The coming revolution in physics education

[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]

.

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...

.

 

[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

 

[physicsponderer]

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.

I guess I have a fascination with physics puzzles and misconceptions of all sorts, regardless of subjects. Perhaps I overvalue them. Physics graduates do understand the physical world well, compared to graduates in other subjects, but I just think they should understand it better than they do.

 

[Dale]

I guess I have a fascination with physics puzzles and misconceptions of all sorts, regardless of subjects. Perhaps I overvalue them. Physics graduates do understand the physical world well, compared to graduates in other subjects, but I just think they should understand it better than they do.

OK, but do you honestly believe that a mere change in curriculum would change that?

 

[physicsponderer]

OK, but do you honestly believe that a mere change in curriculum would change that?

I think changing the curriculum would have some effect, but I have no idea how much. Maybe if to get onto a degree course in the first place students had to show exceptional ability at physics puzzles, that might help more.

 

[Dale]

I think changing the curriculum would have some effect, but I have no idea how much.

Really? I suspect that you would just come up with different tricky puzzles and make the same complaint. I.e. I do not think that the complaint indicates a real deficiency, but an unrealistic expectation. There will always be some set of tricky puzzles that would trick a good number of graduates.

From my experience, physics graduates are well equipped to work at my company where I was a hiring manager for about 15 years. I didn't spend a lot of time deliberately finding puzzles to trick them, but I am sure that such puzzles could have been found. But again, that they should be puzzle experts or untrickable is an unrealistic expectation in my opinion, and wholly unnecessary for my real-world needs.

 

[Dr. Courtney]

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

Of course, but both the overall context of this thread and the specific context of the part of my post you failed to quote make it clear that most of the discussion here is talking about complete physics courses. One does not have a "coming revolution in physics education" without discussing complete courses.

Recall that I wrote:

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

At the high school and college levels, one is not really teaching law or history with the appropriate level of rigor if one does not require the students to _READ_.

So sure, there are some elementary physical principles that can be taught to students without requiring them to do math. But with the exception of physics courses with "Conceptual" in the name, one is not being honest about the rigor if one is teaching high school or college physics without requiring students to do the math.

What would you think of a law school that did not require their law students to read? This is how I regard physics teachers who do not require their students to solve quantitative problems.

You don't get to redefine physics courses (by removing the math) without getting your mathless course descriptions approved by the appropriate bodies and accrediting agencies. And that is the sleight of hand being attempted in many high school and college physics courses these days - they are telling the accrediting agencies and downstream stakeholders (courses, employers, etc.) that their physics courses are still based heavily in quantitative problem solving, yet students who pass these courses are barely able to solve the kinds of problems the course descriptions lead the downstream stakeholders to believe the students can solve.

The most important question I think teaching candidates need to ask is, "Are you going to fire me if I am unwilling to pass students who cannot do the math required in my courses?" Many teaching candidates are afraid to ask this question, and many teachers go ahead and gift grades to keep their jobs. This is just as fraudulent as history and law professors passing students who cannot read.

 

[abcd112358]

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.

In (a part of) germany there was a change in the curriculum about 15 years ago. With this change there was an introduction to a (simple) numerical method where studets of 10th grade use Excel to analyze position, speed and velocity of a pendulum or a falling object including air resistance. Although your proposal seems to be more sophisticated, the basic ideas sound related. There are two (personal und subjective) observations I made:
1. Nearly all teachers I asked about said part of the curriculum told me they were less than impressed by the effect these classes had on their study progress regarding more complex mechanical problems. The only teachers that told me their students actually learned something meaningful were those teachers that made the students calculate the first few steps of the numerical method by hand (and with the use of a simple calculator).
2. After said 15 years there is again a change in the curriculum. The numerical method was dropped. My guess is that it did not have the expected/hoped effects. Else I would assume the decision makers would have extended the application of this (and maybe additional) numerical method(s) to even more parts of the physics curriculum.

My conclusion would be that the introduction of a numerical method to the physics curiculum did not revolutionize anything.

My personal experience (without learning any numerical method at school) is that during my time at university no one I met had real problems teaching themselves the use of Matlab and the likes. Same goes for the application of numerical methods.

