The coming revolution in physics education

[Dale]

I was encouraging a deeper inspection of what is the line, so that as a mentor, you could more fairly apply your authority

Nothing in that exchange had anything to do with applying my authority!

If I had been unfairly applying my authority I would not have asked for references. I would simply have deleted his post and thread banned him.

 

[hutchphd]

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.

But it is already something that has been well and thoroughly thought about.
Please do not miss the other point here. If someone had requested that I provide elucidation and I refused, then @Dale should use his judgment and authority regarding my acquiescence. Conversely that doesn't preclude him from making a request on his own initiative or not. He is a participant in the forum as much as anyone else and certainly should have the prerogative of such requests on his own. His authority to demand factual references is no different from yours or mine.

 

[Jarvis323]

Nothing in that exchange had anything to do with applying my authority!

If I had been unfairly applying my authority I would not have asked for references. I would simply have deleted his post and thread banned him.

Then I retract my criticism.

 

[Dale]

Do you have a supporting reference for this?

My papers on instructional design are at the office, so I don't have the reference where I originally learned it at hand. But making a course narrowly focused in the context of an overall curriculum is not an idea unique to that reference. Here is another: "Department faculty need to agree on a set of emphases for each course in order to function as a building block within the overall curriculum. The course may focus on only one or two of the curriculum goals, but those few goals must guide the learning outcomes that the course pursues"

Idea Based Learning by E. Hansen, 2011, p 30

One comment, in my current role I teach short intense classes to adults. They last from 1 to 3 weeks, 8 hours per day, so the need for a narrow focus is extreme. These courses are always designed in the context of other education. But even in a longer course there is typically more that a teacher would like to teach than there is time allotted in class, so choices must be made and there needs to be a sound basis of what to include and what to exclude. That relies heavily on understanding the course in the context of the overall curriculum and trusting your fellow-teachers to teach the rest of the curriculum.

 

[Auto-Didact]

To get back on topic:

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.

Quoted for relevance. One cannot start early enough with exposing children to mathematical ideas; there is a joke often made about teaching a course in analysis in kindergarten but I cannot find the image. The key point to be made is that one cannot underestimate the value of having a true understanding of something compared to just being able to recall lifeless facts; mathematics is one of the best ways to spark such an understanding. This feeling of understanding is empowering for individuals and naturaly spreads across all domains of an individuals life: this is the true goal of any education.

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"?

The difference is that teaching this at university is already after having done a postselection, i.e. only the STEM students - those who are able to navigate the current education system successfully - will learn this, while teaching in high school all students learn this. The issue of what teaching method is best for which specific aims at a certain age range is essentially a classic epidemiologic problem of how to evaluate a new intervention versus a control intervention within the context of high school education; i.e. the problem is best decided by using a double blind placebo controlled randomized controlled trial, or a less ideal variant if the DBPCRCT is not realistic.

Having mentored hundreds of students, from high school level up to masters level, across dozens of fields, there is one and only one conclusion I have come to: mathematics and physics education in high school is typically quite abysmal. The paradox is that this is not necessarily because the textbooks or teachers are bad, but because both the textbooks as well as the teachers almost universally reliably fail to engage with all the students, i.e. this is to a large extent a marketing problem.

Take note that I am not considering the students who are already interested in mathematics or physics from a young age, but all students. For the students already interested in mathematics and physics, typically about 10% of any given classroom, the current system works quite well; for the other 90% things aren't usually so optimistic. The numbers may not be completely accurate, but we are literally talking about almost the entire population, apart from the few that end up in STEM jobs.

For most, dare I say for all, of the students for which the current system doesn’t work, they do not usually comprehend the impact not grasping elementary mathematics will have on their life; this is after having factored out those who do grasp this through their teachers, mentors or parents upplaying it and making clear that it will be necessary down the line in their careers, obviously if they want to choose a STEM career but actually pretty much independent of which career they end up choosing.

