3 ms·

I feel you're coming at this without appreciating your body of prior knowledge. Intended or not, your statment "But that can't be it, because just two lines abo

by NamTaf 5y ago

I feel you're coming at this without appreciating your body of prior knowledge. Intended or not, your statment "But that can't be it, because just two lines above it we have..." assumes a whole lot of knowledge. You and I both know that it reads as one term, but for someone unfamiliar with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items, because the algebraic 'multiply' is so often implied, e.g. 3x = 3 * x as two individual 'things'. I think there's merit in explaining the concept of delta representing change, because it's not obvious. For example, when I was taught the concept in school, my teacher explicitly started with doing a finite change with numbers, then representing it in terms of 'x' and 'y', then merged them into the delta symbol. That's a substantial intuitive stepping stone and I think it's pretty reasonable that someone may not find this immediately apparent.

ColinWright 5y ago
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.
Someone 5y ago
> with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items But most will already be familiar with the family of goniometric functions such as sin and cos, there’s log and possibly exp and sqrt. There’s min and max; advanced math has inf and sup.

by NamTaf 5y ago

ColinWright 5y ago

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.

Someone 5y ago

> with calculus but exposed to algebra they are drilled to understand separate graphemes as separate items But most will already be familiar with the family of goniometric functions such as sin and cos, there’s log and possibly exp and sqrt. There’s min and max; advanced math has inf and sup.