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There's no need to infer what I mean from my comments because I'll say explicitly what I mean. I mean literally putting pen or pencil to paper, or chalk to a c

There's no need to infer what I mean from my comments because I'll say explicitly what I mean. I mean literally putting pen or pencil to paper, or chalk to a chalkboard, or marker to whiteboard, because if we're talking about algebra and high schools, that's the algebra American kids are taught to do in high school. At least, I was thirty years ago and my daughter was three years ago. That may not be what other people think of when they say they use the knowledge they learned in high school algebra, but I'm not obliged to think in their terms (the obverse is also obviously true).

gnicholas 3y ago
One does not need to put a pen to paper in order to think about how linear functions scale, how they differ from nonlinear functions, etc. These are things you learn in Algebra class, and which are useful for thinking about (and calculating by hand, when precision is necessary) many aspects of life. One example: at my kids' school, they care mostly about whether a student is at grade level. If a student starts the year already knowing 95% of the standards, they make little to no effort to ensure that the student is learning. When talking to parents about this deficiency, I mentioned that the problem is they're looking at the students' position, not their rate-of-change. Were we "doing calculus"? No. But I wouldn't have thought the issue in these terms if I had never taken algebra (where I learned about slope) and calculus (where I learned about derivatives). I would also point out that I pretty much never do long division or long multiplication by hand. I use a calculator, or Siri. But that doesn't meant that students don't need to learn multiplication tables, and the process for doing multi-digit multiplication and division.
- dventimi 3y ago
  And yet putting pen to paper to reduce and solve equations, solve sets of simultaneous equations, factor expressions, and find roots is what I did in algebra and what my daughter's doing in algebra. Personally, I don't believe that investment of her time and the public's resources in order that she think about "how linear functions scale" in some vague distant future should automatically be protected from scrutiny. Life is about tradeoffs. I enjoy math. Then again, other people enjoy chess. That doesn't necessarily mean everybody should be taught them, especially when time, attention, and resources are limited.
  - gnicholas 3y ago
    If you had asked people who wrote down equations on paper and solved them, you would have gotten fewer hands raised. Instead, people would have asked you why that is the relevant question. You somehow think it doesn't count if someone uses algebraic reasoning to figure something out. It feels like you're moving the goalposts. I'll take my leave; good day!
    - dventimi 3y ago
      > Instead, people would have asked you why that is the relevant question. And I would have answered that question, like already did in this thread. > You somehow think it doesn't count If you want credit for using algebraic reasoning, I'll give it to you. What I won't do is say that forcing most high school kids to do pen-and-paper operations which will be useful if they choose to become scientists but probably won't be useful if they don't become scientists, is a good use of their time or our public resources, because I don't believe that it is. And if we're talking about feelings, it feels like you're seeking validation for your math affinity. This sure seems like an expensive way to go about it.
brailsafe 3y ago
I suppose I simply disagree the majority of that sentiment, except that it's to true to say kids on school are physically putting pen to paper. > There's no need to infer what I mean from my comments because I'll say explicitly what I mean. You said "use" which is an abstract concept and absolutely needs to be interpreted. Yes kids in school put pen to paper for algebra, but they also often do this in programming classes, for no useful reason other than to demonstrate knowledge. It's not an inherently good way to do much of anything though, and I also haven't written Java by hand since my Uni days, but that doesn't mean I haven't used code. If your intention is to communicate about specifics, you need to use specifics. > but I'm not obliged to think in their terms Considering how other people might interpret your use of words is paramount to choosing them effectively. You're not "obliged" to do so, but you're also not obliged to participate at all; it's necessary if the subject can take many forms
- dventimi 3y ago
  > Yes kids in school put pen to paper for algebra, but they also often do this in programming classes, for no useful reason other than to demonstrate knowledge It's not just kids in school who are putting pen to paper when it comes to math. Know who else does that? Scientists Pen to paper may have no other useful purpose than to demonstrate knowledge when it comes to programming, but putting pen to paper does have other useful purposes when it comes to math. In fact, it's essential and practically not optional. Producing useful or illuminating results in algebra--solving equations, factoring expressions, finding roots--demands it and most mathematicians and scientists don't do those things in their heads. Moreover, most people won't even become mathematicians or scientists. They won't even be expected to produce useful or illuminating results in algebra. They won't even be expected to have the mathematical intuition developed by dint of years of hard effort. In short, they won't be doing much math as adults, just like most adults don't play chess or play the piano. Chess and piano are wonderful things, but they're not for everyone. Algebra is little different.

