- #61
TensorCalculus
Gold Member
- 275
- 408
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 :)
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 :)