The coming revolution in physics education

[Will Flannery]

More seriously, in my opinion a physics or engineering program is failing their students if they graduate without being exposed to some set of tools they can use to compute rocket trajectories or solutions of Kepler's equation (perhaps with some guidance from standard resources available in the library or online). Whether or not they solved that exact problem in their curriculum is much less important. I've worked with people holding physics and engineering degrees from a number universities. Anecdotally, it has been much more common for new-hires to have conceptual shortfalls or weak analytical skills than to have trouble throwing the computer at a problem.

You are missing the point entirely !

But, before we get to particulars*** ... let's backup a little ... let's assume you've looked at the paper as everything is based on that, then you have seen several graphs that you've probably never seen before and that I claim, and I hope demonstrate, to the point of starting with the physics and ending with the code, are easily obtainable by high school science students. For example, the Apollo trajectory, or even better, the Juno trajectory. The reaction I expect is ... Wow ! ...

Yes? No?

*** can be addressed in subsequent posts

 

[Dale]

demonstrate, to the point of starting with the physics and ending with the code, are easily obtainable by high school science students

Since the results are based on a cherry picked population of the two brightest students with a 2:1 student teacher ratio, I think “easily” obtainable is wholly unsupported by the data.

The reaction I expect is ... Wow ! ...

Why would you expect that? That the two best students in a high school could, with dedicated personalized tutoring, complete a Sophomore-level college project is not that surprising. Advanced students with individualized instruction should be expected to accomplish specific tasks two years early.

I suspect that you could take any sophomore-level college skill, take the two best high-school students, give them a 2:1 student teacher ratio, and they will accomplish the task.

 

[Dr.D]

Did anybody mention that Euler is unstable?

 

[Dale]

Did anybody mention that Euler is unstable?

I did, and recommend using prepackaged ODE solvers instead of hand coding Euler’s method. All the way back in post 2

 

[jasonRF]

You are missing the point entirely !

But, before we get to particulars*** ... let's backup a little ... let's assume you've looked at the paper as everything is based on that, then you have seen several graphs that you've probably never seen before and that I claim, and I hope demonstrate, to the point of starting with the physics and ending with the code, are easily obtainable by high school science students. For example, the Apollo trajectory, or even better, the Juno trajectory. The reaction I expect is ... Wow ! ...

Yes? No?

*** can be addressed in subsequent posts

I didn't miss the point, I just wrote a poor post! Don't get me wrong - I'm sure those two high-school students are impressive and probably gained a lot from the experience. I doubt I would have been up to the challenge (just like I didn't even come close to acing the PSAT!), or had the motivation for that matter. But I agree with Dale on this one, in that it is solid sophomore level work. While spacecraft trajectories are certainly more interesting than the programming projects on nonlinear oscillators (using Runge-Kutta) and the heat equation (using finite differences) I had to code up from scratch in a differential equations class my sophomore year, it is fundamentally at the same level. So it is impressive, but was almost a let-down after all of the hype in your posts. It is hard to say wow! when something doesn't live up to expectations.

But I'm looking at all of this from a different perspective. Most physics majors will eventually end up in industry. I am an engineer working at a company that hires some of those students, although we certainly hire more engineers than physicists. From my perspective, students need certain skills in order to be able to function at my workplace, and an ability to apply standard numerical methods is one of those skills. This is why I think departments are failing their students if they don't learn at least some numerical skills. I know that physics programs are academic so do not have the same job-preparation goals most engineering programs have. But I would hope physics departments would include such considerations a little when they are designing curricula.

So I am actually 100% on-board with forcing physics students to take a dedicated course on numerical methods. A freshman course is certainly better than nothing, but if a student we are hiring is to take such a course I would much prefer an upper-division version than a freshman version. That way they would learn more sophisticated techniques, have deeper understanding of assumptions and limitations, etc. For example, they would know not to use Euler's method to design something that will cost my project time and $$$ if it is wrong ! I suspect an upper-division course would be more useful for those students going to physics graduate school as well. The pedagogical benefits would have to be significant to prefer the freshman version. This likely means that the syllabi of the subsequent physics courses would need to change. I wonder what topics you propose to eliminate from each course to make room for this new numerical work? Or do you think it can be added without removing anything at all? I doubt it...

