When young people ask me why they should learn math, I point out that managing your money requires math, and there are plenty of people who will steal from you if you are unable to recognize it.
An inability to understand compound interest is classic.
But that's basic arithmetic, and we have calculators to do that. Totally agree that understanding the problem and being able to frame a solution are also needed, but again, that's not hard maths.
I think we're more talking about algebra or, really, anything "higher" in maths than arithmetic. Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
And also, if we think that basic financial management is a good thing for kids to learn, why don't we teach that?
No, we don't have calculators to do that. AI, maybe. But a calculator cannot form an equation out of a social context and solve the equation.
If you bought 6 liters of soda for £3/2-liter bottle with 8% consumption tax, how much should it cost?
You have to shape that all into a series of operations for your calculator. The calculator can't do it by itself. Even basic arithmetic takes some education before the calculator can be useful.
> But that's basic arithmetic, and we have calculators to do that.
I would disagree. How to minimize a function, how to calculate interest, first derrivative are all pretty useful in finance, and a bit beyond basic arithmatic.
> I think we're more talking about algebra
"Algebra" as a term covers a lot. Being able to solve for x is a very useful skill and often what people mean by algebra.
If you mean understanding groups, rings, fields, or whatever, then sure that is probably not very useful to the average person's day to day. However i dont think that is usually tought in high school.
> Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
Pretty sure nobody in high school is getting a solid understanding of set theory. That is more university level.
> And also, if we think that basic financial management is a good thing for kids to learn, why don't we teach that?
I guess it depends on where you live, but i had to take a class on that in high school.
Set theory is actually the basis for all of math. This includes basic counting of the number of things in, ehm, sets. Cant be nore practical than this.
A calculator won't help at all if you don't have a grasp on what compound interest is. I've seen many laments on X from graduates who could not understand why they've paid more money to their student loan lender than the amount of the loan, and still have a balance that was more than the loan amount.
These are college graduates.
> Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
Knowledge of statistics will help a person a lot.
Another example. I wanted to put an elliptical brick patio in my yard. The contractor gave a square footage and I signed a deal with the charge per square foot. He staked it out.
It looked a bit peculiar to me. So I measured the major and minor axes and computed the area of the ellipse. It was 1/3 smaller than the contracted amount. The pallet of bricks was sitting in the driveway. I multiplied xyz to get the square footage of the bricks, and walla, it matched the area staked out.
I.e. I was being cheated. The contractor evidently was used to math challenged customers, and discovered how much he could cheat before being noticed. I pointed out the "error" (hahahaha) and the contractor reduced the bill by a third.
> why don't we teach that?
Exactly!
An excellent example that shows the value of understanding very basic geometry.
I'll add that math isn't really just about that sort of practicality though. It's also about a fundamental understanding of numbers and what they mean.
For example, inflation is in the news a lot. It's high, or low. Most people (the US president included) think that if inflation was 0% prices would come down. But that'd be a profound misunderstanding of the topic.
A grounding in numbers, in this case percentages, makes for a better understanding.
Any business owner needs to know fundamental truths to survive. Cost price, markup, margin, selling price, fixed expenses versus variable expenses and so on. All are grounded in basic math. Without that you can't do basic accounting. Without that you can't effectively run a business.
Anti-vax arguments are built on very bad math, and people bad at math fall for it.
We all use math all the time. People bad at math are at a major disadvantage. Populations bad at math are easily manipulated.
nitpick: "walla" -> "voila"
> Does a solid knowledge of, e,g, Set Theory, give any benefit later in life?
Is there any benefit to being able to distinguish logical entailments from non sequiturs?
The things that are taught under the label "set theory" are taught elsewhere under the label "basic logic". The most primitive symbols are intentionally matched: in logic, "and" is ∧ and "or" is ∨, while in set theory, "and" is ⋂ and "or" is ⋃.
The symbols stop matching quite that well after that - compare logical ⟶ and ¬ to set-theoretic ⊆ and ᶜ - but they continue to consist of the same material.