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"Not a single one of them said that the math I described was necessary in their profession."

I know I'm biased. Geek is as geek does, but $deity almighty am I tired of that line. If simple math isn't valuable to your profession, it might at least be worth a think about how valuable your "profession" might be in the first place.

Some of the huge systemic problems we are facing right now may have something to do with the fact that we have entirely too many professions where it really doesn't matter if one could master simple math.

I think that's the difference between academic education, and vocational training.

I've made this point before, but people often conflate the two, and are unable to separate them in their minds.

What this person is saying is "these things do not train a person to perform these specific sets of tasks". That's vocational training, and there's nothing wrong with that. Academic education, on the other hand, is about learning to think, about history, rhetoric, science, and all sorts of things that aren't directly applicable to a particular job, but provide a necessary foundation for critical thinking and enlightenment, so to speak.

What our system really needs is two streams. An academic stream, for those who choose, and a vocational stream, which is what a large proportion of students and seemingly educators like this guy want.

This way, everyone gets what they want. Students truly interested in learning things not directly related to performing a job will have the benefit of a more supportive learning environment, and students who just want to get a job will also attain the required vocational training.

It's really win-win.

Our system already has those two streams, has practically forever. People still abuse the college stream as if it were vocational training.

Unfortunately they are winning and academia is being dumbed down so that everyone can obtain a degree.

How do you reconcile that position with the original article?

The article is a single anecdote from the wrong side of the college continuum. After helping my daughter all year with geometry, it is not surprising to me that he couldn't do the math. Those kinds of tests ask questions like "Can you prove these triangles are congruent" and you have to remember all the SAS, SSA, ASA, etc theorems and postulates to have a chance. You will forget those after 20 years, no matter how much you excelled in high school, if you aren't using them (or derivative concepts in higher math) regularly.

Proving theorem's is often taught very poorly. If you haven't already I highly recommend you read Lockhart's Lament:


I haven't finished reading it yet, but so far it's been pretty eye-opening. It reminds me of how I once took a photoshop course in order to improve my design skills... pretty easy to guess how well that worked.

Perhaps I'm the exception, but in Grade 10 I didn't take math (long story) and had never seen most of the math concepts but still was the go-to math helper. High school math is fairly trivial- easy enough to figure out with just some intuition and general thinking skills.

There's a huge leap from being able to figure it out with a book and all the equations inside of it as opposed to taking a test with only questions, no reference material, and presumably a time limit.

No, I never used a book or any equations. People would give me questions with no context, and I would take a second to think through it and then help them. Things like solving systems of equations are easy - you just need to truly understand algebra. Similarly, high school geometry doesn't get far past the axioms themselves.

As a disclaimer to all of this, I was the type that had fun proving stuff in seventh grade and had already read through Spivak's Calculus by Grade 10.

As a disclaimer to all of this, I was the type that had fun proving stuff in seventh grade and had already read through Spivak's Calculus by Grade 10.

This makes your earlier claim of never having seen most of the concepts rather dubious.

I do not have a high opinion of school board members and the article seems like superficial fluff.

If you don't have a high opinion of them, you should try it, run and fix all of the things they're fucking up.

Absconditus is talking about higher education, I think.

These streams already exist. One of the major issues I see wit this is it assumes a child at 15 years old is capable of making this choice and understands all the implications. I think back to grades 9 thru 13 (Canadian), thank God it's not so long ago, but I realize decisions I made then were primarily based on emotion, testosterone and some social influence. Could I really have imagined life 15 years later? Absolutely not.

This is once again caused by education inflation. It's easier for the HR department to compare formal education than to really look at the applicant. So Master's degree wins over Bachelor's wins over solid vocational training and society carries the cost.

