Oh, on a personal level I totally agree about trig. I've used it a lot in my programming as well. But I think for the average person a basic understanding of probability is way more valuable, not because of the hard skills but because it changes the way you think.
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For the average person a basic understanding of arithmetic would be nice.
People are always complaining that schools don't teach them how to do their taxes, but for most people doing taxes is a combination of addition, subtraction, and following a page of instructions about which numbers to copy from one piece of paper to another.
Imagine trying to teach 16 and 17 year olds that are going to grow into adults that struggle to copy numbers from Box A to Line 3 and then add them correctly the difference between t-value and a t-value.
(I also believe the average person should have a better understanding of probability and statistics ... but we're still working on getting the average high schooler an understanding of why 1/2 + 1/3 is not 1/6 and why you don't need a calculator to calculate 7 * 0)
Taxes are more about having the right training/mindset when approaching a potentially complex set of instructions. It's more about how daunting it feels. Same way I've talked myself out of putting in the work to think long and hard about some proof I had to complete for homework ages ago: "I don't know how much work I'll have to do and how many sub-problems I'll encounter and that stresses me out".
100% agree about probability and stats, that stuff is not intuitive nor easy to pick up outside of school.
I think the argument with taxes is not just the simple math (addition, substraction) that people complain about, it's that taxes become more confusing every year (at least in the US). And not sure how school can help with that.
They don't even need to become "more confusing" -- the simple act of changing, even if they get simpler, forces one to 1) be on the lookout for changes, 2) when/if they land, understand the impact on one's particular requirements, 3) retrain one's processes accordingly. I pay an accountant to tell me how much VAT/sales tax I'm supposed to charge and what tax relief I can ask for, rather than to calculate the actual sums.
This is absolutely not a US problem alone, btw -- every modern country has a yearly cycle for fiscal policies at the very minimum, and often you have additional changes landing throughout the year.
I identify with your view completely. My undergrad degree is in accounting and I know enough not to do my own taxes. I don't trust my ability to guess what are valid deductions and what are not when the laws are frequently updated and I'm not focused on staying current.
TBH most people should be using turbotax or similar. It's easy to screw up on taxes beyond not adding stuff up properly.
We really should be making income taxes automatic for the default W2 case, like new zealand, but there is another story behind that.
Please don't give Intuit (makers of TurboTax) or H&R Block your money. They both actively lobby to keep taxes complicated / non-automatic and are a primary reason why it is so easy to screw up your taxes.
Happy to protest against them but any time you give me the opportunity to choose between paying $50 or manually preparing my taxes from scratch on paper, the answer is a no-brainer.
There is a official service called "free fillable forms" that you can use to file your taxes digitally. The UX is... a bit rough... but it works and is an alternative to preparing your taxes from scratch on paper.
Alternatively, there a number of other tax software companies that do not actively lobby against tax simplification and consumer interests. TaxAct is one example I've seen mentioned on HN, but there are others.
The problem is that "no-brainer" decisions like yours help keep us stuck in the same quagmire we are in now. I think it is worth a bit of time and/or money to push back against these kinds of shady business practices.
I totally disagree with this take, the problem with taxes is that they are a bizarre box filling exercise and not arithmetic.
School doesn't teach you to do your taxes because your taxes are abstruse and incomprehensible on purpose. If numeracy rose to the level it became easy, taxes would become harder.
It's really true that once you get probability, you see the world, read the news, and solve problems differently. If everyone had a good basis in stats, Vegas would be a Ghost town.
But if you spend time thinking about it, trig likely changed your perception of the world (and history) too. I think most mathematics do that to your brain, by virtue of expanding your internal language.
I can only imagine how crazy these conversations must get for the people actually trying to plan curricula.