You take too narrow a view. I think you’re overlooking that learning something like proofs teaches a way of thinking in a stepwise logical manner which is exactly the kind of skill used by people who write software every day. Or more broadly, a skill important for the current fashionable educational buzzword “critical thinking”. You can as well argue that none of us need to know anything about the literature read in high school. When do we use that? But many people use the skills of reading comprehension and writing that were practiced in studying the literature. (I personally think that we could better practice those skills in some other way (using a variety of reading and writing genres rather than the current fixation on certain literature and writing literary criticism), but I don’t argue that studying literature is a waste of time because it teaches no skills of value).
Some of my work has nontrivial (i.e. beyond the calculus series) mathematical basis. Any work that has a substantial amount of math beyond derivatives and integrals is taught in theorem-proof format because that’s the only way to get anything more than a surface level understanding of the material.
Sounds like you haven’t found advanced math to be too useful in your own work, or perhaps you gravitated away from it because you didn’t care for it. And that’s fine, but it doesn’t justify generalizing from “I don’t use math” to “math is only for academics and isn’t useful in the real world.”
I find this hard to believe unless you and your son did not go to high school in an English speaking country.
Re: English Lit. I shouldn’t post late after a long day. When I was in HS English Lit referred to British Lit. That shows how long ago it was. I’d rather see writing better integrated Into other classes, with less literary analysis.
FWIW, my (rural, not terribly well capitalized) school district required one year of American Lit and one year of British Lit (plus one of composition, and then a fourth year of language arts elective)—so it’s certainly not unheard of.
At my STEM–centered public magnet HS, the English lit requirement was 4 years. Also, in addition to our regular workload, seniors were required to complete a 20 page English senior thesis in order to graduate.
One HS friend who felt English lit was a huge waste of his time because he was a hardcore STEM person and aspiring pre-med attempted to circumvent this requirement by sneakily changing around his schedule so no English lit classes were present. He was so good at doing this under the admins’ noses that they didn’t find out until late senior year when he already received several college acceptances…including 2 Ivies.
Despite those acceptances, the admins immediately notified the colleges to rescind their acceptances, refused to allow him to graduate with our graduating class, and retained him for a 5th year as a “super-senior” so he can make up the 4 years of English lit credits and complete the 20 page English senior thesis.
Although being retained as a super-senior was painful not only for the English requirements, but the understandably angry reaction from his parents, it turned out to have been a minor blip in his academic career. After a year at a SUNY, he ended up successfully transferring and finishing up at one of the Ivies which had initially accepted him before rescinding their acceptance on hearing of his stunt with the HS scheduling office, went off to med school, and is now a practicing MD.
How many times have you pasted that story?
@NeoDymium, saying you need to develop proofs at work because you work on things with a nontrivial mathematical basis is so vague that it doesn’t really tell us anything. Can you please tell us more concretely what you need to develop proofs at work for? I can imagine a very tiny number of research-type jobs where proofs might be helpful, but I’ve worked in all kinds of engineering and high-tech companies since I got out of school in 1983, and have never seen someone develop a proof at work. There was a very short period of time, circa 1990, where it was faddish to suggest people develop proofs to prove their programs worked, but that fad came and went very quickly because even though it sounded nice on paper, people found they couldn’t actually do it.
I love practical uses of math. On the other hand, theoretical math doesn’t appeal to me. I’m not one of those people who are drawn towards math because they think it’s beautiful. Learning math takes a lot of effort, and I don’t want to deal with it unless I know there’s a point to that effort. I figure I’m pretty typical in that respect, and it’s why I object so much to the emphasis on proofs, derivations and pointless letter-juggling in math classes. They’re boring and confusing as hell for most students to understand, and in the end, students leave class without any clue as to how math is actually used. They see no point to it all, and therefore flee from the subject as soon as they can.
