Certainly, it has value and a place at the table. I’m not trying to make an argument based in
the “I can just do this on a calculator” argument
this sort of position, necessarily. Learning to derive things from first principles is the most valuable thing you can do. I’m calling into question that current pedagogical practice is the best way to instill that skill in individuals, for sure, though.
Further, the “I can just do this on a calculator” people have something of a point, even if it isn’t the one they’re intentionally making. Math courses and math exams look wildly different before and after cheap handheld calculators became commonplace. It’s not that we teach a largely different body of knowledge and more that we adapt how we show it to students so that it is useful to them. If you live in a world where compute is so cheap that you literally can carry a calculator around all day then learning to do long division by hand… isn’t really important actually. There’s a separation between the actual knowledge of the world and the application of it in practice. It’s always important you know how division works… it’s not so much always important that you get good at doing it by hand… and in the future it will not be so important that you be able to use a traditional calculator to do arithmetic, either - there will be something new or something else that we use. It will still be important you understand what arithmetic is though. In a world, this contemporary one we’re in, where you will be doing most of your non-computerized computation using a calculator, it actually is more important to be able to use a calculator sufficiently than it is to be able to do it on paper, by hand. Those skills are unrelated to the actual cognitive faculties required to meaningfully engage in reason. Or, at least, they aren’t directly correlated.
Certainly, it has value and a place at the table. I’m not trying to make an argument based in
this sort of position, necessarily. Learning to derive things from first principles is the most valuable thing you can do. I’m calling into question that current pedagogical practice is the best way to instill that skill in individuals, for sure, though.
Further, the “I can just do this on a calculator” people have something of a point, even if it isn’t the one they’re intentionally making. Math courses and math exams look wildly different before and after cheap handheld calculators became commonplace. It’s not that we teach a largely different body of knowledge and more that we adapt how we show it to students so that it is useful to them. If you live in a world where compute is so cheap that you literally can carry a calculator around all day then learning to do long division by hand… isn’t really important actually. There’s a separation between the actual knowledge of the world and the application of it in practice. It’s always important you know how division works… it’s not so much always important that you get good at doing it by hand… and in the future it will not be so important that you be able to use a traditional calculator to do arithmetic, either - there will be something new or something else that we use. It will still be important you understand what arithmetic is though. In a world, this contemporary one we’re in, where you will be doing most of your non-computerized computation using a calculator, it actually is more important to be able to use a calculator sufficiently than it is to be able to do it on paper, by hand. Those skills are unrelated to the actual cognitive faculties required to meaningfully engage in reason. Or, at least, they aren’t directly correlated.