You have yet to produce actual evidence that they are not taught. Personally, they were taught to me sophomore year, and I gave several example of different universities that do the same.Will Flannery said:why not teach the computational methods?
Dale said:You have yet to produce actual evidence that they are not taught. Personally, they were taught sophomore year, and I gave several example of different universities that do the same.
bhobba said:I have given an example where they are taught at HS. In the degree I did they are now taught from first year:
https://www.qut.edu.au/courses/bachelor-of-mathematics-applied-and-computational-mathematics
One of the hallmarks of the Upper School is an advanced math and science curriculum that enables students to enter into a two-year calculus, physics, and programming course in their junior and senior years.
* The course integrates the study of calculus, physics, and programming.
* Students develop the mental disciplines of programming - careful, logical, and concrete problem-solving.
* Students learn to create working mathematical models of physical phenomena so that they can better understand physics.
That is also my preference. I would prefer to teach them to use standard ODE solvers rather than hand programming Euler’s method.bhobba said:Anyway as far as this thread goes MATLAB and similar packages that solve differential equations with ease help students forge ahead in physics much quicker.
mpresic3 said:I read both papers by Will Flannery provided.
mpresic3 said:The part I am having a hard time is the coming revolution...
No, it didn’t. It was at my university last century. Maybe you just need to expand your horizon beyond USF.Will Flannery said:But, it missed the university.
Dale said:No, it didn’t. It was at my university last century. Maybe you just need to expand your horizon beyond USF.
The Department of Physics at the University of Florida is making strides toward becoming one of the premier physics departments in the United States. We have active groups in astrophysics, biological physics, condensed matter/materials physics, and elementary particle physics. Our faculty are internationally renowned in their areas of expertise at the various frontiers of physics. Our undergraduate and graduate students participate in cutting-edge research that prepares them for successful careers in a wide variety of fields, many in of them pure or applied sciences but others drawing on the broader problem-solving and communication skills fostered by an education in physics.
And yet you portray its curriculum as being sadly deficient in an important skill that is demonstrably taught at many other universities.Will Flannery said:So, I think it is representative.
Dale said:Why? They already use lots of black boxes. I simply disagree with avoiding black boxes as a desideratum. Will you also teach them how compilers work, or how computer chips calculate floating point arithmetic, or how transistors work, or how CPUs are manufactured, or ...? Why is one black box “to be completely avoided” and not others?
You cannot avoid black boxes, so their avoidance is not a good desideratum. Euler’s method is a poor method, so it seems like a total waste of time to me. Doing something badly simply to avoid one out of a thousand black boxes seems detrimental to me.
Do you want to teach numerical methods or do you want to teach physics? If you want to teach numerical methods that is fine, but don’t bill it as a revolution in teaching physics.
I agree with your use of spreadsheets. I think it is a step that should not be omitted between the calculations and the graph when studying. Learning to make a table is a very useful thing. It can even be used outside of physics, and there is no need to go the whole way and plot a graph. I have used a table to work out how much electricity I was using doing different things by entering times and electricity meter reading into a table on paper (and how much it cost in money) which is sort of physics but also sort of business or just life.Dr. Courtney said:I kind of like Euler's method as a teaching tool and have used it to teach high school students to compute rocket trajectories as well as to compute forces from videos of experiments. For systems where the forces are changing slowly, it is not bad, and it can be implemented in a spreadsheet. Students can learn it even before they have a clue about calculus with the idea that for sufficiently short times, the assumption of constant acceleration is "good enough" for sufficiently short time steps. Then students can shorten the time step and see if their calculations change much. Sure, the spreadsheets might have 1000-10000 rows, but they are all cut and pasted from the first few, and this allows students to easily see how the motion is progressing.
I see use of Euler's method in a spreadsheet as a stepping stone for students to using numerical methods in black boxes. It gives some insight into what is going on inside those black boxes and allows solving a bunch more systems than the assumption of constant acceleration. There will always be a more efficient numerical method just around the corner. But computers today are pretty powerful - it may be a fine approach to sacrifice numerical efficiency for conceptual simplicity for certain parts of introductory training.
But having taught introductory college physics for lots and lots of years, making scientific programming part of the course or a prerequisite for it is going to be a hard sell for most intro courses (except majors courses). It will be a great way to make students hate the teacher. Students in introductory classes are open to spreadsheets, not so much to learning to program.
"Without math, one isn't really teaching physics." I disagree. You seem to be implying that physics is a branch of mathematics. I take the view that maths is an indispensable part of physics, but physics without maths is still physics. It's possible understand parts of physics without maths, and very deeply, too. In fact, too great an emphasis on maths, in the ordinary sense of equations and calculations, can result in losing a certain intuitive understanding, I think. So many physicists who are great at maths, will flunk simple, fun, physics puzzles that are put in the form of words. Relativity Visualized by Lewis Carroll Epstein is light on maths indeed and yet I think gives a better understanding than most degree courses at the time did.Dr. Courtney said:Without math, one isn't really teaching physics. The question is how to approach the challenges to spend less time with the math and more time with the physics. Black boxes are one approach. Euler's method is another. It may well prove to be a revolution in teaching physics, at least for courses that adopt it. I doubt I'll ever teach another physics (or other quantitative science class) without using spreadsheets on a weekly basis. A spreadsheet takes repetitive calculations (and the calculator) out of the student's hands and also leaves a documented trail students can refer back to for what was done. Work on calculators disappears every time the student presses C.