I’m not sure at what level math becomes “advanced,” but my first job out of school was writing graphics programs from scratch for real-time, 3D flight-simulators. Since then I’ve worked on software for modeling radar systems, battlefield analysis, mapping for geographic information systems, and volumetric rendering for movie special effects and medical imaging. I’ve also worked on programs involving financial derivatives and fixed income analytics on Wall Street. Anyone who works on those types of applications knows how math-intensive they are. They involved practical uses of linear algebra, trig, statistics and some analytic geometry. I was able to do those even though I slept through the lectures involving proofs and derivations in school. No deep, theoretical knowledge was required.
I said I use them, not that I create new proofs. You are correct in saying that it’s unrealistic that anyone would have to actually write proofs in an engineering line of work. That, in fact, is something that is generally reserved for pretty much only academics and sometimes PhD’s in the industry. I haven’t actually written my own proofs or derivations since my undergrad (though I’ve used other people’s proofs and derivations frequently enough in work I’ve written).
But I also don’t know how you got that from my post. I use them in that most books and papers at a higher level that use math do work in a theorem-proof style format. It’s because it’s a very useful way to describe anything mathematical beyond a very simplistic level (relatively speaking, mind you). Have a few definitions, then use a few tricks of mathematical logic to show that something that satisfies that definition will have certain properties that are useful. Very compact and universal means to draw useful yet nontrivial conclusions about systems that exist in the real world and can be modeled mathematically. Hard to appreciate without either some training in analysis or graduate level study in a quantitative field.
It’s fair not to care much about “the beauty of math.” I’m not huge on that either, and it is precisely as you say: it’s tough to learn, and without any particular benefit from learning it there’s no reason you should have to. Some people like that, I really don’t.
But what you’re doing goes well beyond the practical. You’re not just arguing against non-practical math, you’re basically saying that anything that you don’t see a practical use for in the immediate future, you shouldn’t bother learning. If you cannot see what it would be used for, then it’s just worthless stuff to be used by academics high in their ivory towers who know nothing about what real work is like. Advanced work, which generally does require a higher degree, is about going beyond what is practical in the immediate future, and creating things that are not necessarily similar to what already exists and is well-established. It’s obviously not for most people, and there’s nothing wrong with that - we’re talking about levels of math well beyond what most people will ever need to use in most jobs (the thread is about algebra 2, not calculus and let alone analysis and beyond). But the general idea of your posts, that because you didn’t see more theoretical math in your work it must be useless and isn’t worth teaching, does not conform to reality. Sure, a lot of people won’t ever have to use too much from the theoretical side of math taught in school, beyond being able to gain a surface-level understanding of what advanced work actually looks like. But that is actually important, and it is something that can be built upon. Academic education is often about learning about what directions you can go to further improve your base of knowledge, and since, as you say, math is difficult to do if there’s no point, the vast majority of people who can’t see where the effectiveness of math comes in will just never understand why it’s valuable, even though it is. And while you are not without a point that it is a failure of the education system that people don’t really see that value while learning math in high school, the answer is to improve the teaching, not to talk about how stupid and worthless that knowledge is, and how only academics would ever care about mathematically advanced work.
To be frank, just because you didn’t have to use more advanced math yourself while working in those fields doesn’t mean that no one else who works there (or that developed the technologies you use) had to have a deep, theoretical understanding of math. And, again, not everyone needs to have that at all - it’s just too much work to get there. But your perception is that because you didn’t have to understand that theory for your specific job within highly mathematical applications that theory isn’t important, is straight-up wrong. A worker who assembles parts for a rocket might not know very much about orbital mechanics, but he/she would be a fool to say that it doesn’t matter because they’ve never used orbital mechanics for their own work.
Why this sudden focus on proofs? Does everything that one learns in school have to have an immediately obvious application to one’s professional life now? Why do we even have high school or college, then—why don’t we just go with an apprenticeship model for everything?
We have several disconnected strands in this conversation.
