The coming revolution in physics education

[Dale]

Isn't there value in understanding what makes a good numerical method?

Of course. That is why it merits a dedicated numerical methods course.

A lot of the courses I've taking in computer science begin with the simplest solution. Then we break it. Then we analyze why it broke, and we find a better solution.

Yes. That is a good way to teach many computer science topics

Do you think I disagree with any of what you wrote in that last post? As I told the OP, I am predisposed to be in favor of his general idea. I object to his “used car salesman” exaggeration and factual distortions. I also think that teaching them to program Euler’s method by hand is a big waste of physics class time. But I support increased use of numerical methods in physics classes and increased focus on differential equations.

 

[atyy]

This article is interesting. As noted above in post #208, Calculus BC requires Euler's Method. For comparison, the A-Level Further Mathematics course in post #208, which also requires Euler's Method, is usually taken in Grades 11-12.

https://www.washingtonpost.com/loca...8d2220-9d4b-11e9-b27f-ed2942f73d70_story.html
Why are so many 8th-graders taking AP Calculus at this school district?

"For decades the public schools in Pasadena, where I have lived on and off for 19 years, have had no better than a mediocre academic reputation. To see such acceleration is startling, and so is this: The program — called the Math Academy — was designed by parents, who are usually told to butt out of school curriculum decisions.

Another group of parents connected to the NASA Jet Propulsion Laboratory, for instance, suggested a more affluent district near Pasadena adopt a similar accelerated math program. They were told their plan was “not fully research-based,” and officials raised “concerns regarding its developmental appropriateness for 13- and 14-year olds.”

Jason and Sandy Roberts, the math-savvy parents who originated the Pasadena program, say that if a district wants to keep families from abandoning its schools, administrators should offer math courses for the best students that competing charters, private schools and wealthier districts don’t have."

 

[atyy]

I got an A in all of my science and math courses in college. But a whole lot of the material that was covered along the way has exited my mind. I feel like all that I am left with is the things I actually understood deeply, had fun with, or applied in some meaningful way. I guess I am one of those students who excelled, even though my intuition/understanding of what I was doing was left in the dust to an uncomfortable degree. The sheer volume of mathematics that one must master to be a physicist has somewhat scared me away. Maybe weeding me out wasn't a bad thing, because I went into computer science instead.

Now, there one MUST demand a reference for the unfounded assumption - do you have any evidence that computer science is "easier" than physics?

I think the important thing about college is to have all that material that one has supposedly learmed exit one's mind. Incidentally, this anecdote is told by a discrete mathematician (though obviously, discrete maths nowadays intersects with calculus)
https://www.ams.org/notices/199701/comm-rota.pdf
" I often meet, in airports, in the street, and occasionally in embarrassing situations, MIT alumni who have taken one or more courses from me. Most of the time they admit that they have forgotten the subject of the course and all the mathematics I thought I had taught them.However, they will gladly recall some joke, some anecdote, some quirk, some side remark, or some mistake I made. "

 

[Jarvis323]

Of course. That is why it merits a dedicated numerical methods course.

Yes. That is a good way to teach many computer science topics

Do you think I disagree with any of what you wrote in that last post? As I told the OP, I am predisposed to be in favor of his general idea. I object to his “used car salesman” exaggeration and factual distortions. I also think that teaching them to program Euler’s method by hand is a big waste of physics class time. But I support increased use of numerical methods in physics classes and increased focus on differential equations.

Maybe the disagreement is subtle? I though it was a disagreement about whether an inferior method is worth teaching at all, and whether overlap between courses is acceptable.

If a dedicated numerical methods course happens later on, it wouldn't seem to be a solution to the problem the OP is trying to solve. If using numerical methods early on is helpful in the way the OP hopes it would be, then maybe the overlap between that early course and a later more rigorous one would be worth allowing. And not everyone will go on to take a dedicated numerical methods course. If black boxes solve the same problem, then maybe the overlap can be reduced with the same effect. I don't think we can objectively say if that is true or not, and it might vary depending on the individual students.