In any case, my anecdotal evidence is that our newly hired employees from both physics and engineering programs typically know enough about numerics to be useful. I'm sure they are teaching themselves some of it on-the-job, but that is always expected. Perhaps some of my coworkers learned a little in a standard differential equations course, while others may have taken dedicated courses on numerical methods. I had the benefit of both. Our new-hires (including me, when I was new) are much more likely to have other significant weaknesses than they are to struggle with the kind of basic numerics we need them to do. Advanced numerics are something else altogether of course; there are a few engineers on staff who are expert numericists and we track them down when needed.

jason

 

[Dale]

So it is impressive, but was almost a let-down after all of the hype in your posts. It is hard to say wow! when something doesn't live up to expectations.

That is my main issue here too. I am in principle highly supportive of using numerical methods and computational tools in physics, but the blatant overselling is a real turn-off.

I would much prefer an upper-division version than a freshman version. That way they would learn more sophisticated techniques, have deeper understanding of assumptions and limitations, etc.

At my institution it was a sophomore year course, but I cannot remember the course number so it may have technically been an upper division class. At that point in our studies we had all taken at least one programming language (mandatory freshman year) so the class did not need to cover programming-specific topics, but straight numerical methods concepts. We covered many different methods as well as which methods failed on what types of problems and why.

 

[physicsponderer]

Not at all. What if I had said, "Without reading, one cannot really teach law" or "Without reading, one cannot really teach history"?

I would have disagreed. You don't get to redefine English words. Physics does not only mean a good complete physics degree course. Law does not only mean a good complete law degree course. History does not only mean a good complete history degree course.

Physics is (the study of) the the fundamental things of the universe: energy, mass, time, fundamental particles and so on. I was careful to specify that by 'maths' I meant the ordinary sense of the word meaning equations or calculations, and not some broader sense where merely mentioning kilograms is maths, for example. It's possible to teach years and years of physics without requiring students to use equations or do calculations, even if the bedrock of physics is mathematical, and most of physics is mathematical. Have you looked at "Relativity Visualized" by Lewis Carroll Epstein? He uses word and pictures to explain the basics of special relativity.

Telling someone that the Earth goes around the sun in an elliptical orbit is physics. It's not all of physics, or even all of the physics of orbits. But some of physics is still physics, and teaching some of physics is still teaching physics.

It seems to me that most physics graduates are sorely lacking in understanding the meaning of the maths they have learned to use. They don't understand how the world works. They believe all sorts of misconceptions about physics. I suspect that the reason is a neglect of nonmathematical physics in physics degree courses. Most graduates do not even understand Newton's third law of motion, nor can they tell you what causes wood to float on water. These things can be explained nonmathematically, but are parts of physics, and in my opinion, very important and interesting parts of physics. Physics puzzles ('What if' type questions in words, requiring no calculations) show how shallow the understanding of how things work can be, of graduates and even professors of physics. I believe that acting as if physics is a branch of maths is part of the problem.

 

[physicsponderer]

That is my main issue here too. I am in principle highly supportive of using numerical methods and computational tools in physics, but the blatant overselling is a real turn-off.

If he is basically right, I can forgive him for being passionate about the point he is making. Why is the 'overselling' such a turn off for you?

 

[physicsponderer]

Anecdotally, it has been much more common for new-hires to have conceptual shortfalls or weak analytical skills than to have trouble throwing the computer at a problem.

What the paper shows is use of a computer to solve a problem. It is no more a case of throwing a computer at a problem than solving a problem with pencil and paper and ruler is throwing a pencil, paper, and ruler at the problem.

 

[hutchphd]

It's possible to teach years and years of physics without requiring students to use equations or do calculations, even if the bedrock of physics is mathematical, and most of physics is mathematical.