First, “math is not taught well in the country.” Yup. Probably the same can be said for science and foreign languages and maybe English, music and art. That should not be an argument against teaching each of these subjects, but should cause us to try to teach them better.I watched my son’s top tier public HS do a miserable job of teaching writing. The bright kids tend learn to write at least reasonably well by osmosis. My daughter’s top tier private HS took a very structured, systematic approach to teaching writing and it really worked – the vast majority of the kids write quite well. It can be done well but often isn’t. Our schools don’t try to learn from other schools that do better, from other countries that do better, etc. In general, our ed schools get students who are, based on test scores, fairly weak at math. As individual parents, you can’t wait for systemic fixes and you may have to take things into your own hands. For my extremely bright, severely dyslexic kid, we partially homeschooled him – he did math and English at home, largely with tutors. The honors math was painfully slow for him. I used his desire to compete in and win at Moot Court to help him learn to write well. It worked. So, if your kid is struggling with basic math, find another approach to teaching him/her.
Second, “I didn’t use algebra” or “my parents the doctors didn’t use advanced math” and they didn’t suffer so therefore my kids don’t need to learn this. Another variant is “I work in a technical area and don’t use really advanced math” and therefore my kids don’t need to learn it. As I posted earlier, the world is different than when you or your parents were advancing in their careers. Medicine is/will resist the use of Big Data to provide more evidence-based diagnoses that will become increasingly better than the diagnoses of individual doctors because the whole system teaches the doctors that their individual judgment is king but over time, it will change. Then doctors, who even now have to be consumers of lots of experimental and observational studies, will really need to understand more about statistics/data analysis. And as we move, again slowly, from genomics to medical treatment, doctors will need to be intelligent consumers of genetic test results. In addition, we don’t know the counterfactual – would the posters without math or the doctors in question perform better if they could have done algebra. Quite plausibly. [My wife is a well-known painter and you should see the rules of thumb/mental gymnastics to figure out where to put the nails/hooks she uses when she hangs paintings in her studio for gallery/curator visits – I just solve her problem using algebra in seconds. I doubt this would help the quality of her paintings, but she would spend less time hanging work]. I like to tell the story of an old GF of mine whose father was a professor of something artsy (maybe music) at a major midwestern state university that was surrounded by farming country. The school district included the university town and lots of farm towns. The district school board district was voting to introduce mandatory foreign languages or earlier foreign language or something like that. At the hearings, a farmer stood up and said, “If English was good enough for Jesus Christ, it’s good enough for my kid.” Not all backward looking arguments are right (and it’s not clear that Jesus wouldn’t have benefitted from speaking languages other than his own tongue, even if that wasn’t English).
Third, “No one really uses proofs in their work” so my kids shouldn’t have to learn how to do proofs. My observation is that people who have learned to do proofs understand reasoning from premises to conclusions better than all but the best of those who haven’t had that education. I see this is social science research. I see it in law (I work with lots of lawyers). I see it in philosophers, who aren’t precise about definitions and then think they are arguing for opposing conclusions when in fact the issues that drive their conclusions are actually different, imprecise definitions. My only concern with teaching proofs – and this can be done well too – is that it is not clear to me that you get much mileage from that at the HS level.
Fourth, “I don’t want my kids to take math that wasn’t useful to me, isn’t going to be practically useful to them, etc.” As either or both of @NeoDymium and @ucbalumnus said, I think we don’t know today what will be useful in the future. I asked a friend who is a brilliant economist who focuses on management issues what areas of math he’d found useful as an economist, and in particular whether he’d found (college-level abstract) algebra useful as my then sophomore in college son would have to take algebra to become a math major in addition to econ & psych. He said, "Algebra was not useful to me, but you never know what will be useful next. Who knew that symmetry principles (algebra) would become an important part of physics before it did?
Look, Americans!
It is all your choice. If you think that math is useless, and nothing shall be taught above the basic arithmetic - good luck. Make a referendum, special elections, lobby your legislators.
Please, don’t restrict immigrants from teaching our kids what we think is useful. Sun would not orbit the Earth, even if your political science guru would argue for it. Math is useful to understand how the world works.
Again, if you don’t want math - it is your choice. Math would not be offended. Sun doesn’t care what you think about it, or what are you teaching your kids.