Maybe I've just become accustomed to the “used car salesman” stuff. It seems like that is a problem in research in general. People are often selling their ideas in such ways. Maybe it's because they themselves believe it passionately, and they are trying to convince you, and maybe also because they are put in the position of being a sales person for their work. Sometimes, if they believe in what they are doing, and they want others to give pause and listen to them, that approach works in practice. So they have to compete with the other sales people for attention. The blame is at least partly on how people think on average and our systems work. In my ideal world, misleading advertising wouldn't even exist, because it wouldn't work. And we wouldn't be bombarded with click-bait constantly. But that's not the world we live in.

Putting a question mark in the title might help. To me, however I don't find the OP to be deceptive. I have more of a problem with research that is very carefully attempting to appear more objective and supported factually than it is, where people write like lawyers, or politicians, using lots of clever wording to make claims which are subtly misleading, and technically defend-able. It is often done in a manner to checkoff all of the boxes that the reviewers must go through, and to make it difficult for a reviewer to dispute or objectively articulate criticisms of the work. I actually don't mind the OP's writing in this sense. I can tell what parts are unproven beliefs or opinions. I subconsciously attach the question marks myself. If you are giving a sales pitch, I prefer it to be obviously a sales pitch.

 

[Dale]

To me, however I don't find the OP to be deceptive.

I guess this is our main disagreement then.

He has stated many false claims and has continued to do so even after clear contradictory evidence has been cited. Knowingly repeating false statements is deceptive, by definition.

 

[Jarvis323]

However, they will gladly recall some joke, some anecdote, some quirk, some side remark, or some mistake I made. "

I've taken courses where the instructor spent most of the time deliberately making mistakes (or pretending to have deliberately made mistakes). The class was always asked to spot the errors. I don't know, maybe the instructor just didn't know what they were doing. If I were ever asked to teach a course in a subject I didn't know well, maybe I would have to do that.

In one physics course I took, the lecturer would come in with a cup of coffee disheveled. He would ask us to remind him what we did at the last class session, and then he would look in the book for a few minutes trying to figure out what he was going to teach for the day. Eventually he started doing some problems on the board, but forgot how to do the problems. Then the whole class would sort of work together trying to figure out how to do it. Somewhere in the middle, the subject would change to something like beer brewing. There would be some jokes told, some stories of being in college, or working at CERN. Most of the time, the instructor figured out the problem in the end. He didn't grade our homeworks, or our exams, and gave almost everyone in the class an A. Maybe we all deserved A's for participation. Maybe the approach was successful?

 

[Jarvis323]

I guess this is our main disagreement then.

He has stated many false claims and has continued to do so even after clear contradictory evidence has been cited. Knowingly repeating false statements is deceptive, by definition.

Maybe, but I didn't feel personally deceived. It wasn't some diabolical scam in my opinion. Lots of things could be considered deception in this way, if you take opinions to be statements of facts.

 

[Dale]

Maybe, but I didn't feel personally deceived. It wasn't some diabolical scam in my opinion.

Well, we aim for a higher standard than “not a diabolical scam”.

 

[Jarvis323]

Well, we aim for a higher standard than “not a diabolical scam”.

I think you might have earned yourself a solid place in the notable quotes from PF members thread with this one. lol

 

[Vanadium 50]

I object to his “used car salesman” exaggeration

It reminds me of Professor Harold Hill's "Think Method". (The Music Man, available on DVD. Features a young Shirley Jones and a younger Ron Howard as well as some of Onna White's best work)

Mothers of River City!
Heed that warning before it's too late!
Watch for the tell-tale sign of corruption!
The minute your son leaves the house,
Does he rebuckle his knickerbockers below the knee?
Is there a nicotine stain on his index finger?
A dime novel hidden in the corn crib?
Is he starting to memorize jokes from Capt. Billy's Whiz Bang?
Are certain words creeping into his conversation?
Words like, like 'swell?"
And 'so's your old man?"
Well, if so my friends,
Ya got trouble,
Right here in River city!