 

[Will Flannery]

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!
...

Up to this point your post is exactly right. You've made my case. Let's have a look ...wiki - SPICE

Unlike board-level designs composed of discrete parts, it is not practical to breadboard integrated circuits before manufacture. Further, the high costs of photolithographic masks and other manufacturing prerequisites make it essential to design the circuit to be as close to perfect as possible before the integrated circuit is first built. Simulating the circuit with SPICE is the industry-standard way to verify circuit operation at the transistor level before committing to manufacturing an integrated circuit.
...
The birth of SPICE was named an IEEE Milestone in 2011; the entry mentions that SPICE "evolved to become the worldwide standard integrated circuit simulator".[13] Nagel was awarded the 2019 IEEE Donald O. Pederson Award in Solid-State Circuits for the development of SPICE.[14]

 

[Dr.D]

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

Looks like I missed that! Mea culpa, mea ...

But it seems like a lot of others did also. There is simply no point in learning to apply an unstable method. Agreed that Euler helps to explain the ideas behind numerical solution of ODEs, but it should never be used if you want valid results.

 

[hutchphd]

Up to this point your post is exactly right. You've made my case. Let's have a look ...wiki - SPICE

Was there any discussion of pedagogy in this article?
Revolution?
paradigms (shifted or otherwise)?
Design method?
Integrated circuits are expensive up front. SPICE is a fabulous tool and I use it myself to test that a circuit performs as expected. Perhaps my paradigm shifted when I wasn't looking...geez I didn't even notice. Again give me a break.

 

[Will Flannery]

Was there any discussion of pedagogy in this article?

? There was no discussion of pedagogy. The article demonstrates that the computer and computational calculus have revolutionized the analysis of physical systems outside of the university. A complete paradigm shift. It is inevitable that they will revolutionize physics/STEM education as well.

 

[atyy]

? There was no discussion of pedagogy. The article demonstrates that the computer and computational calculus have revolutionized the analysis of physical systems outside of the university. A complete paradigm shift. It is inevitable that they will revolutionize physics/STEM education as well.

How can there be a coming revolution if numerical methods have long been part of undergraduate physics and engineering curricula?
https://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/
https://faculty.math.illinois.edu/~laugesen/285/syll.html
https://faculty.math.illinois.edu/~laugesen/286/blog.html

 

[atyy]

https://sites.lsa.umich.edu/michigan-math-in-action/2017/03/06/the-effectiveness-of-change/
The Effect(iveness) of Change
By Gavin LaRose

Article about numerical methods and other stuff in the differential equations course at Michigan. Euler's method has been part of the course since at least the mid-90s.

 

[jasonRF]

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.

Here is the rest of the paragraph that didn’t all make it into the part you quotes. Here I have italicized the part you are bringing up

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...

 

[jasonRF]

#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.

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.

The bottom line is computational calculus is the only way real systems can be analyzed.

The fact that most problems have no exact analytical solution should not be news to anyone with a technical degree. I would hope everyone agrees that a good physics or engineering education should include at least some numerical methods. The issue in the thread is whether your proposed "numerical methods before we have learned anything about calculus or thermodynamics or waves or electrodynamics...", followed by an overhaul of most courses in the curriculum, is preferred to some other approach.

Here I will expand on the sentences I italicized in my prior post:

Part of the concern for me is that it isn't clear to me how much change you would make to upper-division courses in mechanics, electrodynamics, thermal physics, etc. The word "revolution" usually implies a lot of change, much more than one week of lecture and one numerical project in place of one of the current weekly homework assignments. Also, would subsequent physics courses teach more advanced numerical techniques or simply apply those learned in the freshman class? The more they do, the more decisions need to be made about what to eliminate from the current syllabi. As a concrete example, if you assume a current electromagnetics sequence teaches everything in Griffith's book, what sections would you eliminate in order to make room for the new numerical work? How many weeks would that allow you to spend on your new content?

