I'm really wary of this. House wiring would be more useful than Shakespeare. That's not to knock house wiring, or statistics. I'd love to know more about both.
But don't deny yourself an understanding of the meaning of limits. Almost all mathematics before calculus leaves you with a misimpression that neat formulas exist to solve problems. In reality, you've learned to draw straight lines with a ruler, and maybe a few curves with a compass. Before Calculus, you might actually believe that numbers that can be expressed as the ratio of two integers are typical, and that numbers like pi and the square root of two are "irrational" rarities (and until calculus, you probably don't know about Euler's constant unless it was introduced in precalc as another one of those odd and rare numbers).
Look out at nature, where are the triangles, rectangles, and circles? Maybe a wasp nest? Nah, not really. Try to draw a cloud, a tree, a tiger, or a human face. How useful is that straight line or compass? How useful is a line at all, other than to hint at something you can't actually draw, maybe by implying it exists as an ever vanishing limit from above and below? Math required calculus the instant humans decided to describe the world as it is, rather than by the limits of what we impose on it.
Also - in stats, how do you know what the area is under the probability density function?
Education is a Hard Problem TM because the knowledge of those links isn't useful without sufficient existing knowledge, and you need to introduce things in a way such that the things you hand-wave away are tolerable knowledge gaps. Knowing that a CDF is an integrated PDF isn't useful for someone who doesn't even have a notion of what a PDF is. Describing a state machine that satisfies conditions X Y Z as an Abelian group is similarly not useful for someone who doesn't have an intuition for groups or fields.
My claim is that, given the finite amount of time allotted to mathematics in a secondary school curriculum, it's better to spend that time learning about medians/means, regressions, statistical tests, and so forth, instead of memorizing power laws and derivatives of trigonometric functions.
What would someone other than a scientist use regressions for?
I've used one once. I wanted to make a volume control that I thought sounded subjectively even across the range and gave the right amount of control. So I used a polynomial regression calc on a random website and gave it some data points I wanted it to go through.
But that's not actually doing a regression, just knowing it exists and computers can do them.
Is there any math that has any use whatsoever unless you know a whole lot of it and plan to do some technical projects? I thought the whole point of learning any math(Even arithmetic, since phones exist now) is just so you can learn other more advanced math, and maybe someday be a solid state chemist or something.
Statistics lets you read a scientific paper, but you don't actually need to understand it, unless you're actually going to be reviewing their raw data. Most everyday people just trust the p values and move on to wondering about confounders they forgot.
Seems like you could cover all the statistics people will actually use it about 4 hours.
Basically every person who writes papers using statistics has taken a course in statistics. Medical doctors do it, psychologists do it etc. And the statistics course you'd replace calculus with would be even lower level than that, basically worthless to everyone. At least calculus trains you to think about rate of change and slopes, statistics gives you nothing practical. It isn't like people remember those formulas so they can apply them in their daily lives.
People don't need to remember and apply formulas. They just need an intuition that they could be applied and how that might change the appearance of the statistics, as a kind of gauge of reliability. A tool for rationalization.
The problem with this approach is your basically teaching this as a side effect and hoping they're smart enough to actually connect all of that together vs. teaching those concepts directly and being far more understandable.
If you want people to understand that numbers are concepts / descriptions of something potentially infinite, and that it's ok to totally work with non-finite describable numbers without ever really writing out their values, just fucking start with that. I honestly think the start of most undergrad math curriculums should be a logic & foundations class with proofs, sets, number theory and the whole "numbers are more logical concepts, not really specific values" vs. calculus. Then teach calculus, with a big dose of 'what is infinity, really?'.
I think it's actually a great disservice and the hand wave that most calculus math classes do about those exact concepts really fucks over a lot of people. It makes calculus a weed out class because the fundamentals are not explained properly so a good amount of people just go into it as yet another thing they have to ape without real understanding. And for the people who don't work well with things they half understand, they really struggle, like I did. It really made my computer science degree a lot worse, because of the instance of starting all undergrad math with hand wavy calculus, for 3 or 4 classes.