This is true but what you seem to ignore is how much simpler it is when you know the appropriate mathematics. At some point the easiest way to learn is to bite the bullet and learn the mathematics. It is taught that way not because of some mathematical fetish among practitioners of the craft.
At some point in a foreign country one learns the language or has a much diminished experience.

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[Dale]

If he is basically right, I can forgive him for being passionate about the point he is making. Why is the 'overselling' such a turn off for you?

Passion doesn’t excuse deception. When someone uses exaggeration and misrepresentation to push their product then they lose credibility. It weakens their persuasiveness and feels like a traditional high-pressure used-car sales experience.

It seems to me that most physics graduates are sorely lacking in understanding the meaning of the maths they have learned to use. They don't understand how the world works. They believe all sorts of misconceptions about physics. I suspect that the reason is a neglect of nonmathematical physics in physics degree courses. Most graduates do not even understand Newton's third law of motion, nor can they tell you what causes wood to float on water

Have you any actual evidence for this bold claim? Most means >50%. Do you have any peer reviewed study or survey or standardized test that actually demonstrates that >50% of graduates from an accredited physics program don’t understand Newton’s 3rd law?

If so please provide that evidence. If not please retract your exaggerated claim.

 

[hutchphd]

If he is basically right, I can forgive him for being passionate about the point he is making. Why is the 'overselling' such a turn off for you?

This is like the drunk guy looking for his keys
He is not "basically right". His premise is that computers are useful in physics so why should we mess with all this other difficult stuff. Over and over and over.
Indeed computers are useful. But they do not substitute for comprehensive and global understanding afforded by the symbolic mathematics. Every good physicist needs both. The fact that the computer part is easier does not imply we should spend more time there.

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[physicsponderer]

Passion doesn’t excuse deception. When someone uses exaggeration and misrepresentation to push their product then they lose credibility. It weakens their persuasiveness and feels like a traditional high-pressure used-car sales experience.

Have you any actual evidence for this bold claim? Most means >50%. Do you have any peer reviewed study or survey or standardized test that actually demonstrates that >50% of graduates from an accredited physics program actually don’t understand Newton’s 3rd law?

If so please provide that evidence. If not please retract your exaggerated claim.

That sounds like a demand. Is it?

 

[hutchphd]

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Sounds like a reasonable request to me. Having taught in several accredited programs I find your statements difficult to believe and would like proper documentation

 

[Dale]

That sounds like a demand. Is it?

On PF it is expected that all posts be consistent with the scientific literature. It is common to ask for references here, and such requests should always be honored, even if you think the point is obvious. If one cannot provide such a reference then it is expected that one will retract the unsupported claims. This is a key part of the PF culture that keeps our quality high compared to other science forums.

 

[physicsponderer]

This is true but what you seem to ignore is how much simpler it is when you know the appropriate mathematics. At some point the easiest way to learn is to bite the bullet and learn the mathematics. It is taught that way not because of some mathematical fetish among practitioners of the craft.
At some point in a foreign country one learns the language or has a much diminished experience.

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I was responding to Dr Courtney's claim that you are not teaching physics if you do not require your students to perform calculations. Have you had a look at 'Relativity Visualized' by Lewis Carroll Epstein?

'At some point the easiest way to learn is to bite the bullet and learn the mathematics. ' you wrote.
You can't say that that is true for every individual. Some people have terrible trouble with maths, perhaps even a sort of mathematical dyslexia. Others have a strong aversion to maths. Surely, everyone should have an opportunity to study physics. Why not have a nonmathematical physics course for such people? I think it was done by the author of 'Physics for the Inquiring Mind' about thirty years ago. I'm not sure the name of the author (I think he based the book on a course he had run at an Ivy League university in the US) as there are several books of that title, it seems, but it's a wonderful book. There are simple calculations, including mental arithmetic tricks and ways to get approximations, but the maths is kept to a minimum, as I recall. The emphasis is on understanding, it delivers. Maths is used only where strictly needed.