 

[Auto-Didact]

Any time spent teaching physics students how to program Euler's method is wasted time. That time is doubly wasted because we are not teaching physics and we are not teaching a good numerical method.

That would be failing to see the forest for the trees. We would have lost the opportunity to teach good physics and squandered it to teach a bad numerical method.

Here is where the disagreement is: you are already assuming the given suggestion is to encroach upon physics class time i.e. to teach this at a certain age or to teach it given some courses within in some given curriculum: I am interpreting the OP's suggestion far more radically, i.e. throwing out entire courses and merging others for whatever reasons if deemed necessary. What is necessary in education is conveying an understanding; knowledge can be forgotten, but an understanding lasts.

The careful seperating out of subjects such as 'this belongs to physics' or 'this is a numerical method for physics and should therefore be marketed as such' is already part of the problem for conveying understanding to students in education, for the simplest of reasons imaginable: the average student will ask 'why?'. A good teacher may be able to answer some why's, but given sufficient time they will pretty quickly end up getting stumped, exposing that the teacher doesn’t understand why. As usual Feynman, as well as many other great science communicators have spoken on this issue at length.

I had this experience in school myself and it is a recurring theme I see in the students I mentor, i.e. it is symptomatic of the problem that the majority of students have with physics education, i.e. why they don't like physics: they do not understand what it is about and the teacher, probably being mediocre in physics himself - i.e. not capable of explaining physics to the kids at the level of say Walter Lewin, Richard Feynman or Carl Sagan - is unable to offer them a satisfactory answer.

Euler's method is part of the A-level Further Mathematics syllabus. This is not required, but recommended as one of the subjects for entry to electrical engineering at Imperial College and to physics at Oxford. It's not quite what you are thinking, as it still refers to the better students, but Euler's method is already routinely taught to many high school students.

https://www.seab.gov.sg/docs/default-source/national-examinations/syllabus/alevel/2020syllabus/9649_y20_sy.pdf
https://pmt.physicsandmathstutor.com/download/Maths/A-level/FP3/Worksheets-Notes/AQA FP3 Textbook.PDF
https://www.imperial.ac.uk/electrical-engineering/study/undergraduate/entry-requirements/
https://www.ox.ac.uk/admissions/undergraduate/courses-listing/physics

In the US, AP Calculus BC also requires Euler's method. It seems that about 14% of US high school students take calculus, about 7% of them take an AP Calculus test, and about 2% of them take a Calculus BC course, with about 1% taking the Calculus BC exam. You can also find Euler's method taught in some AB courses.
https://www.maa.org/external_archive/columns/launchings/launchings_06_09.html
https://fiveable.me/ap-calc/unit-7/...ler-s-method/study-guide/XZF01jg29LPjZaV7jKjE
https://cty.jhu.edu/online/courses/advanced_placement/ap_calculus_ab.html

That's nice and all, but not only is this course not compulsory (of course it isn't, why should it be?) this is already only focused on AP students taking physics; not just those who want to do STEM but all the students have to be gotten at a much younger age, I'd guess around 12-14 at the latest and preferably outside the context of physics which means it shouldn't be part of physics class, but part of a new class in a new curriculum which prepares for applied mathematical reasoning, similar to how pre-algebra prepares for all things kids might need later down the line e.g. calculus, linear algebra or even topology.

This is what I mean by not being able to see the forest before the trees: any revolutionary intervention aimed to improve education should not be trying to specialise a little bit more within some given subject, but instead be uprooting some specific idea out of any given subject by generalizing this idea in order that the student understands the broader picture of the subject itself. To illustrate this: if one would ask almost anyone 'what is the subject of biology about?' typically one pretty quickly gets the answer 'life', which should be obvious given that biology loosely translates to 'the study of life'; this single unified coherent answer can give context to anyone - children included - if they take the time to reflect that all possible questions about life are in principle questions in biology, i.e. once they understand this they automatically become interested in biology.