One of my ex-colleagues (in his 40s, and is exceptionally good in programming) continues to learn new stuff every day - often I'd find him learning some obscure programming language or algorithm, which he'd never ever use in his "day job" or "profession". I asked him why he does that, knowing well that he'd never use that knowledge - his answer was "you don't need to directly use everything you learn. the more you learn, the better you entire thinking faculty develops, and you'll solve your existing problems better/quicker".

Just because basic calculus (or other math) isn't used in our everyday life, doesn't mean it is wasteful to learn it. So yeah, I'm tired of that line too.

But it wouldn't even be calculus in 10th grade.

In 10th grade most kids have done a year of algebra and are doing plane geometry along with simple proofs.

That must be it: the scientific sample of people he described the test contents too did not use proofs in their work. Therefore, introducing mathematical logic in 10th grade is not going to prepare students for the high-tech jobs of the future.


From what I've seen from tutoring 3 younger siblings in math throughout their high school days, I think they should spend the first 3 years of high school drilling Algebra into their heads. Then in the last year they can spend half a year on geometry and half a year on trig.

From what I've seen the biggest problems my sibs had with higher math wasn't the higher math, it was the algebra underlying it. They get one year of Algebra in 8th grade and the move on to Geometry assuming they have mastered it, but they havent.

I agree. I'd rather people graduate high school actually knowing algebra than pretending to know calculus.

We have quite the conundrum in this country: not enough qualified workers for high tech jobs, and a strong resistance to teaching kids the skills to do those jobs. I think it's going to take a major cultural shift for us to move past this and have parents demanding their kids learn more math and science. There seems to be an incipient movement in this direction but man is there a lot of inertia!

"a strong resistance to teaching kids the skills to do those jobs"

There is a strong resistance from the kids because its either boring, too hard or not explained in a way that is relevant to them to see how it can be applied. This is among the main reasons why in the US the number of SMT college/uni graduates has not increased since 1980, while humanities has more than doubled.

I'm not sure this argument really has any force. Doctors need less math than engineers. Is "medical doctor" therefore a less valuable profession?

Similarly, electricians need very little math at all. We clearly need electricians. Should we just not educate the students we think are likely to be electricians? Or should we have a real discussion about what topics are most likely to enrich the lives of the most students?

We just yesterday had an article posted about the 1850's Harvard entrance exam. Surely, if they had a time machine, there'd be quite a few antebellum Harvard freshman willing to tell us all how important it is to memorize Thucydides in the original Greek.

The stronger variant of that argument is, I think, that you don't know how much better you could do your job with math until you know a substantial amount of the math that would improve it.

For instance, a large number of doctors tested (in a study I can't locate the citation for) fell prey to Base Rate Neglect[0] when doing a mock diagnosis. This seriously affects the amount of money wasted and the amount of illnesses cured in medicine. Along with a wide swath of related problems, it could be cured with an intuitive understanding of basic probability theory.


A way to bring this back to the productive side of the thread would be to point out that both sides can be right: the math taught in schools can be so irrelevant that nobody (outside engineering) retains it, meaning, we should teach more stat and less "pre-calc".

I agree. There's only so far you can go in probability theory without knowing calculus--but learning up to that point in probability is far more useful to 19 out of 20 non-engineers than calculus is.

The funny thing is that over here in the UK the press have claimed that schools are dumbing down maths education based partly on the fact that they don't teach calculus or geometry as part of the compulsory curriculum. It's been replaced with (amongst other things) basic probability and statistics which apparently wasn't taught until university before.

Interesting! The response of the press is predictable; but I'm actually very curious what the results will be for the generation raised on probability.

> Doctors need less math than engineers. Is "medical doctor" therefore a less valuable profession?

If you fail to recognize the importance of understanding math in your profession, then yes: http://www.ted.com/talks/peter_donnelly_shows_how_stats_fool....

Both you and the article are confusing the issue. The value to be gained from a good mathematical education is problem solving skills. These skills are neither the focus of high school mathematical education nor what is being accessed by standardized tests.

