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Imho, the better question is should calculus be taught without physics? None of it clicked for me, I stumbled to make any meaning out of any of the hand wavy e

Imho, the better question is should calculus be taught without physics? None of it clicked for me, I stumbled to make any meaning out of any of the hand wavy explanations my poor teachers gave me… until I took my first calculus based physics class and a hundred light bulbs went on as to why any of this stuff needed to exist, but more importantly why.

seanmcdirmid 2y ago
You could teach calculus via a video game programming class, physics as well, just through the things you need to build a video game. Calculus and even physics never clicked for me until I actually used them productively.
- globular-toast 2y ago
  This is also a good example of why we teach things that might seem "useless". You just don't know what someone will find useful in their life. The teachers probably didn't even think of video games having physics and needing to understand it for that. In my uni class I think I was the only one to use forces and masses (and therefore acceleration) instead of just speed. I initially used speed but then my school learnings came flooding back and I did a full physics model (it's really easy if all your objects are rigid bodies on perfect planes). I'm actually pretty sure I've used everything I've ever learnt in school at one time or another. But the the meme amongst normies is you don't use any of it...
  - seanmcdirmid 2y ago
    I'd rather start the other way around: teach things steeped in the context that they are useful in. Everything is useful, so teach them usefully. Not all of us are great at storing away knowledge and accessing it much later when we find it actually useful.
    - globular-toast 2y ago
      But then you won't be able to teach as much. I think this whole thread boils down to pedagogy is difficult.
soulbadguy 2y ago
Interesting, I have had the complete opposite experience. I could never relate to the physics interpretation tag onto differential calculus. Only when I was introduce to the proper foundation of measure theory and topology that I really "got" multi variate calculus
globular-toast 2y ago
I was exactly the same. I was good at integrating but had no idea why we were doing it. Then we did a physics-based module (called mechanics) and it was like you: a hundred light bulbs went on. Nowadays I "see" numbers in a totally different way. If I see a time axis I can't help but see the rates of change etc. I wonder if it could be taught in a more top down way: start thinking about rates of change in some discontinuous functions, like finance. How growth of assets over time relates to income. Then move to continuous with distance, speed, acceleration. Then do the thing where you differentiate symbolically.

seanmcdirmid 2y ago

You could teach calculus via a video game programming class, physics as well, just through the things you need to build a video game. Calculus and even physics never clicked for me until I actually used them productively.

globular-toast 2y ago
This is also a good example of why we teach things that might seem "useless". You just don't know what someone will find useful in their life. The teachers probably didn't even think of video games having physics and needing to understand it for that. In my uni class I think I was the only one to use forces and masses (and therefore acceleration) instead of just speed. I initially used speed but then my school learnings came flooding back and I did a full physics model (it's really easy if all your objects are rigid bodies on perfect planes). I'm actually pretty sure I've used everything I've ever learnt in school at one time or another. But the the meme amongst normies is you don't use any of it...
- seanmcdirmid 2y ago
  I'd rather start the other way around: teach things steeped in the context that they are useful in. Everything is useful, so teach them usefully. Not all of us are great at storing away knowledge and accessing it much later when we find it actually useful.
  - globular-toast 2y ago
    But then you won't be able to teach as much. I think this whole thread boils down to pedagogy is difficult.

soulbadguy 2y ago

Interesting, I have had the complete opposite experience. I could never relate to the physics interpretation tag onto differential calculus. Only when I was introduce to the proper foundation of measure theory and topology that I really "got" multi variate calculus

globular-toast 2y ago

I was exactly the same. I was good at integrating but had no idea why we were doing it. Then we did a physics-based module (called mechanics) and it was like you: a hundred light bulbs went on. Nowadays I "see" numbers in a totally different way. If I see a time axis I can't help but see the rates of change etc. I wonder if it could be taught in a more top down way: start thinking about rates of change in some discontinuous functions, like finance. How growth of assets over time relates to income. Then move to continuous with distance, speed, acceleration. Then do the thing where you differentiate symbolically.