A more conservative, incremental approach to better incorporating numerical methods would be to make no changes to the standard theory and experimental courses, but ensure that all graduates learn some numerical methods along the way. Many departments already do this to some degree. Those that don't may simply need to strongly recommended students use one of their electives for that purpose. The debates here would be whether the brief introductions provided in may differential equations classes are adequate, or if a dedicated numerical methods course should be required.

If students are to take a dedicated numerical course we could argue about the level. I believe Dale mentioned he had a sophomore-level option, which is late enough that it could cover similar topics as your course but at a higher level and with more sophisticated methods. I also had options starting sophomore year, but took a senior-level course which freely used material from the junior-level prerequisites (electrodynamics, Fourier analysis, ...), so could include things like spectral methods, assume we knew electrodynamics when we developed models for and simulated electromagnetic waves in nonlinear media, etc. By the way, the three-body problem ( spacecraft -moon-earth) was the first project.

My opinion is that courses taken after the students have at least learned calculus and intro physics would be more useful post-graduation than your pre-calculus version. So the pedagogical benefits need to be significant to prefer your course over a later course. I'm also skeptical that it makes sense to reduce the analytical content of the current curriculum. Physics graduates need strong analytical skills and they take many hours to develop - many more than numerical skills do. Indeed, I think it is much easier to learn to use numerical techniques on the job than it is to gain analytical skills.

jason

 

[Jarvis323]

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.

To play devils advocate, has your opinion on the topic been oversold? Have you provided references supporting the belief that black boxes are good teaching tools?

 

[Jarvis323]

How can there be a coming revolution if numerical methods have long been part of undergraduate physics and engineering curricula?
https://ocw.mit.edu/courses/mathematics/18-03-differential-equations-spring-2010/
https://faculty.math.illinois.edu/~laugesen/285/syll.html
https://faculty.math.illinois.edu/~laugesen/286/blog.html

I think that a lot of people in this thread are missing the point of the OP's idea.

It's not like the idea is to teach them numerical methods for the sake of gaining a practical skill that they take with them along their education and career.

The idea is to give them a simple intuition about what differential equations are and what we do with them. The other side is that a simple hands on approach might introduce them to the subject in a way that is less scary, less abstract, and more fun. The possibility is that for some students this could inspire and motivate them to want to and not be afraid to get into physics, because they can wrap their heads around it to some extent to begin with. So the point is that it is an early course, rather than a later one. And the measure of success is more about the potential students subsequent confidence and interest.

Whether subsequent courses in numerical methods are redundant or will replace what was learned, is only of concern if the students end up deciding they want to be physicists.

 

[Dale]

To play devils advocate, has your opinion on the topic been oversold? Have you provided references supporting the belief that black boxes are good teaching tools?

Please quote any claims that I made which you would like to see supported. I am happy to provide references for any factual claims I made (or retract/modify the claim).

The issue wasn’t @physicsponderer’s opinion, he is entitled to his opinion (as am I). It was the “facts” that he asserted in support of his opinion. He has now corrected the fact claim with no need to change his opinion.

 

[Jarvis323]

Please quote any claims that I made which you would like to see supported. I am happy to provide references for any factual claims I made (or retract/modify the claim).

The issue wasn’t @physicsponderer’s opinion, he is entitled to his opinion (as am I). It was the “facts” that he asserted in support of his opinion.

I don't see the line. It looks like the "fact" he asserted (something like, physics students seem to lack intuition about the math they're using) is no less an opinion than your opinion that they don't seem to.

As an example, post 150 from hutchphd, in bold, "the easiest way..." is just as easily interpreted as a statement of fact. And you even threw in a like.

I'm just playjng devils advocate.

 

[Dale]

I don't see the line.

Ok, let me know when you find it.

As an example, post 150 from hutchphd, in bold, "the easiest way..." is just as easily interpreted as a statement of fact. And you even threw in a like.

If you object to that claim then, by all means, ask him to provide a reference.

 

[Jarvis323]

Ok, let me know when you find it.

If you object to that claim then, by all means, ask him to provide a reference.