When I was first exposed to numerical methods as an undergraduate, it was a real eye opening experience. The challenges of tough integrals, derivatives, and differential equations melted away, and I realized that the real challenge of physics was reducing the problem to an equation that could then be solved on the computer. Before then - I saw reducing the problem to an equation as about the first 30% of the problem and then beating that equation into submission with the traditional analytical (pencil and paper) techniques as the last 70% of the task at hand. Physics was mostly math, and I was not good at math, and I did not like math. About the same time, I also felt cheated by realizing that all the prior problems had been cherry picked to be solvable with traditional pencil and paper methods - most problems cannot be solved with pencil and paper. These revelations should really occur before a physics major is a junior in college.
So, I do think an approach to empower physics majors to solve more general problems in their first year would be a revolution in physics education, at least for majors. Some of the students I mentor are beginning to see similar things in their introductory undergraduate courses.
I'd like to know more about the "years of false physics" and the technology needed to counter their effects.Tom Hammer said:I taught high school physics for 15 years with some success. The difficulties were not in solving problems once the underlying physics was understood but in undoing the years of “false physics” that most students arrived having internalized. In the 90s there was a movement to measure the basic physics beliefs of incoming students and then to do a second measurement after taking basic physics. Most students in traditional courses never improved their basic understanding, so in response a course was developed with much success at Dicinson College and elsewhere. Unfortunately, thought the course had a high rate of success in improving basic understanding, it required a lot of technology to implement and never caught on widely.
You're missing something. v(1) is not the velocity after 1 second, it's the velocity at the beginning of the first subinterval, that is, when t = 0, then v(2) is the velocity at the start of the 2nd subinterval, and so on.physicsponderer said:A slightly bigger nitpick/question: wouldn't it have been better to have the MATLAB variables labelled the same way as in the equations? As it is, the by hand calculations have v(1) = -9.9 does which does not match v(1) = 0; % Initial velocity in the code. Wouldn't it reduce the cognitive load if the labeling was the same? Or am I missing something?
I didn't say it was the velocity after 1 second, I said there seemed to be an unnecessary cognitive load caused by the mismatch.Will Flannery said:You're missing something. v(1) is not the velocity after 1 second, it's the velocity at the beginning of the first subinterval, that is, when t = 0, then v(2) is the velocity at the start of the 2nd subinterval, and so on.
Great Scott, on going back and checking, you're right. Actually, the variable does have the same name, v in the hand calculation and v in the program, it's the change in the nature of the argument that creates the cognitive dissonance, v(1) = -9.9 and v(1) = 0. In the hand calculation v(1) = -9.9 the argument is time, in the program statement v(1) = 0 the argument is an index into an array, with v(i) being the velocity at the start of the ith subinterval. As we sometimes say on the bandstand, my bad.physicsponderer said:I didn't say it was the velocity after 1 second, I said there seemed to be an unnecessary cognitive load caused by the mismatch.
physicsponderer said:"Without math, one isn't really teaching physics." I disagree. You seem to be implying that physics is a branch of mathematics.
Dr. Courtney said: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.
Will Flannery said:So, I claim that there is very little physics without differential equations.
Dr. Courtney said:No need to chase all those rabbits.
Will Flannery said:I can't imagine even trying to teach it to unmotivated students.
Thanks for saying I was right, but I did not say 'cognitive dissonance', but rather 'cognitive load.'Will Flannery said:Great Scott, on going back and checking, you're right. Actually, the variable does have the same name, v in the hand calculation and v in the program, it's the change in the nature of the argument that creates the cognitive dissonance, v(1) = -9.9 and v(1) = 0. In the hand calculation v(1) = -9.9 the argument is time, in the program statement v(1) = 0 the argument is an index into an array, with v(i) being the velocity at the start of the ith subinterval. As we sometimes say on the bandstand, my bad.
Well, it's a sticky wicket ... that I recognized from the beginning but I didn't have an easy solution so I just let it slide and forgot about it. I still don't have an easy solution.physicsponderer said:Thanks for saying I was right, but I did not say 'cognitive dissonance', but rather 'cognitive load.'
Can the lesson in your paper be changed to get rid of the mismatch? If so, how? Not sure what you mean by 'As we sometimes say on the bandstand'. Could you please clarify that for me?
This is a bad basis for a pedagogical opinion. The two brightest students with a two to one student teacher ratio is essentially a guaranteed success regardless of how good or bad the pedagogical approach itself is.Will Flannery said:I base my opinion on just two students, the best in my kid's high school, whom I taught in a pilot class. They went through the stuff in the OP paper like fish through water.
As an 18 year-old I was a lot like you were - I thought a lot of things that weren't true!Will Flannery said:Well ... on the other hand ... I remember when I was a freshman at UF taking an honors physics course, and thinking to myself ... here I am 18 years old in an honors class and learning Newtonian physics, when I should be learning Einsteinian physics, 100 years (not really!) after the fact. It was only as a post doc working at Honeywell that I discovered I had not learned Newtonian physics in the freshman class, what I had learned was pre-Newtonian physics, and that Newtonian physics was much more difficult than I'd thought. It is so difficult that I think it's rare to see a solution to the Kepler problem, which marks the beginning of modern science and technology, in college physics.
I've had a copy for years and agree that Whittaker and Watson has a lot of gems that aren't easy to find other places. While it does cover some real analysis, the majority of the text is on functions of a complex variable. As caz wrote, many of the topics in that book are standard fare in mathematical physics texts/classes. At least where I was in school, every physics major I knew took at least one (and most took 2 or more) upper division courses in mathematical physics or applied math that included some combination of complex analysis, method of Frobenius, various special functions such as Bessel and Legendre, integral-transform and series solutions of PDEs, etc. I took a couple of those classes even as an engineering major.Will Flannery said:**and I've just become aware of another type of math that used to be very prominent in physics but seems to be less so now(?), real analysis as is typified by A First Course in Modern Analysis - Whitaker - pdf. There is a section on 'The Equations of Mathematical Physics' that seems to be various functions useful for solving PDEs, e.g. Legendre functions, Bessel functions.