't very good (as a bunch) in explaining science to non-scientists, or perhaps it's just that non scientists don't want to do the conceptual legwork to understand what the science is saying. In the information age, we have come to expect factoids in soundbites, but as XC said earlier, maths and physics builds understanding in a pyramid from the ground up. Without the building blocks, you can't get to the top. The best you can hope for is some kind of idea of what the pyramid looks like without really understanding why the picture might change.....

[Xamonas Chegwé]

Thanks for that post, Twiglet. You reminded me of a fucking huge point I missed in my list of improvements to be made in maths education.

NO FUCKING CALCULATORS UNDER PAIN OF DEATH!!1!! (OK. No calculators except where necessary - said necessity to be determined by the teacher alone!)

Kids need to learn to use them, sure, but NOT while learning to do simple arithmetic. Whenever I have worked as a private tutor, one of the first things I have done is to make the student learn their times tables. There are kids these days that reach for a calculator to multiply 2 by 3! I would estimate that the majority of 12 year olds cannot tell if a number is odd or even and can't even multiply by 10 by adding a '0'! This is all due to a reliance on calculators. Sure, they have their place in maths lessons - as a superior replacement to logs and and trig tables - but they should NOT be the first port of call when faced with ANY arithmetic problem as they so often are with the youth of today.



On your other point about the difficulty of scientists explaining things to non-scientists, that is a real problem. It doesn't apply solely to maths and science by any means - but other subjects are easier to pick up through 'osmosis' - even if you don't quite get what the teacher is saying, you can absorb what you can and fill in the gaps for yourself later. With technical subjects, this is much harder. The gaps are what stop you from progressing. You can read War and Peace and get something out of it without understanding every word. You cannot read a textbook on Special Relativity if you don't understand differentiation, algebra, or even multiplication!

One key skill of any good teacher is being able to see where and why the pupil is struggling. I also teach guitar and I found that my learning curve was as steep as my students' for the first few months - I needed to understand why they couldn't do what I found so simple and obvious - I needed to step into their shoes. literally standing behind them, adopting the same body and arm postures and holding my guitar exactly as they held theirs, before I could see where they were failing. It is the same with maths, or any other subject, you need to be able to forget that you know how to do something and find that mental blockage that is preventing the student from doing it - usually (always?) it is something far more basic than what you are trying to show them.

[JimC]

Great posts above from Twiglet and XC, almost all of which I agree with fervently. The calculator issue is an interesting one. Certainly, it should never be used to replace knowing one's times tables, or being able to do basic addition and subtraction. Factorising and similar skills in algebra require proficient mental arithmetic. Even long division has its place, at least knowing how to do it, since there are some techniques of factorising polynomials that use a very similar method. Skills with fractions also become vital later on, not just letting a calculator do the heavy lifting of finding common denominators...

However, later in secondary school, proficiency with calculator use is an absolute must.

One point I would like to make about physics is the vital necessity of practical work, particularly the sort that accumulates a decent amount of numerical data, and requires subsequent analysis and graphing, as well as intelligent interpretation of the underlying physics, as well as uncertainty levels etc. Nothing beats letting trolleys roll down ramps, smashinhg into other trolleys, while students are measuring every aspect they can. And students love it!

[Farsight]

SInce we kicked off a few threads with A level maths & physics problems, a couple of people passed comments about "schoolboy" problems in a rather depreciating way, so I looked up a couple of articles (uk based) to see just how many schoolboys (and girls) would have much of answering the problems Jim & I were posing. The source docs I found are:

http://www.buckingham.ac.uk/news/pressr ... ics-2.html
http://www.aps.org/publications/apsnews ... udents.cfm

Most worryingly, from the Bucks uni study:

"Only just over 3.8 per cent of 16-year-olds took A-level physics in 2004 compared with about 6 per cent in 1990."

This is why I'm doing what I'm doing. Our two teenage children gave up maths and all their science subjects, so I felt like a bad parent, and was motivated to contribute homework help on forums. I was also upset by the demolition of the Manchester University maths tower in 2005 - I had classes in that. So I was giving homework help, not answers, but guidance, only the naive questions like "What is energy?" caused me problems. Then I realised that the stock answers were sometimes circular and didn't get to the bottom of things. Then I realised that people didn't understand what the terms mean, even in simple expressions like E=mc². To explain what they mean, you can't use maths. If you do you're describing one term only in terms of others, and it just isn't enough. Hence one has to use evidence and analysis and analogy and logic, but then guys like you dismiss it as arm-waving. It isn't. It's plumbing the depths of fundamental physics.