In very expensive private schools we somehow see this problem far less, i.e. somehow they have figured out a way how to engage all students, not just the ones who go onto do a STEM degree. How have they done this? Easy: by spending enormous amounts of money to let hugely influential charismatic public intellectuals - i.e. guest teachers such as Leonard Susskind, Hannah Fry or Brian Cox - come and convince their kids that STEM is awesome.

This educational strategy seems to work with these students, in multiple ways, namely they understand why science is important, they understand how it benefits them and society, they understand what mathematical literacy can do for them, they even understand the beauty of mathematics. This is revolutionary especially for those not going into STEM in that they typically end up having or wanting a strong mathematics background.

A digression: when I was in university, there were two girls majoring in psychology and law which I came across during my undergrad physics classes. Both of them came from two such private schools and both of them were taking complete course in calculus with the one a course in differential equations and the other mathematical methods for physicists. Coming from medicine, and therefore being an intruder in physics, I was extremely interested in their reasons for taking these courses; their answer was simple, like was mine: they understood mathematical beauty and wanted to expose the mathematical beauty within thrir own disciplines.

Can you imagine what an edge a psychologist - or literally any social scientist or scholar within the humanities for that matter - can have within their own discipline if they can create mathematical models at the same level of sophistication as a physicist, instead of relying purely on less than stellar undergrad statistics course to do quantitative research? Based on this experience, while still a student myself, I started mentoring students in all areas, teaching them not to be afraid of mathematics, but I digress.

To come back to the main question of how to engage high school students in mathematics, without necessarily spending millions of dollars on celebrity scientists to personally come dazzle the kids, it is almost obviously that a change to the curriculum is necessary. There have been large educational experiments in the past who have tried this and there are as I illustrated many smaller experiments which try this, but nothing as of yet in a truly integrative manner.

Garnishing an understanding for the average student - be it by demystifying something as relatively simple as differential equations from physics using something as simple as Euler's method - is a step in the right direction. Suffice to say the advocation of teaching black boxes is failing to see the forest for the trees; this is similar to arguing that all that is needed for one to be able to produce literature such as the works of Shakespeare is an understanding of English grammar.

 

[Dale]

Suffice to say the advocation of teaching black boxes is failing to see the forest for the trees; this is similar to arguing that all that is needed for one to be able to produce literature such as the works of Shakespeare is an understanding of English grammar.

I think you misunderstand the suggested role of black boxes in this context, and as a result you have this exactly backwards. The idea is not "teaching black boxes". The idea is to teach physics, that is the forest. My recommendation is to use the black boxes so that you can focus on the physics and not on the details of the numerical methods.

Euler's method is not physics, and it isn't even a good numerical method. It is a tree, and not even a particularly good tree at that. 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.

 

[jasonRF]

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.

"Throwing the computer" at a problem is a phrase I sometimes use (but probably shouldn't, at least in a post online) when I've exhausted whatever low-hanging analytical work I can do, and have no choice but to use numerical methods. I don't use the term for a simple numerical integral or to evaluate an analytical expressions.

For example, at work right now I am working on some electromagnetics problems. I spent a fair amount of time deriving analytical approximations for some "toy" versions of the problems and plotted the results to gain physical insight and intuition. Now I am at the point where I need to get real numbers for a real design, so I am using expensive commercial software to run large numerical simulations. I would call this "throwing the computer" at the problem.

Again, I should not have used the phrase in my post, since it could easily be interpreted as derogatory. In reality I highly value numerical simulations, but I usually gain more physical insight from simpler analytical or semi-analytical approximations. Plus, comparing the simulation to the simpler approximation often yields insights into the effects of features that are not captured by the "toy" models.

jason

 

[atyy]

To come back to the main question of how to engage high school students in mathematics, without necessarily spending millions of dollars on celebrity scientists to personally come dazzle the kids, it is almost obviously that a change to the curriculum is necessary. There have been large educational experiments in the past who have tried this and there are as I illustrated many smaller experiments which try this, but nothing as of yet in a truly integrative manner.