My impression is that at schools and universities around the world, explanation and context is kept to a minimum in physics courses in order to teach as much maths as possible.

I've found that maths graduates are at least as good at solving physics puzzles as physics graduates. I suspect that is partly because maths students think more carefully, having less confidence about physics.

 

[physicsponderer]

On PF it is expected that all posts be consistent with the scientific literature. It is common to ask for references here, and such requests should always be honored, even if you think the point is obvious. If one cannot provide such a reference then it is expected that one will retract the unsupported claims. This is a key part of the PF culture that keeps our quality high compared to other science forums.

What happens if I don't retract my statements?

 

[hutchphd]

What happens if I don't retract my statements?

If you say things that you cannot verify on a regular basis, no one will care what you say. And then you will be asked to not participate. Pretty simple. So please provide documentation.

 

[physicsponderer]

This is like the drunk guy looking for his keys
He is not "basically right". His premise is that computers are useful in physics so why should we mess with all this other difficult stuff. Over and over and over.
Indeed computers are useful. But they do not substitute for comprehensive and global understanding afforded by the symbolic mathematics. Every good physicist needs both. The fact that the computer part is easier does not imply we should spend more time there.

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It seems to me writing a computer program that simulates a physical system requires at least as much understanding as learning to use an equation. I don't see how you can write a program to simulate something without a fairly good understanding of the fundamentals of that thing. 'Plug and chug' is a phrase that means plug the values of the variables into the correct formula (after rearranging it if need be) and then do the arithmetic to get the answer. Unfortunately, many students are able to learn how to plug and chug with little or no understanding of the meaning of what they are calculating.

 

[Dale]

What happens if I don't retract my statements?

@hutchphd is right, you can read about the details of the system in the rules, but why wouldn't you want to retract the statement? If you know that your statement is false why would you not want to retract it and say the correct statement instead?

One of the big differences between scientists and politicians is that scientists are willing to change their opinions when their opinions are not consistent with the facts. I know that when I have said something wrong I try to correct it as soon as I realize the mistake.

 

[physicsponderer]

@hutchphd is right, but why wouldn't you retract them? If you know that your statement is false why would you not want to retract it and say the correct statement instead?

One of the big differences between scientists and politicians is that scientists are willing to change their opinions when their opinions are not consistent with the facts.

What exactly does retracting a statement mean to you? Does it involve deleting the original statement?

 

[Dale]

What exactly does retracting a statement mean to you? Does it involve deleting the original statement?

No, at this point there have been too many subsequent posts. It usually isn’t a good idea to edit a post after it has been responded to. You can just say “oops” and whatever you think the correct statement should be instead.

 

[physicsponderer]

No, at this point there have been too many subsequent posts. It usually isn’t a good idea to edit a post after it has been responded to. You can just say “oops” and whatever you think the correct statement should be instead.

I'm tired. I'll have to think about this. I'll respond later.

 

[hutchphd]

thanks to @Janus

The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts. (Bertrand Russell)

It is hoped to limit these discussions to wise people.
Having taught Newton's Laws to many freshmen I am ashamed to admit I can't always remember the numbering correctly. So some of your claim may involve my former students scarred for life by my confusion...

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[Dale]

I'm tired. I'll have to think about this. I'll respond later.

I understand, everything is difficult when you are tired. In any case, when you approach it with fresh eyes hopefully you will see the merit of having discussions based on facts.

 

[jasonRF]

What the paper shows is use of a computer to solve a problem. It is no more a case of throwing a computer at a problem than solving a problem with pencil and paper and ruler is throwing a pencil, paper, and ruler at the problem.

That is a fair criticism of my statement - I should have used words that were unambiguously neutral.

jason

 

[physicsponderer]

That is a fair criticism of my statement - I should have used words that were unambiguously neutral.

jason

I wasn't asking for neutral words. I guess I would like you to expand on 'throw the computer at' because I don't know what you mean. The minuscule amount of knowledge I have about coding has led me to believe that the computer is a tool that needs to be used with great care and insight, or otherwise you almost always get unexpected results.