However, when a similar question is asked namely 'what is physics about?', almost no one seems to actually know the answer; my diagnosis is that this is the actual root problem with physics in school. In fact, not just with physics education, but with the image that society has of physics in general. In my experience, even those who have a physics degree, i.e. professional physicists, typically are unable to answer this question satisfactorily; they usually give tangential answers that they learned which were fabricated in school, which does not go straight to the core of the matter; an actual answer can only be gotten through reflection.

The marketing problem in education is that students want to go straight to the core of the matter; anyone telling you giving them an actual answer isn't possible simply doesn't know or understand the answer themselves; both Feynman and Einstein wrote extensively on this topic, but little to no attention is given to this in physics classes, therefore most of the children do not even get to get interested in physics class. In any case, any new course which attempts demystifying physics should definitely not be named 'numerical methods for solving differential equations', this is like the worst name imaginable for marketing purposes to children or parents!

I think that people learn differently, and one approach cannot be optimal for every person, and I have myself as evidence of that. For me, I probably would have been better off starting with analysis (in some limited and simple enough introductory form), before calculus, and taking foundations of mathematics before geometry and algebra. Maybe the revolution in education will be to figure out how to teach different people with different approaches. Maybe the OP's idea could be an approach that works better for some people.

I agree with everything that you have said.

My solution: skip all classes where a why wasn't given for any arbitrary reasons; unfortunately this included physics class. In mathematics I had to invent why's for myself; I learned that this was possible quite young, because I just so happened to be learning synthetic geometry; what I took away was not merely synthetic geometry but through reflection that proving things in principle a priori was actually possible. After that subject was done, the method of proving sticked with me quite closely, and in math class I would usually do that instead of doing what was asked by the book or teacher because it was capable of answering the why question.

In this manner I reinvented mathematics for myself and used the textbook as a test to see if the things I invented were already known. For example, when I saw a question on an algebra exam which without explanation said that the volume of a sphere had a formula, I ignored the entire test and focused on deriving that formula from first principles. Around this time I also realized that even math teachers were limited in understanding, when my math teacher when teaching us analytic geometry didn't recognize that I reinvented the derivative (Fermat's version) but was more bothered that I didn't care to answer the given homework questions.

I came to find mathematics the only important subject, steadily getting better at it, not an A such as some others, but far more well-rounded than them in that I could do things they weren't even dreaming of. Around the end of high school I finally reflected upon physics using everything I invented in mathematics for myself, more specifically I mathematically analyzed a few laws of physics which were relevant in my final experimental project; during this process I ended up reinventing dimensional analysis and the rest is history.

I guess this is our main disagreement then.

He has stated many false claims and has continued to do so even after clear contradictory evidence has been cited. Knowingly repeating false statements is deceptive, by definition.

"Never attribute to malice that which is adequately explained by stupidity"; I mean this in the most non-inflammatory and positive way possible: the inability for one to express themselves absolutely clearly is usually the result of some lack of proficiency in language (NB: often remediable by taking a few writing classes) instead of deliberate deception as you either are interpreting or portraying it. The key to navigating in such murky waters is to listen to what someone means, not to what they say; this of course requires effort both on the part of the speaker as well as the listener.

 

[Dale]

you are already assuming the given suggestion is to encroach upon physics class time

That is not an assumption. That is precisely what the OP did and what he has discussed here as a revolution in physics education. It is this to which I recommend the use of black box solvers.

If you suddenly have a different approach in mind then you cannot assume that any previously-stated objections or agreements to the OPs position hold for your different approach. Perhaps it would be better to make a new thread for your idea since it does not appear to be what has been discussed here for more than 200 posts

I am interpreting the OP's suggestion far more radically, i.e. throwing out entire courses and merging others for whatever reasons if deemed necessary.

Then your blanket assertion that any teaching of black boxes is missing the forest for the trees is rather absurd. When looking at completely redesigning the curriculum, to assert a priori that there is no place anywhere for black boxes makes no sense. Every tool will have some place. Particularly given that other black boxes already abound and are embraced elsewhere for valid reasons.

"Never attribute to malice that which is adequately explained by stupidity"

We also aim higher than stupidity here.

 

[Auto-Didact]

That is not an assumption. That is precisely what the OP did and what he has discussed here as a revolution in physics education. It is this to which I object.