I even wrote blog articles about it, it was probably the worse part of my computer science degree, and if math education was done differently where they didn't handwave, I probably would've had a much better time.
Well, AP statistics covered the area under a probability distribution function and people seemed to understand that -- you look up the answer in a table (or use the TI-83 function). Presumably they'd do the same for a cumulative distribution function.
Teaching people that there are lots of problems where solving them numerically is the best way of solving them is often just the truth. Also, you then get to discuss some of the really cool numerical techniques which tend to get short-changed in traditional math classes.
We already do that in elementary and high school with logarithms, square roots, sin, cos, tan, pi, radians, e, irrational & imaginary numbers, etc. The tables are just built into pocket calculators instead of paper. Even Pythagoras is a bit weird.
House wiring and Shakespeare are completely different subjects. (I’d expect someone professing Shakespeare to avoid such a straw man, but I see your point!)
Most people don’t need mathematical statistics, but far more will find meaning/interest in the immediate applications of lighter statistics than the another-math-class-full-of-equations that calculus feels like to many.
Anecdotally, most universities are scrambling to add lighter data science courses to their humanities majors. These all teach basic stats, and many ignore the low-level calculus required for those methods (again, speaking of the humanities versions here).
We dont need proofs, calculus, reasons, process, principles and theorems actually. Just results and facts are in demand for our lives. But it may make us subordinate to people who have invented theories of statistics or calculus, because we have no choice but refer to and based on their theories, I mean, depend on them even if the theories are absolutely correct or truth of the universe.
In my experience, neither intro calc classes nor intro stats classes are that useful at teaching the underlying principles. The classes mostly just test whether students can learn an algorithm to solve a certain class of problem, whether it's differentiating a function or running a statistical test for scenario X.
I was a math major and didn't understand calc all that well until I took advanced calc, and I didn't understand statistics all that well until I took the upper-level mathematical stats courses.
But Shakespeare is incredibly useless. People don't even talk or write like that anymore. Any imagined benefit of Shakespeare is just fanciful wishful thinking.
When I was younger, I thought like you did. Now that I get older, the value of culture and an understanding of where it came from, how it developed, makes my life just so much richer. That does not necessarily mean that I need to have memorised the whole corpus of Shakespeare, but understanding a reference when it comes around is adding more layers of meaning to other works.
This does not only extend to literature. I have had similar experiences with religion (which I thought of as utterly useless and potentially dangerous, as it "deactivates critical thinking and creates sheep-people which will follow whatever their shepherd/priest/guru tells them"), creative arts (both painting as well as music), and the basic sciences (biology, chemistry, physics).
Now, I don't genetically engineer the stuff in my garden, but understanding Mendel was useful. I don't speak in iambic pentameters, but I can appreciate when it is being used as a stylistic choice. I am in no way a church-going, devout Christian, but I have found meaning in some of the deeper wisdom enshrined in the Bible (and the Koran, and the Bhagavad Gita, and about half a dozen Sutras.)
Would I have come to that if I didn't have primers in school? Maybe. But the primers certainly helped.
On the other hand, I didn't learn plumbing in school, or laying electrical wires, or "doing my taxes", but these are things I can simply have someone do for me who is a lot better equipped and trained to do so, or - for the small stuff - I can figure them out on the fly.
There is a ton of stuff that makes life richer. That doesn't mean we should be teaching it at schools. I can think of movies, games, novels, TV shows, blogs, and music that have had orders of magnitude more impact on my life and thinking than Shakespeare. Should we be teaching any of that stuff at school?
I'm willing to believe that some people like Shakespeare, but it's a small minority. You can tell by the number of people who read Shakespeare for pleasure - is that number larger or smaller than the number of people who read JK Rowling? Why should we teach the entertainment that a small number of people prefer in schools? I believe the only reason we actually do is tradition.
