126
The US is COOKED
(hexbear.net)
Banned? DM Wmill to appeal.
No anti-nautilism posts. See: Eco-fascism Primer
Slop posts go in c/slop. Don't post low-hanging fruit here.
the majority of them would refuse to do 285 - 271 without a calculator, let alone fractions.
So, I can do it mentally, but it does technically take more effort and brain work than using the calculator. In this example it's obvious that we should be able to reason out the answer, but I would hardly say calculators are ever the problem. Ultimately they are a tool, and for most people knowing how to use a tool is good enough.
I always think of calculating triangles with sin cos tan, and the fact that we were taught how to use the calculator and only the calculator. I assume there is a long handed version you can do with pen and paper, and I assume you eventually know it if you study mathmatics, but for most people knowing how to use the calculator is probably sufficient.
And as we've learned now, they probably don't even know that.
i absolutely said that about calculators for a long time before working with students trying to learn algebra. they genuinely largely struggle to understand what they're doing because their ability to manipulate fractions and arithmetic is so stunted. it's not that drilling long division would be good, but the calculator dependence is absolutely not helping. it also makes most of them deeply allergic to fractions as opposed to decimal approximations, that they also don't really understand correctly. in ways that greatly harm their willingness to even try to learn math. it is unfortunately absolutely not like learning sin cos tan ratios. which they also struggle to understand are functions because they have trouble with functions because they have trouble digesting even basic algebraic concepts like substitution. not that i mean in any way to comment on your own abilities, these are my observations from working with the kids.
No I'm sorry, I think I was truly speaking out of turn. I haven't been in school for a while now, and I only experience some interactions with the younger generation. I think it was wrong of me to discredit the importance of the basics.
You learn the alphabet before you learn to read.
no need to apologize, i have a math degree and i was of the mind that people were overreacting about the extent of calculator use since most of the arguments are reactionary before i started working in a school.
but lo and behold, no, for reasons entirely other than what most people would think, it's absolutely killing the kids.
It's absolutely true, you can give someone a basic arithmetic problem (addition, subtraction, simple multiplication) and the first reaction is to grab a calculator. I have to interrupt my learners, and be like, "no, you don't need a calculator to multiply this by ten, I promise you will waste more time pulling it out then just thinking about the answer".
I have had classes where I get my learners to look at their calculator history, and they realize how many really basic things they offloaded to their phones that they absolutely knew if they were just willing to consider it for a few seconds.
it's been really stunning to observe for me. a lot of the students i work with, when i've insisted on trying to do the arithmetic without a calculator, has been to simply fucking guess.
this is partly a problem i think of our local education system and how little effort they require from middle-school students (ages ~12-14) to simply pass them through, but it's still off-putting to observe.
I'm not in the US, but a very similar country, and I don't work with kids; I work with adult learners (the majority of whom have learning disabilities and/or external learning barriers). So my learners are all people who have been entirely failed by the education system. And from my experience it starts really early. Those first few years of educational development are completely cocked. Most parents can't (the majority) or won't (fewer, but still exists) take any of the early education on as a parental responsibility. So the very beginning of someone's educational journey doesn't start until like, five years old, where they are already behind their peers.
And then, and I will especially focus on math here, those early ages of number sense development are abysmal. Under-resourced and over-populated classrooms, a complete lack of necessary supports, and often just terrible pedagogical practices lead to kids falling behind immediately. But they're pushed through, though of course without the early number sense they can't understand the arithmetic. And this continues the entire time they're in school.
Essentially set up to fail from the start. And of course many of them develop math aversion because they never mastered the fundamentals so every subsequent step just grew farther out of their comprehension until they internalize that they're just not good at math, or aren't math people, without considering that math is a skill that can be learned like any other.
I'm very fortunate that my work lets me teach math in a very different way, from number sense to trig; I've seen people who have spent thirty, forty years thinking they would never do arithmetic grow comfortable and confident in algebra. For those working with kids and knowing that they are going to leave that school without having learned, for instance, basic financial skills...that's gotta be bleak as hell. Kids are getting majorly screwed over.
It's sad how institutional failures mount. The educational death by a thousand cuts.
that's really cool work, very much the same phenomenon at work here in large swathes of the u.s..
I don't think there is a reasonable way to calculate trigonometric functions by hand. The computer solves a number of terms in an infinite series to approximate it. Back in the day there used to be books of tables, that had a lits of trigonometric functions logarithms, and so on for different numbers. I guess you could also use a slide rule. As a side note, there is an old timey isekai by an American author, I forget the name, were the magician has to give up his magic to get a book of tables and it's considered a good deal.
The closer thing to solving trigonometric functions by hand that can be taught in grade school is the unit circle. Incidentally when you buy a ruler set, it comes with 2 triangles and a compass, the 2 triangles have 30 and 45 degree angles Wich are the ones used for the unit circle.
all correct, there is not a nice work around for general computation of trigonometric functions. this is partly why the algebra of trigonometry is emphasized. the closest one might find to simple reasonable approximations of trig functions are the approximations one uses in physics for "small angles" which is a trick employed to get a model out of a differential equation without a solution in terms of elementary functions. so for "small angles" one can substitute
xforsin xand1forcos x.