If you have a different approach in mind then you are off-topic in this thread cannot assume that any previously-stated objections or agreements to the OPs position hold for your different approach.

Again, this is why I ended the post with listen to what he means, not to what he says. I think a lack of clear communication is what is causing much of the disagreement in this thread, and an unwillingness to actually seriously reflect and listen to each other instead of answer every point with 'but I already have the answer' which unfortunately causes the discussion to end up getting heated and inflammatory for no good reason (ad hominems, projecting malice, etc).

This is simply a discussion about how to improve the understanding of physics within the context of education, namely that differential equations are not just important but pretty much the key for understanding physics and that this fact is almost universally not mentioned early on. And moreover that even university courses do not prepare one adequately for dealing with differential equations. All of these are real actual issues in physics education, which feed back into the problem at the foundation: the context of learning physics in high school.

In this discussion there are different users falling on different sides of the pro and contra line of the argument at different points for different reasons ranging from more relevant to less relevant w.r.t. the original argument (for example the argument that DEs aren't relevant for physical laws but instead some mathematical abstraction thereof; this argument would just be pedantic detail in the context of high school physics). Assigning malice to these reasons where there may be none if creating clarity by streamlining the discussion is also counterproductive by stifling the discussion.

Then your knee-jerk assertion that any teaching of black boxes is missing the forest for the trees is rather absurd. When looking at completely redesigning the curriculum to assert a priori that there is no place for black boxes makes no sense. Particularly given that black boxes already abound and are embraced elsewhere.

I am not against black boxes at all, more than 90% of what I do involves black boxes and I embrace them when and because there is no other option; the difference is that I understand them as generalizations of simpler models which taken as is are inaccurate. What I'm against is offering black boxes as a serious alternative in a spot where an actual explanation conveying an actual understanding can be given but then is foregone and chosen for a blackbox instead because some Joe decided this might be a good idea without reflecting even for a moment on the deeper issue.

If we're going to go down the road that an education should offer good black boxes instead of an understanding because the good black box can produce more accurate answers to questions that are on exams - i.e. for utilitarian instead of pedagogical reasons - while being completely shrouded in what is going on, then one might as well argue to scrap calculus altogether because Siri & WolframAlpha can answer many if not most calculus problems that the kids will throw at it.

It should be clear that the above reductio ad absurbdum demonstrates why going down the road of black boxes in the context of this argument is unproductive for the goal at hand: finding a way to engage more children with physics through letting them actually understand a key process in physics, namely that physical processes are described by differential equations. The solution in the OP may be helpful for this, or it may not be. It is an experimental question whether it actually is or is not, and like any experiment, there are various parameters which can be varied experimentally; not taking this to heart is throwing out the baby with the bathwater.

 

[Dale]

Assigning malice to these reasons where there may be none if creating clarity by streamlining the discussion is also counterproductive by stifling the discussion.

At greater than 200 posts I think it is pretty evident that there has been no stifling of the discussion whatsoever.

This is simply a discussion about how to improve the understanding of physics within the context of education

I think this is not a correct characterization of the discussion. It is a discussion about one very specific proposal. One of the issues raised and discussed early on (which you may have missed since you joined late and apparently didn’t read all 200+ posts) is that there is no evidence that this specific proposal actually improves the understanding of physics.

I am not against black boxes at all,

Good.

What I'm against is offering black boxes as a serious alternative in a spot where an actual explanation conveying an actual understanding can be given

Agreed. I recommend in favor of black boxes specifically for the context of this thread where the time spent teaching Euler’s method is taken away from the time spent teaching physics. As far as I am concerned that is not “a spot where an actual explanation conveying an actual understanding can be given”.

If we're going to go down the road that an education should offer good black boxes instead of an understanding because the good black box can produce more accurate answers to questions that are on exams - i.e. for utilitarian instead of pedagogical reasons - while being completely shrouded in what is going on, then one might as well argue to scrap calculus altogether because Siri & WolframAlpha can answer many if not most calculus problems that the kids will throw at it.

