3 ms·

I agree completely that I'm coming at this with a lot of background knowledge, but if I'm reading in an unfamiliar field and I see a symbol I don't recognise, I

I agree completely that I'm coming at this with a lot of background knowledge, but if I'm reading in an unfamiliar field and I see a symbol I don't recognise, I look in the surrounding text to see if the symbol appears nearby. As I say, "Δt" appears immediately above ... that's a clue. As you say, it's drilled in at school that everything is represented by a single glyph, and if these are juxtaposed then it means multiplication, and that is another thing to unlearn. But I think the problem isn't the specifics of the "Δ", it's the meta-problem of believing that symbols have a "one true meaning" instead of being defined by the scope. I agree that explaining the delta notation would be helpful, but that's like giving someone a fish, or making them a fire. They are fed for one day, or warm for one night, it's the underlying misconceptions that need addressing so they can learn to fish and be fed, or set on fire and be warm, for the remainder of their life.

NamTaf 5y ago
I absolutely agree with your comments regarding teaching the underlying approach to digesting a paper. You definitely raise good points, especially the 'one true meaning' comment. I should state that I'm not discounting the value of your point, especially given this clarification, however I guess that when I reflect on my experience in my time learning this, the time I best learnt was via initial expalnation, then worked example, then customary warning of corner-cases and here-be-dragons. e: I also think, on reflection, that a signfigicant part of your ability to grok a new paper per your comments is your comfort in approaching these concepts due to your familiarity. Think of learning a new language - once you have a feel for it, you're likely more comfortable exploring new concepts within it, however when you're faced with it from the start you probably feel very lost and apprehensive. I feel that understanding calculus is a fairly fundamental step in the 'language of maths', teaching that symbols don't necessarily represent numbers but can represent concepts (e.g. delta being change). This isn't something you encounter until then, but once you do you begin to understand the characters associated iwth integrals, matricies, etc. in a way that you may not have previously with algebra alone.
- ColinWright 5y ago
  Agreed ... I think we're pulling in the same direction ...
erichocean 5y ago
> a symbol That's literally the whole problem: he sees two symbols.

NamTaf 5y ago

I absolutely agree with your comments regarding teaching the underlying approach to digesting a paper. You definitely raise good points, especially the 'one true meaning' comment. I should state that I'm not discounting the value of your point, especially given this clarification, however I guess that when I reflect on my experience in my time learning this, the time I best learnt was via initial expalnation, then worked example, then customary warning of corner-cases and here-be-dragons. e: I also think, on reflection, that a signfigicant part of your ability to grok a new paper per your comments is your comfort in approaching these concepts due to your familiarity. Think of learning a new language - once you have a feel for it, you're likely more comfortable exploring new concepts within it, however when you're faced with it from the start you probably feel very lost and apprehensive. I feel that understanding calculus is a fairly fundamental step in the 'language of maths', teaching that symbols don't necessarily represent numbers but can represent concepts (e.g. delta being change). This isn't something you encounter until then, but once you do you begin to understand the characters associated iwth integrals, matricies, etc. in a way that you may not have previously with algebra alone.

ColinWright 5y ago
Agreed ... I think we're pulling in the same direction ...

erichocean 5y ago

> a symbol That's literally the whole problem: he sees two symbols.