Garnishing an understanding for the average student - be it by demystifying something as relatively simple as differential equations from physics using something as simple as Euler's method - is a step in the right direction. Suffice to say the advocation of teaching black boxes is failing to see the forest for the trees; this is similar to arguing that all that is needed for one to be able to produce literature such as the works of Shakespeare is an understanding of English grammar.

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

 

[Jarvis323]

My papers on instructional design are at the office, so I don't have the reference where I originally learned it at hand. But making a course narrowly focused in the context of an overall curriculum is not an idea unique to that reference. Here is another: "Department faculty need to agree on a set of emphases for each course in order to function as a building block within the overall curriculum. The course may focus on only one or two of the curriculum goals, but those few goals must guide the learning outcomes that the course pursues"

Idea Based Learning by E. Hansen, 2011, p 30

One comment, in my current role I teach short intense classes to adults. They last from 1 to 3 weeks, 8 hours per day, so the need for a narrow focus is extreme. These courses are always designed in the context of other education. But even in a longer course there is typically more that a teacher would like to teach than there is time allotted in class, so choices must be made and there needs to be a sound basis of what to include and what to exclude. That relies heavily on understanding the course in the context of the overall curriculum and trusting your fellow-teachers to teach the rest of the curriculum.

This makes sense, but don't see it as so clear cut that any overlap between courses is "incorrect". I don't know what correct should mean in this context. There is a difficult trade-off. Like you've pointed out, time spent teaching one thing takes away from the amount of time that can be spent teaching something else. Teachers have the difficulty that they have to make sure they get through all of the material, and the curriculum has to be completely covered through all of the courses. But a lot of students get left in the dust when everything is flying by so fast, and they're already lost to begin with.

On the one hand, you have all of the information that needs to be shown to the students at some point. On the other hand, students benefit from also exercising their minds, and learning how to think in general. This opportunity will be squandered if the student's experience is reduced to memorization, and if they are distracted, get lost, or lose interest. If the OP's idea has merit, it implies that there might be conflict between having 100% disjoint courses and achieving these other goals.

I suspect that a lot of people on PF were those exceptional students who didn't get left in the dust, so it might be hard for a lot of you to relate.

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.

In my education as a computer scientist, I've ran into quite a bit of redundancy in the courses I've taken. For example, discrete mathematics, theory of computation, and combinatorics. However, I found that the overlap rather solidified my understanding in a valuable way. In each of these courses, it's not memorization of facts that are so valuable, it's learning how to think abstractly, and how to find and write proofs. I also liked these subjects a lot because I was easily able to understand them from the bottom up, and a really solid understanding of the fundamentals could go a long ways. In physics, maybe that's not the case? Or maybe I just never found that beginning thread in physics that I could latch onto like I did in computer science.

I like the OP's idea because I suspect that such an approach would have worked better for me. Maybe using black boxes would have worked also. But I figure that some approach to better capture the attention of some students like me is warranted. Maybe the exact idea the OP has will work, maybe not. But it sounds promising to me. I'm not sure it is the perfect solution, or that it will help all students. I suspect it would be in large part dependent on the teacher and how they engage the students as individuals.

And I will admit that I am one of those people that looked at differential equations, and just saw a bunch of symbols, then learned how to manipulate them in abstract ways, into different forms, and so forth, while having little intuition about what the point was, or what they meant. It seems like it was only down the line, after a lot of abstract manipulation of equations, and memorization of a lot of rules and procedures, that I ever did anything meaningful with them.

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.

 

[Jarvis323]

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.

Isn't there value in understanding what makes a good numerical method? Wouldn't seeing those flaws and limitations in action be valuable? How will they know the appropriateness of one black box model over another, if they don't understand them at all besides their inputs? Should there be a rule book or diagram they memorize that tells them which one to use and why?

The way I see it, experience running into problems and limitations with methods, is valuable experience that teaches you generalizable skills and pragmatism. 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. Then we break that solution, and find a new solution, and so forth. Finally, we might learn theories about the problem domain that say something about our limitations and trade offs. I generally liked going through this type of thing.

 

[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.