> I think we do a disservice in introductory physics when we have things like massless ropes that do not stretch, massles pulleys and neglect air resistance.

This might actually be a good point.

A lot of students struggle with these ideas because they can't match the naive model to reality and so it's a struggle to understand the purpose of it.

Then, a lot more students struggle to get past this type of naive model because they understood the naive model was the point of what they were learning and it turns out - not really close to the end goal.

Sure, most anyone can learn the naive model of mechanics well enough to pass high school physics. But, it takes an excellent teacher and/or an excellent student to get past those two cognitive obstacles and progress any further. I recall physics to have a shortage of students, shortage of teachers and shortage of practitioners, a deficit that's getting worse.

I understand you are trying to make an ironic point but it's not obvious that it should be ironic. Is a naive model the best way to teach people mechanics? It works for some people but it's at least arguable.

Indeed. I remember clearly asking my high-school teacher why, if photosynthesis was so simple, didn't we use it to produce sugar artificially? I felt a little irritated that it turned out we spent so much time, and put so much emphasis on such a simplistic model... when apparently it wasn't very useful for any kind of analysis/further work etc.

There is absolutely an art to finding the correct way to simplify models. I'm reminded of Alan Kay's comment at his Ted talk, where he holds up the Gapminder-project for a useful simplification and highlighting/illustration of (rather complex) data, and derides a 3d model of biological processes in cells -- because they show proteins magically dancing stately around and matching up to form reactions -- which is completely different from what is actually happening (large complex molecules spinning really fast, thus making the incredible improbable matching of to such proteins just so possible).

That said, when it comes to mechanics, I think most realize that the model is naive -- students don't feel "deceived" -- and the ratios etc do actually translate to some useful intuitions when doing real-world work (eg: clearing rocks with wire, winch and tackle).

> A lot of students struggle with these ideas because they can't match the naive model to reality and so it's a struggle to understand the purpose of it.

Truer words never said. I'm one of those data points.

Luckily I had the fortune of having a science teacher who identified this and did teach me the basics of the underlying theories in high school. My mind rejects "rules" and wants "reasons." While everyone else was learning about Newtonian gravity, I was grasping the basics of special relativity. While everyone else was learning the "rules of bonds" in chemistry I was learning the basics of QCD. From these base theories I was able to remember via back-tracking all the way back up to the "rules" that I had learnt along with the rest.

It's about being a student versus being a parrot. Wanting insight into the underlying complexities is being a student while regurgitating information in an exam is being a parrot.

I started off with VICBASIC at 8, then QBASIC at 10. I only started C# when I was 16 or 17. Even then C# has a lot of abstractions away from the hardware. The only time I ever truly learnt what was going on is when I was thrown into the deep end: a customer was having problems and I had a memory dump, WINDBG and SOS. Only recently have I been taking the time to actually learn C/++.

Now that I am no longer "parroting" code I am starting to identify parroted code. No care is given to memory usage "because the GC will deal with it." Mutexs are sprinkled everywhere "because that's how you deal with concurrency."

At some point every developer needs to be thrown into the deep end. I would say that learning Python as your first language is fine.

However, if you never take the time to learn the nuances of how Python works, you are a dangerously ignorant.

If you have stretchable ropes, massive pulleys and air resistance, you'll need to be able to solve some complex differential equations which, in the North-American context, would not be taught until 2nd year university. Yet, the simple concepts of conservation of energy and momentum can be taught using simple algebra at the high school level with these idealized systems.

As for the deficit of practioners ... there are at least 10 times as many people getting a Ph.D. in Physics in Canada and the U.S. as there are positions ... so, no, there is no real shortage. (There is a shortage of qualified high school teachers though.)

You absolutely don't need to solve complex differential equations for this purpose, unless you want a closed form. Let's be more imaginative: Numerical analysis of the same model would be fine for high school level and is likely to give a great and relevant insight into mechanics.

Why is the closed form considered a prerequisite for a numerical approximation? Just because we ultimately end up at the latter, doesn't mean it should be taught in that order.

I may be mistaken about the practitioners but I doubt many Physics PhDs are short of work. It certainly seems like employers want more of them.

Whether you find a closed form solution (and, for most realistic systems you will not) or you want to solve it numerically ... you still need to write a set of differential equations. Before you learn about differential equations, you need to have done some basic calculus. You can not teach high school students what differential equations are, how they describe mechanical systems, and how to solve them numerically. However, using the math they know, you can teach them to find solutions to idealized systems that illustrate conservation of energy and momentum which are fundamental physics concepts.

OK. I accept much of what you say.

But it's perhaps not a coincidence that calculus and classical mechanics were invented at the same time in history - indeed, both were advanced significantly by the same person. Classical mechanics and calculus are two sides of the same coin.

Fundamental Theorem of Calculus: <=1670 Principia Mathematica: >=1687

So which order do you prefer to teach them?

In truth, HS math students do learn about differential equations, and easily have the capacity to apply them numerically. Some historical context and a little creativity in teaching could greatly help the understanding of both and benefit many students.

Well, what?

The massless ropes that do not stretch and massless pulleys and cogs are great approximation for the real world in nearly everything available at home.

If kids can not relate to those, it's because they don't look into the machines they have around them, not because the model isn't realistic.