So in short, even with the basic problems we've been playing with, only a pretty small number of people (1 in 15 to 1-20) would have much hope of answering or understanding the solutions to those questions. We live in a world which relies very strongly on technology created through the understanding of science, but it seems that understanding science is a low priority for most students. Even back in 1990 in the uk, the percentage of students taking physics to A level was small, much less the number pursuing it to university. Physics and maths are perceived as "hard subjects"...

Yes they are. UK physics A-levels are down 57% in 25 years. I'm guessing that part of the reason is an imbalance between mathematics and experiment, a disconnection from reality and application, and health & safety issues which have eroded the "wow factor" that engenders curiosity and a desire to find out how the universe works. But I'm not a physics teacher, so I don't really know.

What are the reasons people find science hard? I have a few ideas. I think that in the 1990s physicists were in very high demand in technology and industry sectors, and remain so in professions like accountancy, so given teachers salaries and the state of education, you'd really have to love to be a teacher as a graduate physicist. The other reason is that it's very hard to bullshit physics. In social sciences, you can know nearly nothing, and come out with a D or C just by being articulate. In physics and maths, if you don't know anything, you can flunk out with zip. By the same token, if you know your stuff, you can ace out with 90+%, something which is very hard to do in arts and social sciences.

I wouldn't disagree.

Still "schoolboy physics" shouldn't be frowned upon. Only about 3.6% of the uk population can perform schoolboy physics, and a much smaller fraction than that can do it well, and an even smaller fraction go on to take their skills any further.

I frown upon "schoolboy mathematics" when it's employed to derail a thread and avoid discussion of the evidence and logic and fundamental physics.

Rambling aside, how accessible do you find physics?

Not very. I'd say that too many theoretical physicists dwell too much on the mathematics and don't spend enough time on "what it means". The result is papers that present a torrent of difficult-to-follow mathematical expressions but get nowhere.

What do you think scientists could do to make science more accessible?

Realise that physics isn't maths. Mathematics is a vital tool for physics, but in itself mathematics is not a science. It doesn't follow the scientific method, and too much focus on mathematics can result in theoretical physicists losing their connection with reality and then making untestable speculations concerning things like time travel and the multiverse.

What aspects of science are you most curious about?

Fundamental physics. Note that I've given paid-for mathematics tutoring to schoolchildren up to A-level. Generally I'd say those who struggle are lacking interest and inspiration, and are convinced that it's both difficult and irrelevant. IMHO a book called How Long Is a Piece of String? by Rob Eastaway and Jeremy Wyndham demonstrates a good approach for addressing this.

[ChildInAZoo]

To explain what they mean, you can't use maths. If you do you're describing one term only in terms of others, and it just isn't enough. Hence one has to use evidence and analysis and analogy and logic, but then guys like you dismiss it as arm-waving. It isn't. It's plumbing the depths of fundamental physics.

What you do is worse that arm waiving. You are actually harming the intellectual development of people (e.g. Brain Man) because you offer a pleasing fiction. The job of actually explaining physics has to go to those who understand physics, and people who do not understand, even in a superficial way, the important mathematical relationships of the specific theories of physics do not understand physics. You do not understand physics, but you can string together what looks to be a meaningful story to those who are ignorant of physics. This will hurt them in understanding real physics.

[Twiglet]

This is why I'm doing what I'm doing. Our two teenage children gave up maths and all their science subjects, so I felt like a bad parent, and was motivated to contribute homework help on forums. I was also upset by the demolition of the Manchester University maths tower in 2005 - I had classes in that. So I was giving homework help, not answers, but guidance, only the naive questions like "What is energy?" caused me problems. Then I realised that the stock answers were sometimes circular and didn't get to the bottom of things. Then I realised that people didn't understand what the terms mean, even in simple expressions like E=mc². To explain what they mean, you can't use maths. If you do you're describing one term only in terms of others, and it just isn't enough. Hence one has to use evidence and analysis and analogy and logic, but then guys like you dismiss it as arm-waving. It isn't. It's plumbing the depths of fundamental physics.

Questions like "what is energy" or "what is mass" are deep questions, but they are essentially philosophical ones. Science probes the relationship between testable parameters. We can agree how to measure energy in a lab, and the mechanisms by which it's measured are repeatable. Likewise spatial dimensions.

I'm actually quite open to the idea that there is some as yet unexplored relationship between mass, gravity and time - but i don't think you or I will arrive at it by pretending that existing theories substantiate fictitious arguments.

The methodology in those schoolboy problems which you dismissed so lightly elsewhere is exactly the same methodology applied in much more complicated equations to predict outcomes. They were designed to be so, after all, school examinations are designed to prepare students for undergraduate courses. Special relativity can be taught with basic algebra and elementary calculus, but conceptually, it is out of synch with how we experience the world at classical speeds.