 

[physicsponderer]

I understand, everything is difficult when you are tired. In any case, when you approach it with fresh eyes hopefully you will see the merit of having discussions based on facts.

Please tell me where I can read the rules of this site.

 

[physicsponderer]

I understand, everything is difficult when you are tired. In any case, when you approach it with fresh eyes hopefully you will see the merit of having discussions based on facts.

I guess I was a bit tactless. Maybe a bit of hyperbole crept in. I take it all back.
What I meant to say was:
In my experience, most physics graduates have been somewhat lacking in understanding of the meaning of the maths they had learned to use. They didn't seem to understand how the world works as well as I would have expected. Most of the ones I talked to believed at least one misconception about physics. I suspect that the reason is a neglect of nonmathematical physics in physics degree courses. Most physics graduates that I talked to seemed not to fully understand Newton's third law of motion, nor were most of them able to explain to my satisfaction what causes wood to float on water.

 

[physicsponderer]

thanks to @Janus

The whole problem with the world is that fools and fanatics are always so certain of themselves, and wiser people so full of doubts. (Bertrand Russell)

It is hoped to limit these discussions to wise people.
Having taught Newton's Laws to many freshmen I am ashamed to admit I can't always remember the numbering correctly. So some of your claim may involve my former students scarred for life by my confusion...

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Well, the original numbering has for some time seemed a bit odd. Perhaps Newton liked the number three. I have read that the first law is properly part of the second law. F = ma implies that when F is zero, a will be zero, for constant m which is what the first law is saying, right? Then F = ma would be the first law and for every action there is an equal and opposite reaction would be second law. I've read that Newton added indigo so there would be exactly seven colours, because that matched some other groups of seven in physics (known planets at the time, and musical notes, as recall).

 

[Dale]

Please tell me where I can read the rules of this site.

The rules are here: https://www.physicsforums.com/threads/physics-forums-global-guidelines.414380/

You can always find them under the Info tab at the top.

In my experience, most physics graduates have been somewhat lacking in understanding of the meaning of the maths they had learned to use. They didn't seem to understand how the world works as well as I would have expected. Most of the ones I talked to believed at least one misconception about physics. I suspect that the reason is a neglect of nonmathematical physics in physics degree courses. Most physics graduates that I talked to seemed not to fully understand Newton's third law of motion, nor were most of them able to explain to my satisfaction what causes wood to float on water.

That is interesting. My experience is exactly the opposite (although I have not had any "wood on water" discussions with physics graduates).

I have found physics graduates to be mostly impressive people with good understanding of math and the way the physical world works. I have not met a single physics graduate that didn't understand Newton's third law. I wonder what is different between our two sets of anecdotal experiences?

I suppose if I had pressed and dug I could have uncovered at least one misconception with each. Since eminent physicists like to make wagers on physics and since at least one side of the wager must have a misconception, I don't think that having one misconception is a substantive criticism. I am sure I have many more than one.

 

[Will Flannery]

So I am actually 100% on-board with forcing physics students to take a dedicated course on numerical methods. A freshman course is certainly better than nothing,...

I'll try a different tack. You have apparently condensed my 'revolution' down to taking a numerical methods course early, but that's only part of it. So, let's examine this idea in context, something which has been entirely missing from this thread, and that is my fault. In the beginning I didn't think context was important. However, at the editors insistence I did include context in the published version of the paper ... the editors asked for a literature review but ... there is no literature for the basic idea of teaching numerical methods in high school ... so I included this section ...

IMPROVING PHYSICS EDUCATION
The early introduction of differential equations, but not computational calculus, into the university engineering curriculum is one of the primary features of an ongoing NSF sponsored project at Wright State University that has had great success.7

Computational calculus is one of the primary components of computational physics, and there is a growing awareness that universities have been slow to incorporate computational physics into the physics curriculum. A group of physics professors, Partnership for Including Computation in Undergraduate Physics (PICUP)8, has formed to promote the incorporation of computational methods into university undergraduate physics education. The PICUP approach is ‘top down’, in that the goal is to introduce computational methods into already existing physics courses. 9,10 One well-known textbook integrates computational methods, but not differential equations, into introductory college level physics.11

The proposed course represents a new approach that is ‘bottom up’ and introduces computers, differential equations and computational calculus into the physics curriculum at the beginning, independently of the math curriculum beyond high school algebra and geometry.