You mention that you can simply have someone learned in plumbing or sundry skill do those tasks for you. I can do one better. I can simply have no one read Shakespeare for me and I can not read it at all and nothing is lost. That is, of course, because unlike plumbing or laying wire there is no reason to need Shakespeare.
It's good that you enjoy Shakespeare, but some people enjoy plumbing. Plus, plumbing has a practical purpose, unlike Shakespeare. There is no real reason to teach Shakespeare, other than tradition, and people trying to seem smart or educated. There are many other subjects that make a much stronger case for deserving to be in school curriculum.
I read a quote somewhere that goes something like "A society that separates warriors and scholars will have an army led by fools and thinking done by cowards." Similar logic, with different vocabulary, applies, I think, to a society where scholars can't do manual labor.
I like to believe that school works as a catalyst here, showing you stuff you wouldn't normally encounter - you have no trouble accessing popular culture, so there's no need to teach you about that (that's being said, one of my more memorable music lessons was the teacher analysing the composition of Pink Floyd's "Shine on you crazy diamond" with us. I can absolutely see Harry Potter becoming an object of academic study and literature teaching in 50-70 years, it is happening with Tolkien already).
On the other hand, less-than-popular culture still is the foundation for our popular culture today - the amount of times "Romeo and Juliet" or "Macbeth" has been adapted, referenced and deconstructed in (popular) media is astonishing, and without knowing the original, you wouldn't fully get the modern references.
You don't need to love Shakespeare (I don't exactly, though I like to see the "Scottish play" every few years) to reap these benefits.
School is not about what people like. If you go by that measure, there's no real need in math, because you will find a lot less people doing calculus for fun, as compared to people who play fantasy football. Of course, you can't really understand the ideas behind fantasy football if you don't know maths, but who cares, it's not popular...
Please note that I did not claim physical labour has no value and one should not know about it. I said that it's relatively easy to pick up, and that it may be more worthwhile to get a professional when the job demands it (a professional, I would like to add, who learned his craft after school, ideally in some kind of apprenticeship). In my country, to get a driver's license, you need to know basic first-aid procedures (and yes, there's a one-day course you need to attend). That doesn't make you a neurosurgeon, and if you have persistent headaches, it's probably better to ask a professional than to depend on me with my first-aid course - or some guy who "learned about surgery techniques" in high school.
Shakespeare may have a profound impact in the English speaking world. But from the perspective from any other language than English, Shakespeare is an esoteric subject with limited impact. I do agree that the Christian Bible is of immense importance to European and American culture. Today we blithely dismiss all things religious, but I would argue 99% of modern European/American culture has been affected in some way by Christianity. Pretending it doesn't exist has been a major disservice to students.
I think it is because we have gutted the idea of a liberal arts education.
Shakespeare is supposed to be read along with a massive amount of other literature going back to the Greeks. We have ditched most of that though besides Shakespeare for some reason so it doesn't make sense and makes him stick out more than he should.
But don't deny yourself an understanding of the meaning of limits. Almost all mathematics before calculus leaves you with a misimpression that neat formulas exist to solve problems. In reality, you've learned to draw straight lines with a ruler, and maybe a few curves with a compass. Before Calculus, you might actually believe that numbers that can be expressed as the ratio of two integers are typical, and that numbers like pi and the square root of two are "irrational" rarities (and until calculus, you probably don't know about Euler's constant unless it was introduced in precalc as another one of those odd and rare numbers).
Look out at nature, where are the triangles, rectangles, and circles? Maybe a wasp nest? Nah, not really. Try to draw a cloud, a tree, a tiger, or a human face. How useful is that straight line or compass? How useful is a line at all, other than to hint at something you can't actually draw, maybe by implying it exists as an ever vanishing limit from above and below? Math required calculus the instant humans decided to describe the world as it is, rather than by the limits of what we impose on it.
Also - in stats, how do you know what the area is under the probability density function?