<hacker, a="" professor="" emeritus="" at="" queens="" college,="" argues="" that,="" most,="" only="" 5="" percent="" of="" jobs="" make="" use="" algebra="" and="" other="" advanced="" math="" courses.="" he="" favors="" curriculum="" that="" focuses="" more="" on="" statistics="" basic="" numbers="" sense="" less="" (y="" -="" 3)2=“4y” 12.=""></hacker,>
I had a wonderful general contractor, who renovated our home. Hardworking, diligent, handy guy. Unfortunately, he constantly missed the deadlines and was pretty … disorganized. Giving me hard time. Once, I took a piece of paper and asked him to sit together and make a plan. Basic plan. What is the sequence of work? What material does he need at any given day? How long would it take him to do it? I was shocked how little math and planning he could do. we spent one hour together writing a plan, and it worked, tremendously.
I think some people know algebra and use it every day, on many occasions. Some people don’t know algebra, live on, and don’t understand how much they are missing. They substitute math with some business / logic / planning / accounting / statistics / critical thinking classes. They do not realize that the basic math has it all: critical thinking, statistics, accounting, reasoning, etc.
<does someone="" really="" need="" two="" years="" of="" algebra="" to="" figure="" out="" compound="" interest?="" it’s="" just="" a="" matter="" plugging="" numbers="" into="" formula.="">
And where do you take the formula? From internet? (Yes, I used proofs to make my own formula for compound interest, when I was shopping for my first house. I did not know that I can just plug in numbers into something from internet. 
Anecdote: Why do we have to spend money to launch satellites to monitor and forecast weather? We can get all the answers from internet, for free.
Talking about mortgages let me share a real story. In 1998 I was working for a consulting company. I just returned from an international assignment and was sitting in the office doing nothing (this was called consultant on a beach :-* ). Suddenly I got a sales call from a mortgage broker who wanted to make me refinance my house from 30 years fixed mortgage to some product called COFI mortgage. As I had nothing to occupy my brain I decided to try to understand this thing and started asking questions. The salesman quickly referred me to an “expert”. My discussion with the “expert” lead to nowhere but he told me that the “real expert” will call me and answer all my questions. So eventually I got to talk to the “real expert” and we were going through the formulas. At some point I asked him - and where do you get this number from? He said - I pressed the F35 button on my HPXXXX calculator. And what did this button do? He said - I do not know.
So I did not refinance my house. I did realize that we should have probably applied for this mortgage originally when we were buying the house and were on the cusp of qualifying for the fixed rate.
So it is your choice - to be an “expert” or to be an expert without quotation marks.
Enjoy:
https://www.mortgageloan.com/An-Overview-of-COFI-Loans
@californiaa, I’ve been a librarian for 25 years. I know very well not to blindly trust what’s on the Internet, as well as how to find it in a reference book.
We have a lawn. I spent a little time figuring out which ways take less time. I get “free” time as a result of using some math (yes, including algebra).
I took a trip recently, and thought it would be good to know how much it was going to cost, how long it would take, and where might be good to stop for breaks and gas. This also required some very basic algebra. (yeah, I solved for ecks like a boss).
Now if a person likes spending too much time mowing the lawn, that’s their business.
If they don’t mind running out of gas occasionally because 350 miles with a 10 gallon tank at 25 miles per gallon feels like it ought to work and too much “advanced” math is needed toknow rather than just feel: also their business.
I don’t like those things.
@tutumom2001: “However, I have never again needed to recite “The Canterbury Tales” in Old English.”
Oh, but darling, then you have never truly lived.
My linguistics professor self can’t let pass the point of fact, since it got brought up a second time:
[ul][]The Canterbury Tales are in Middle English.
[li]Beowulf is in Old English.[/li][]Shakespeare’s plays and the King James Version of the Bible are in (early) Modern English.[/ul]
That is all. Carry on.
@dfbdfb Thank you … I haven’t recited The Canterbury Tales in more than 30 years, and I’ve slept A LOT since then … and apparently forgotten everything I knew (probably because I have never needed to use it again).