I frown upon "schoolboy mathematics" when it's employed to derail a thread and avoid discussion of the evidence and logic and fundamental physics.

I'd say that too many theoretical physicists dwell too much on the mathematics and don't spend enough time on "what it means". The result is papers that present a torrent of difficult-to-follow mathematical expressions but get nowhere.

Thats not really an issue for schoolkids. If anything physics is pretty dry at A level. Lenses, Kirchoffs law, stress, strain, elastic and plastic deformation, basic scalar e-m, Newtons equations of motion, Newtons laws of gravity, very basic quantum physics, radiative decay, HR diagrams for astronomy electives, dimensional analysis, moments of inertia in mechanics options....

Mostly students learn (and struggle to learn) methods to solve simple scalar problems by selecting from a toolbox of rules. They conduct experiments with voltmeters, chucking ball bearings off tables and timing their fall, that kind of stuff.

At undergraduate level, there is still a stong emphasis on experiment, but the experiments and theories become more complicated, in fact, a big transition is between basic theory and experimental model, where real world approximations are made to account for the imperfect conditions in which experiments happen. Skills like error analysis are developed. The "certainty" of experiments is quantified. There's a good mix between theory and practice.

PhD and MSc level physics usually focus on research based issues, such as the formation of liquid crystals, or propogation of optical pulses in fibre-optic media and waveguides. There is a mix between learned theory, experiment, and dissertation work geared towards producing or assisting in the production of academic papers.

Research fellows work under the directive of a unit head exploring specific aspects of an experiment, or a theory, or both. There is usually a very strong focus on a specific area of expertise, and elements of teaching - perhaps delivering tutorials. That's the bread and butter of practical academic science farsight.

The way you post seems so adversarial to that, I really don't understand why.

I can agree to a point that many scientists don't ponder the "deep questions" of what charge is or energy or whatever as part of their work. Most practical science gears towards creating experiments to test new ideas and come up with useful applications for those ideas by developing prototype products which go forward to find use in industry, or shed light on existing phenomena we've observed in a lab, but can't fully explain yet. Liquid crystal science is an example from 18 odd years ago which had huge focus, and the research on it has led to widespread adoption of superb LCD screens and thin films. Physics over the last 20 years has contributed immensely to the creation of new devices, many of which are probably in your home and certainly in mine. Much of those developments rely on a rock solid understanding of quantum theory, electromagnetism, chemistry, material science and so forth.

The innovations and discoveries of modern physics are tightly woven into the fabric of our daily lives.

Now it is fair to say that we haven't had huge paradigm shifts like the transition between Newtonian mechanics and relativity, and the fundamentals of quantum theory remain unchanged, but that is a function of how successful existing theory is at modelling reality. If anything, the efforts to unify the areas in which quantum theory and relativity overlap are the province of physics' explorers. The very people who are thinking at the margins, and I imagine farsight, the same people who are very dismissive of you - if any have given you the time of day. But I don't think they are being dismissive because your concepts are so radical farsight.

What do you think scientists could do to make science more accessible?

Realise that physics isn't maths. Mathematics is a vital tool for physics, but in itself mathematics is not a science. It doesn't follow the scientific method, and too much focus on mathematics can result in theoretical physicists losing their connection with reality and then making untestable speculations concerning things like time travel and the multiverse.

Maths provides a useful set of tools which can appropriated to show what theories predict, and mathematical exploration of those ideas can yield new results and ideas in it's own right. For example, the div,grad and curl identities provide very useful techniques for reformulating and solving Maxwells equations when applied to real life problems. Many more examples exist.

[colubridae]

To explain what they mean, you can't use maths. If you do you're describing one term only in terms of others, and it just isn't enough. Hence one has to use evidence and analysis and analogy and logic, but then guys like you dismiss it as arm-waving. It isn't. It's plumbing the depths of fundamental physics.

What you do is worse that arm waiving. You are actually harming the intellectual development of people (e.g. Brain Man) because you offer a pleasing fiction. The job of actually explaining physics has to go to those who understand physics, and people who do not understand, even in a superficial way, the important mathematical relationships of the specific theories of physics do not understand physics. You do not understand physics, but you can string together what looks to be a meaningful story to those who are ignorant of physics. This will hurt them in understanding real physics.

Couldn't agree more...

What farsight's stuff is to physics as alternative medecine is to real medecine.

There is no excuse for it.
It's why several people have been annoyed by the bullshit.

Maybe you 'believe' your stuff, maybe you feel guilty about your kids, maybe you are doing a mandelson. I don’t honestly know.

I do know if you are teaching your kids this stuff you are fucking up their chances for a scientific career. They will have a hard time unlearning your nonsense.