gnicholas 3y ago

One does not need to put a pen to paper in order to think about how linear functions scale, how they differ from nonlinear functions, etc. These are things you learn in Algebra class, and which are useful for thinking about (and calculating by hand, when precision is necessary) many aspects of life. One example: at my kids' school, they care mostly about whether a student is at grade level. If a student starts the year already knowing 95% of the standards, they make little to no effort to ensure that the student is learning. When talking to parents about this deficiency, I mentioned that the problem is they're looking at the students' position, not their rate-of-change. Were we "doing calculus"? No. But I wouldn't have thought the issue in these terms if I had never taken algebra (where I learned about slope) and calculus (where I learned about derivatives). I would also point out that I pretty much never do long division or long multiplication by hand. I use a calculator, or Siri. But that doesn't meant that students don't need to learn multiplication tables, and the process for doing multi-digit multiplication and division.

dventimi 3y ago
And yet putting pen to paper to reduce and solve equations, solve sets of simultaneous equations, factor expressions, and find roots is what I did in algebra and what my daughter's doing in algebra. Personally, I don't believe that investment of her time and the public's resources in order that she think about "how linear functions scale" in some vague distant future should automatically be protected from scrutiny. Life is about tradeoffs. I enjoy math. Then again, other people enjoy chess. That doesn't necessarily mean everybody should be taught them, especially when time, attention, and resources are limited.
- gnicholas 3y ago
  If you had asked people who wrote down equations on paper and solved them, you would have gotten fewer hands raised. Instead, people would have asked you why that is the relevant question. You somehow think it doesn't count if someone uses algebraic reasoning to figure something out. It feels like you're moving the goalposts. I'll take my leave; good day!
  - dventimi 3y ago
    > Instead, people would have asked you why that is the relevant question. And I would have answered that question, like already did in this thread. > You somehow think it doesn't count If you want credit for using algebraic reasoning, I'll give it to you. What I won't do is say that forcing most high school kids to do pen-and-paper operations which will be useful if they choose to become scientists but probably won't be useful if they don't become scientists, is a good use of their time or our public resources, because I don't believe that it is. And if we're talking about feelings, it feels like you're seeking validation for your math affinity. This sure seems like an expensive way to go about it.

brailsafe 3y ago

I suppose I simply disagree the majority of that sentiment, except that it's to true to say kids on school are physically putting pen to paper. > There's no need to infer what I mean from my comments because I'll say explicitly what I mean. You said "use" which is an abstract concept and absolutely needs to be interpreted. Yes kids in school put pen to paper for algebra, but they also often do this in programming classes, for no useful reason other than to demonstrate knowledge. It's not an inherently good way to do much of anything though, and I also haven't written Java by hand since my Uni days, but that doesn't mean I haven't used code. If your intention is to communicate about specifics, you need to use specifics. > but I'm not obliged to think in their terms Considering how other people might interpret your use of words is paramount to choosing them effectively. You're not "obliged" to do so, but you're also not obliged to participate at all; it's necessary if the subject can take many forms

dventimi 3y ago
> Yes kids in school put pen to paper for algebra, but they also often do this in programming classes, for no useful reason other than to demonstrate knowledge It's not just kids in school who are putting pen to paper when it comes to math. Know who else does that? Scientists Pen to paper may have no other useful purpose than to demonstrate knowledge when it comes to programming, but putting pen to paper does have other useful purposes when it comes to math. In fact, it's essential and practically not optional. Producing useful or illuminating results in algebra--solving equations, factoring expressions, finding roots--demands it and most mathematicians and scientists don't do those things in their heads. Moreover, most people won't even become mathematicians or scientists. They won't even be expected to produce useful or illuminating results in algebra. They won't even be expected to have the mathematical intuition developed by dint of years of hard effort. In short, they won't be doing much math as adults, just like most adults don't play chess or play the piano. Chess and piano are wonderful things, but they're not for everyone. Algebra is little different.