It just seems that the authority a mentor has should not be leveraged to further their own opinion, it should be applied fairly to maintain quality and civility. So I think it is equally your responsibility to demand hutchphd provides a reference as it is to demand physicsponderer does if the line is crossed. I guess optimally, that line should be clearly drawn by mentors and acted on logically and consistently, independent of one's own leanings. Of course that never happens in the real world, where we're all human, and both interesting and purely objective discussions aren't easy to have.

 

[hutchphd]

Anyone who finds any statement of mine to be blatantly false or not supportable is free to question it. The full statement from me in this case was "at some point (in the process of learning all physics) the easiest way is to bite the bullet and learn the mathematics" . This is clearly an opinion but to me an obvious one. Similar to "if you go out in water over your head far enough you will drown".
If anyone can provide cogent reason why this is not obvious I will try to provide further justification. (And someone playing devil's advocate is not sufficient cogent reason. } A request from a Mentor would be sufficient on its face.
As would my use of the term "paradigm shift" in any context..

 

[atyy]

I think that a lot of people in this thread are missing the point of the OP's idea.

It's not like the idea is to teach them numerical methods for the sake of gaining a practical skill that they take with them along their education and career.

The idea is to give them a simple intuition about what differential equations are and what we do with them. The other side is that a simple hands on approach might introduce them to the subject in a way that is less scary, less abstract, and more fun. The possibility is that for some students this could inspire and motivate them to want to and not be afraid to get into physics, because they can wrap their heads around it to some extent to begin with. So the point is that it is an early course, rather than a later one. And the measure of success is more about the potential students subsequent confidence and interest.

Whether subsequent courses in numerical methods are redundant or will replace what was learned, is only of concern if the students end up deciding they want to be physicists.

George Jones and Dr Courtney have both taught Euler's method in high school. See post #3 and post #8. I agree that's a good idea. And you can see it's pretty standard in the introductory differential equations course that many physics and engineering majors take at university (it's Chapter 2 of Edwards and Penney, one of the standard texts; Boyce and DiPrima, another standard text, have it later, but mention early in the text that elements of the chapter can be taught early). If Euler's method is already commonplace in university and at least sometimes taught in high school (as George Jones and Dr Courtney relate), why is the OP's proposal a "coming revolution"?

 

[Dale]

It just seems that the authority a mentor has should not be leveraged to further their own opinion

I didn’t. Absolutely anyone can request references. Frankly, it is offensive that you would say that. Nothing I did in that exchange was leveraging my authority as a mentor.

So I think it is equally your responsibility to demand hutchphd provides a reference as it is to demand physicsponderer does if the line is crossed.

I neither accept your charge that I abused my authority nor your assertion that therefore I need to demand references from everyone.

If YOU want a reference from someone then YOU can ask for it precisely because asking for references is not a mentor function in the first place. It is something everyone can and should do as they see fit.

Also, asking for references is not always something done for claims that you dispute. I have also asked for references for ideas that I found interesting and wanted to learn about more.

I find your accusation here quite offensive and completely unfounded.

 

[Jarvis323]

I didn’t. Absolutely anyone can request references. Frankly, it is offensive that you would say that. Nothing I did in that exchange was leveraging my authority as a mentor.

I neither accept your charge that I abused my authority nor your assertion that therefore I need to demand references from everyone.

If YOU want a reference from someone then YOU can ask for it precisely because asking for references is not a mentor function in the first place. It is something everyone can and should do as they see fit.

Also, asking for references is not always something done for claims that you dispute. I have also asked for references for ideas that I found interesting and wanted to learn about more.

I find your accusation here quite offensive and completely unfounded.

I think you're exaggerating what I said. We were going down the path, of what is considered a statement of fact, vs a statement of opinion. My argument was just that it's sometimes not clear. As a devils advocate, I was encouraging a deeper inspection of what is the line, so that as a mentor, you could more fairly apply your authority without risk that you let your own opinion bias how you apply your authority.

The bit about what I think a mentors responsibility is, was rather what I think the ideal is in terms of resolving these issues, not a full on indictment of you. I'm not saying you're infallible.

This is a human level thing that we all ought to think about. It's something to strive for. I apologize if I caused offense.

 

[Jarvis323]

A correct course design must be ruthlessly narrow in only teaching that which only that course will teach.

Do you have a supporting reference for this?