The rest of the paper is dedicated to establishing two things: #1 - it is possible to teach powerful numeric methods in high school or the first year of college, and #2 - the benefits of teaching numeric methods early are enormous.

#1 - in order to show how trivially easy computational methods are an example is worked in complete detail to the point of calculating the trajectory of Newton's falling apple by hand. The next step is to program the procedure in MATLAB, and the translation from hand calculation to MATLAB statements is essentially 1 to 1 and by rote. The details are in the paper.

And, thanks to this thread and post #108 we know that MATLAB programming is introduced in high school at the Wilberforce Academy, and I looked into this and Wilberforce uses the Trinity curriculum that is used in three Trinity Schools, and includes computers, differential equations, an computational methods , one of the schools is Trinity Greenlawn where MATLAB is introduced in grade 11 and the 12th grade physics course description reads .

Physics B, C (2 Semesters) Students continue their study of physics using calculus in problem-solving. Some topics in mechanics are revisited using the calculus, culminating in the solution of the Kepler problem. ...

I think the paper establishes #1 beyond any reasonable doubt, and this confirms it. I'm trying to get more detailed info on Trinity program.

#2 - the central force motion examples in the paper dramatically demonstrate the enormous benefits of teaching computational methods. Newton's solution to the Kepler problem represents the beginning of modern math and science, and it is almost unsolvable analytically, you have to use the computer. And yet, I have not found one traditional university physics text, upper or lower division, that gives a solution.

So, what happens in a typical high school physics class is that the physics of central force motion is easily presented, the model for central force motion is derived by one division statement. And the class has arrived at an almost unsolvable problem, see the analytic infinite series solution here wiki Freefall.

And white Kepler's problem is almost unsolvable analytically, the three-body problem, e.g. a rocket trajectory from the Earth to the moon, is completely intractable analytically.

What is true for central force motion is true for every branch of classical physics, that is, after the physical laws are stated and the system model derived, the student is faced with unsolvable or nearly unsolvable differential equations.

The paper includes examples from electric circuit analysis and 2-D rigid body dynamics that illustrate how these systems are analyzed outside the classroom. My new paper includes examples for heat transfer, wave phenomena, stress and strain in materials, fluid dynamics, and electrodynamics.

A previous post, #104, gives examples from upper division texts for classical dynamics, heat transfer, vibration, and fluid dynamics, where the text defers to numerical methods because the systems they've described cannot be analyzed using traditional methods.

The bottom line is computational calculus is the only way real systems can be analyzed.
*** the wider context is that the NSF has realized for a long time that something is wrong with math education and spent millions in the 1990s trying to improve it with no results, and is now spending millions to improve STEM education with studies that are almost comical, e.g. Computational Thinking for Preschoolers'>>

 

[Dale]

You have apparently condensed my 'revolution' down to taking a numerical methods course early, but that's only part of it.

What was the other part of it? (not the context but the other part of the "revolution" besides an early numerical methods course)

 

[Will Flannery]

What was the other part of it? (not the context but the other part of the "revolution" besides an early numerical methods course)

The revolution is to introduce differential equations, computational calculus, and computers into the curriculum at the start and to use them to analyze physical systems in all classes in classical physics, specifically mechanics, electric circuit analysis, dynamics, heat transfer, wave phenomena, stress and strain in materials, fluid dynamics, and electrodynamics.

 

[hutchphd]

Look at how well the availability of circuit simulation has improved the analytic capabilities of analog electrical engineers! Its a revolution! Paradigm shift! Everybody knows it!
No.
It is a tool among many tools. And good practitioners learn all the tools. Chacun a son gout