Whether one uses specific knowledge directly in their profession is irrelevant. The knowledge is required to teach the concepts and skills. There is also more to life than one's profession.

Sometimes the things you've forgotten are important indeed!

The other day I was building something and realized that I hadn't done a trig problem in at least 10 years. I felt pretty sad when I had to look up how to solve it. I still remembered the general concept, but the details were lost on me. Yet, it was important that I knew how to do it.

I'm trying to go through Khan Academy in my spare time to learn and relearn the math that has slid out of my memory.

Yes but isn't that better than having never known it in the first place; better to have a known unknown than an unknown unkown?

At least in this case you know what things to look up; imagine never having learned those things in the first place.

How about "latent" knowledge?

I try to quickly learn about every concept I come across to the point that I understand when and why you would want to use it, but not the point that I understand how to implement it. When I encounter a problem that fits the concept, then I can look it up and learn how to do it fully.

I don't know, I feel it has served me well anyway. I like to jump on problems in all kinds of industries, so it is impossible to study everything ahead of time.

I agree with this way of seeing knowledge. Knowledge of subject X shouldn't be represented as a binary field, since everything is fractal and you could spend infinitely long trying to understand it.

Absolutely. I knew there some something with an opposite angle and a hypotenuse, and it only took me a minute or two. If I had never known it, there's no way I could have done that so quickly.


"sucka-toe-ah" that's how we remembered it in high school :D

Personally I can't tell how thankful I am about Khan Academy because there are really mathematical concepts that I simply couldn't digest back when I was in high school mostly because I either got lost in 1-2 chapters (back then) and instead of understanding the concepts I ended up drowning in them.

You know what is even funnier? That after learning the logic behind programming I was able to perceive mathematical concepts under a whole different view and had so many fulfilling "oh that!" moments so far!

That is why our educational system should be based on capability and progress, not age, from grade one. Kids shouldn't be put in a situation where they will drown as it only sets them up for more difficulty later.

A lot of people have voiced similar concerns on this thread and I strongly disagree, at least with the part where you say "no math=no value". I know plenty of people at my work who probably can't add two fractions together but are still extremely valuable to the company as a whole. Managers, lawyers, graphics designers, salespeople, the list goes on. Though a passing knowledge of math may be mildly useful in a few situations, having no knowledge of the subject at all really isn't any kind of problem for some people.

I agree that everyone should learn math in school, but that's so they can learn how to think and analyze. If the skills have atrophied through disuse I would conclude that they have found other ways to achieve the same goals.

Managers Sales people, and Lawyers with poor understanding of math as basic as adding fractions are vary risky. It's not that they can't preform most job fuctions it's that they are extreamly likely to make costly mistakes. When should I add one more person to keep people from charging as much overtime. Or the old should I offer overtime or comp time etc. As to sales people and Lawyers effective negotiation require them to be able to say: I can't drop the price any more but I can do X (which costs us less) etc.

Graphics designers often use a lot of math directly when working out layout's and things. An intuitive understanding and lot's of effort can help compensate but it's a significant loss if they can't do simple math on how tall / wide things are when you scale them.

What about poor language skills? You made a mistake in nearly every sentence in your comment.

I apologize if English is not your native tongue.

What about poor language skills? You made a mistake in nearly every sentence in your comment.

Then I guess he won't be using his comment history on HN as a reference for his next interview.

I would argue that inside a company it's communication that's important not polish. It's only when your company is interacting with the public that polish becomes important.

I have found that those who write poorly in the corporate world generally think poorly as well.

That's a pretty low blow. What he wrote was extremely clear, though clearly his punctuation was terrible and his spelling was shaky. If it had been read to you out loud, you wouldn't have noticed an issue:

"Managers, salespeople, and lawyers with [a] poor understanding of math as basic as adding fractions are very risky. It's not that they can't perform most job functions, it's that they are extremely likely to make costly mistakes. 'When should I add one more person to keep people from charging as much overtime?' Or, the old: 'