Rethinking Physics Education

[Beyond3D]

Chuck gets a charitable 1 point only to distinguish his answer from no answer at all. Chuck has failed to establish a relation between the numbers and physical reality and it doesn't matter that the answer is "20" as opposed to "42".

Was that one on purpose?

 

[weirdoguy]

I had always assumed I was not unique in realizing this.

To the contrary, you were quite unique A lot of students "know" that, yes, but really knowing and realizing, well that's a different thing.

 

[kuruman]

Was that one on purpose?

This is a hypothetical example

If I were grading this hypothetical exam, this is what I would do and why.

It never happened. The example illustrates how I would evaluate the extent to which each hypothetical student has understood the connection of their mathematical manipulation to the underlying physics.

 

[Beyond3D]

This is a hypothetical example

It never happened. The example illustrates how I would evaluate the extent to which each hypothetical student has understood the connection of their mathematical manipulation to the underlying physics.

I meant was the reference on purpose (42)

 

[Beyond3D]

"Is he telling me that all this math I had so far can be used to predict where the rock would be at any time $t$ that it spends in the air?" This revelation made me realize that the math I learned up to that point empowered me to understand the world around me in a way that I hadn't before. I decided to continue my study of physics after high school. Once I tasted this empowerment, I couldn't see myself doing anything else.

In terms of my colleague's statement, it turned out that I am one of the people to whom thinking unnaturally comes naturally. I am not alone. Physics Forums is full of such people.

Oh man, I remember those good old days. Physics started out just okay at first, but once it clicked, I couldn't see myself doing anything else. I remember when I first understood projectile motion. I'm getting goosebumps just thinking about it. Doing physics was the first time I could focus for hours on end. It (physics) just "thinks" like I do.

 

[Mark44]

From post #13:

Visual Definitions:​

• V: The displacement an object would cover in 1 second after acceleration is complete — that is, its final velocity.
• U: The displacement the object would cover in 1 second before acceleration begins — its initial velocity.
• a: The change in displacement per second between two consecutive seconds — in other words, how the velocity changes each second.

This has become a fairly long thread. I've quickly read most of it, so I might have missed some comments. What I've quoted above has a heading of "Visual Definitions." How are these definitions visual?
For another thing, the definitions for V and U seem to conflate the concepts of average velocity and instantaneous velocity. In the video, the definitions are given as average velocity over an interval (i.e. $\frac{\Delta s}{\Delta t}$ rather than as instantaneous velocities that involve the time derivative of displacement.
Also, the definitions for V and U give incorrect units; i.e. distance vs. distance/time. There is a similar problem with how acceleration is defined, especially the part "between two consecutive seconds." This sounds more like an average acceleration rather than the acceleration at a particular moment, which is not necessarily constant.

 

[Sudarshan_Hebbar]

From post #13:

This has become a fairly long thread. I've quickly read most of it, so I might have missed some comments. What I've quoted above has a heading of "Visual Definitions." How are these definitions visual?
For another thing, the definitions for V and U seem to conflate the concepts of average velocity and instantaneous velocity. In the video, the definitions are given as average velocity over an interval (i.e. $\frac{\Delta s}{\Delta t}$ rather than as instantaneous velocities that involve the time derivative of displacement.
Also, the definitions for V and U give incorrect units; i.e. distance vs. distance/time. There is a similar problem with how acceleration is defined, especially the part "between two consecutive seconds." This sounds more like an average acceleration rather than the acceleration at a particular moment, which is not necessarily constant.

Well, The idea at least was that since both velocity and Acceleration are defined with the help of displacement and displacement is visual quantity. It should be possible to define Velocity and Acceleration in a Visual way.

 

[Mark44]

The idea at least was that since both velocity and Acceleration are defined with the help of displacement and displacement is visual quantity. It should be possible to define Velocity and Acceleration in a Visual way.

Velocity and acceleration are defined in terms of positional displacement and time (a temporal displacement). If you want to define velocity (i.e., instantaneous velocity) in a visual manner, it's the slope of the tangent line to the curve s = f(t) at a specific point on this graph. Your video should clarify that what you're calling "velocity" is actually the average velocity.

 

[gleem]

I see a lot of steps here. Which one do you want to consider? And if you treat all of it as one step, then I don't really think that you will find a "physical meaning" to all of this. Derivations are derivations.

It's all about the Unreasonable Effectiveness of Mathematics, as noted by E. Wigner. Math can take us from one physical realization to another as a guide might take us from one location to another through unfamiliar territory. Without that guide, we would be lost.

 

[vela]

Well, The idea at least was that since both velocity and Acceleration are defined with the help of displacement and displacement is visual quantity. It should be possible to define Velocity and Acceleration in a Visual way.

I don't know about defining velocity and acceleration, but Knight, for instance, uses what he calls motion diagrams to illustrate uniform and uniformly accelerated motion. Try taking a look at Hewitt's Conceptual Physics book. He uses a lot of drawings to try get ideas across.

 

[TensorCalculus]

Okay, as someone who is still learning really basic physics, is still curious, and wants to help improve physics education yet was sceptical of the method of teaching that the OP was teaching, I agreed to try it out. We discussed the derivation below, and I'm going to provide my unbiased (I don't know why I would be biased, but this view is unbiased for the record) opinion on how I found walking through the derivation in this physical manner.

The first step:
We discussed this in the most detail out of all of them.
At first, the idea was to represent this as a piston, where each small change in volume $dv$ had a corresponding work done, $dW$
This felt intuitive, however as someone who had seen this equation before, I pushed for the OP to use a description that was more universal, rather than try and encompass the whole meaning of the equation with just one example in one scenario. This ended up with the definition of "The current form of the Work equation, Is a form of an experimental equation where if we want to find the work then we have to measure the Pressure values manually at every infinitesimal change in volume and multiply with dv and sum it all up manually to get the total work." - which I wasn't a huge fan of, because to me this feels imprecise: you can't manually measure infinitesimal changes, it's just something that's impossible in real life, so it felt odd to give this as a "real life, physical interpretation" of what was going on. I suggested a definition that was a bit too mathematical, and then refined this to make it into a more physical meaning. But in my definition, I had also basically just restated the meaning of an integral, and shoved it into a physical context. Of course, many students learning this derivation would hopefully already know the definition of an integral. In trying to acquire a definition that was both technically correct but also "in plain English", we just restated what the students hopefully would be able to infer themselves.

We quickly skimmed over the next few steps, with the OP commenting that maybe we should instead just focus on the meaning of the final result, which I agreed to, since the explanation for the rest of the steps felt like just restating what to me was the obvious. I think this is what many of you in this thread also were pushing to do since the start.

We also looked at one of the steps which involved integrating $\frac{dV}{V}$. The OP wanted the mathematical reasoning behind why the result of this was $\ln V$ , to which I provided the standard mathematical proof for and a few videos that talked about why it was intuitive, why it made sense. The OP did eventually say that maybe the pure mathematical manipulation was fine here, but they wanted visualisations, which I understand. (I then proceeded to point them towards the wonderful You tube channel 3Blue1Brown which I am sure we are all familiar with).

Here are my opinions on the whole process:
Did I feel like I had learnt something, or that walking through the derivation in that way was useful?
Surprisingly, yes, I did. Maybe not in the way intended, but I often found that the OP would ask me how I would describe this step, and I told them something that I thought was perfectly fine, except I later realised I had been talking maths all along. I realised how prone I am to thinking of physics derivations through the lens of mathematics, and whilst I don't see it as a bad thing, I did find it surprising just how much I had to think when trying to describe something without using super mathematical terminology, as the OP puts it, explaining things in "simple English". It was a proper workout trying to describe steps in a truly physical manner.
Do I think that we need to implement this in our everyday schooling system?
No. I think it's more rigorous than is necessary and that A lot of it, while it made a lot of sense, was pretty obvious anyway. I definitely learnt from it, that's true, but I don't think it's worth going out of the way to make students do this every single time they learn a derivation. Once? Maybe. It was a fun exercise, and interesting, but it's not the kind of brain workout a student should have to do every time they learn a derivation. Maths, and not English, is the language of physics for a reason.

Nevertheless, I would like to thank the OP for their time and patience when discussing the descriptions with me! Just because I do not think it should be widely/regularly implemented, does not mean I did not find it interesting and didn't also have a lot of fun in the process :)

 

[shishykish]

Although mathematics is rightly seen as the language of physics, there is often a disconnect between the mathematical expressions used and their precise physical meaning. Many students learn to manipulate equations without understanding what those mathematical steps represent in terms of physical definitions and principles.

I’m looking to collaborate with someone to create a course that bridges this gap—one that focuses on interpreting the exact meaning of mathematical operations through the lens of physics, ensuring that every equation is grounded in a clear physical understanding.

Hi, I'm new here as a physics teacher. I've been teaching since 2007. A lot of students have a lot of trouble with relating the physical reality to terms in an equation. I find analogies and models very effective in helping students. For example, the friction formula is a good one. As you already know, it's directly promotional to the normal force exerted. I'd ask students to slide their fingers across a table, ask them what forces are occurring. Then, I'd ask then which force increases as I push down harder. The response one would expect would be normal force. I'd then move on to ask how does friction feel when you slide your hand across a table as you push down harder than before. Finally, I'd show the equation, then finish off by asking about the direct proportionality between the terms. Then I'd relate this to how they felt before.

To teach resistivity, I like to use a classroom to demonstrate the metallic bonding inside metals. I'd ask students to be the electrons. Then I'd roleplay the current model whilst restricting the paths and areas the students can move in. Then I'd show.the formula and pose questions relating the role play to the terms in the formula.

To summarise, analogy/model -> formula -> relate -> test with a new situation