It should be clear that the above reductio ad absurbdum demonstrates ...

As reductio ad absurbdum usually does, it mostly demonstrates that you are mischaracterizing my argument. Frankly, when you are discussing complicated topics with reasonable people and you find yourself making a reductio ad absurbdum argument then you can be pretty confident that your argument is actually a straw man fallacy, as you have done here.

I don’t want to lose time for teaching good physics in order to teach poor numerical methods, that is the context for the thread and the justification for the specific recommendation. The recommendation was not made for any of the disparaging reasons you gave, nor was any hint of getting rid of calculus suggested. That is all a straw man.

 

[hutchphd]

I think that how one teaches physics depends upon the audience and their likely utilization of their knowledge. Roughly I would designate the three populations of learners (with examples):

1. Those who wish to appreciate physics (poets, lawyers)
2. Those who wish to understand physics (MDs, architects, scientists, engineers )
3. Those who wish to use and extend physics (physicists, chemists, engineers)

Each of these groups requires different pedagogy and the present curricula at every institution I have known recognizes these three levels.

The requirements for those who wish to "do" physics (level 3 as designated) are really quite different from the other two groups. In my experience it requires an unusual synthesis of conceptual thought (the world) and symbolic logic (the equations). One must be facile at the manipulation of each and it is the interplay that produces novel thought. I do not think using Euler and turning the crank teaches this process.

The OP recommendations may be of use for groups 1 and 2 and there is some data to recommend further research. But I fear he does not truly understand what physicists need to learn. They need to tutored by professors in this process of synthesis. Not how to turn the crank.

 

[Jarvis323]

Roughly I would designate the three populations of learners (with examples):

1. Those who wish to appreciate physics (poets, lawyers)
2. Those who wish to understand physics (MDs, architects, scientists, engineers )
3. Those who wish to use and extend physics (physicists, chemists, engineers)

Can we get a reference about the three groups?

I don't relate to anyone of them, because I'm driven by curiosity and mystery, and I want to appreciate and understand the things I am doing.

There is also an issue with making assumptions about which type of person someone is and deciding their future for them. I don't like the idea of taking people who seem to want to appreciate physics, and decide they should be poets or lawyers.

 

[Dale]

Can we get a reference about the three groups?

I am pleased that you are asking for references, but given that the claim is “Roughly I would ...” I think that the statement is its own reference. He said he would, and then he did.

 

[hutchphd]

Here is the description at UVa. I think it is self-explanatory. Look at any school it will be similar

 

[hutchphd]

There is also an issue with making assumptions about which type of person someone is and deciding their future for them. I don't like the idea of taking people who seem to want to appreciate physics, and decide they should be poets or lawyers.

The can take any course they want! I had a premed in my junior level quantum course. Relax, man.

 

[Jarvis323]

The can take any course they want! I had a premed in my junior level quantum course. Relax, man.

Hmm a premed, sounds like an "understander". It makes sense one of those would want to take a quantum course.

 

[hutchphd]

I have no idea what you are trying to say. I wrote him a really good recommendation for med school.

 

[Jarvis323]

I have no idea what you are trying to say. I wrote him a really good recommendation for med school.

I was just joking. I thought premed is probably a cat 2. So they must have been there because they wanted an understanding. They probably asked a lot of off the wall questions right? The doers (cat 3) were probably all like, "just shut up and calculate already".

Sorry, I'm just in a weird mood. I'm not trying to denigrate what you said. I'm just imagining poets and lawyers and architects, etc. in a QM course and wondering what questions they ask and finding it a humorous thing for some reason.

 

[hutchphd]

He was a good addition to the class and did well. I'm not the one are who is categorizing the people. My intent was to categorize the "flavor" of the course. If I were to categorize students, the premeds were usually my least favorite because, given the pressure to get all A's, their usual question was "is that going to be on the test?" Sigh. My least favorite question.
I'm certain he is a great Doc.

 

[Dale]

Since this topic has been discussed more than sufficiently and since recent posts have started going off topic considerably it is past time to close it.