And why is calculus or statistics important. My wife hated math and even would get 0 on some tests and yet she is a very successful nurse today. Math is not important at all for the vast majority of adults today. Why should children be forced to study it? (I say this as someone who did enjoy math and did very well in it)
I hated maths and wound up with an Economics major and a job where an above average grasp of stats is greatly beneficial. Go figure. I suspect the proportion of adults for whom some form of mathematics assumes at least some basic importance in adulthood vastly exceeds the proportion of kids that would voluntarily turn off MTV to do arithmetic puzzles.
Put another way, if you drew a Venn diagram of "stuff that would be useful for adulthood" and "stuff most kids would study until they were at least adequately skilled entirely of their own volition", the circles would barely overlap.
Sure, this doesn't apply to the average Hacker News reading autodidact, but one of the first things you learn in statistics is not to make judgements based on outliers.
Nicely said. An argument could be made that if kids learn to study on their own they'll be motivated as adults to catch up on the stuff they weren't interested in as kids. However, as a parent I feel at least partially responsible for ensuring my kids spend their time in a useful way.
Put another way, if you drew a Venn diagram of "stuff that would be useful for adulthood" and "stuff most kids would study until they were at least adequately skilled entirely of their own volition", the circles would barely overlap.
I think the second statement applies perfectly well to most adults. Our whole system is based on having people maximally specialize into their element of greatest comparative advantage, to the exclusion of most of what we regard as maturity, wisdom, and humanity.
Learning statistics has been a fundamental part of the development of my critical thinking. Being able to understand that 'many' is a weasel word and why (see my other comments). It makes me less susceptible to things like yellow journalism, and makes me require more rigorous arguments to sway my opinions.
Statistics gets a bad rap, but it is far more important for day-to-day life than people give it credit for.
Math is not important at all for the vast majority of adults today.
This is just plain not true. I can't speak for calculus, but in addition to what I mention above, there's plenty of day-to-day need for math by the general public - money handling skills, for example, are something that almost everyone should have.
No, because as I said, learning statistics has helped my critical thinking improve - and that's something everyone needs. There was even an example in my comment regarding reduced susceptibility to yellow journalism, which can only be a positive to both the individual and society in general.
I also use simple algebra a lot in my every day life. By solving simple equations you can with little effort derive formulas for calculations you have never done before.
Statistics are useful in the way the parent post mentioned.
Logarithms are useful for better understanding some statistics, but this has less every day use than the two above.
And while I do not use calculus in my every day life I still find it very useful to reason about ordinary things in the terms of derivates and integrals. It has given my new ways to think about problems.
I had a high school principal who used to be an English teacher. He used to call school assemblies to get on stage (in the auditorium) and talk about how useless math is. He would say "you're always trying to find x, I don't want to find x."
A cursory grasp of correlation and probability theory would do wonders for the general public in so many regards (voting, trends, debunking scientific claims made in popular media and commercials, etc).
The point of learning math is there's an inflexible scorecard of reality for an incredibly complicated logic puzzle, and the only determiner of adequacy in the subject is persistence. Now if you want to excel you need the knack or genetics or whatever, but mere adequacy only takes a certain amount of sweat.
So it teaches that at least some times there's certain logical rules where one follows from the other or can be combined with another, and if you're persistent you can figure it out. Or just summarize to persistence and logic.
I really don't care if your wife can solve 2x=4 for x, but I would be unhappy to be under her care if she would give up on complicated situations (oh he's not breathing AND no pulse? I'll just give up), or refuses to notice cause and effect relationships.
Exactly. Math isn't a set of procedures, it's a way of thinking. Without understanding that way of thinking it is impossible to be an educated person.
"Most mathematicians at one time or another have probably found themselves in the position of trying to refute the notion that they are people with "a head for figures." or that they "know a lot of formulas." At such times it may be convenient to have an illustration at hand to show that mathematics need not be concerned with figures, either numerical or geometrical. For this purpose we recommend the statement and proof of our Theorem 1. The argument is carried out not in mathematical symbols but in ordinary English; there are no obscure or technical terms. Knowledge of calculus is not presupposed. In fact, one hardly needs to know how to count. Yet any mathematician will immediately recognize the argument as mathematical, while people without mathematical training will probably find difficulty in following the argument, though not because of unfamiliarity with the subject matter.
What, then, to raise the old question once more, is mathematics? The answer, it appears, is that any argument which is carried out with sufficient precision is mathematical, and the reason that your friends and ours cannot understand mathematics is not because they have no head for figures, but because they are unable [or unwilling, DRH] to achieve the degree of concentration required to follow a moderately involved sequence of inferences. This observation will hardly be news to those engaged in the teaching of mathematics, but it may not be so readily accepted by people outside of the profession. For them the foregoing may serve as a useful illustration."
College Admissions and the Stability of Marriage, Gale & Shapley, The American Mathematical Monthly (Jan 1962)
If all you're looking for is a scorecard for persistence and logic any rule based system will do, e.g. music. You also overestimate the general population's capacity for understanding math, in my experience. Your tone renders your comment equivalent to "The beatings shall continue until morale improves."
> I really don't care if your wife can solve 2x=4 for x, but I would be unhappy to be under her care if she would give up on complicated situations (oh he's not breathing AND no pulse? I'll just give up), or refuses to notice cause and effect relationships.
You really don't know what you are talking about here. How you can make the link from not being good or enjoying math to just giving up on something critical is completely illogical.
A great idea shared by many. A point that my European history teacher made that stuck with me works quite well here:
When, after high school, will you have to factor a quadratic or describe to me in detail how a cell works? Who after high school does that? A very small population. However, who lives in an organized society with a set of beliefs that will have to judge and effect those beliefs? EVERYONE! Who will have to read something or judge a document put out by the government? EVERYONE!
(The full caps is somewhat required as he would always stand on top of his desk and yell it at the class...)
Educators tend to be big on calculus because it correlates with college success [1].
Independent of the studies (there are more) I think that stats is very underserved in society. Nurses should know statistics. Knowing joint %s and Bayesian stats are useful in treatment and diagnosis. Much of health care is moving from doctors to nurses, and it's important for them. Stats are also important for people making investments. And buying lottery tickets. And buying a house. And making judgements in daily living.
Totally agree - not important for most adults to lead a happy and useful life.
However, a grasp of calculus and statistics (those two came to mind, there are surely others) is useful if you want to break past existing boundaries because they give you some tools to think abstractly. Personally, I want my kids to learn that. They already have plenty of time to explore on their own - the time spent in a classroom should, in my opinion, be spent on learning fundamentals very deeply.
It's not only hard to teach yourself calculus, it's also something you wouldn't think of doing unless you're Gauss or one of those guys.
It's not only hard to teach yourself calculus, it's also something you wouldn't think of doing unless you're Gauss or one of those guys.
Agree with the rest, kind of disagree with this part. Measure the slope of a curve, measure the area under a curve. No big whoop. Sure, the details get fiddly but 90% of anxiety over calculus comes from its arbitrary place as the capstone of a suffocatingly rigid elementary math sequence, not its inherent difficulty or magisterial importance.
Stats and discrete math are harder imho, and people teach themselves those all the time. Helps that they're much more useful (outside physics and engineering anyways...)
I've been considering trying to teach my middle school kids the basics of calculus as an experiment to see what happens. I'm curious to see whether I'm capable of explaining it well enough because I agree with you - the basic concepts are not that hard.
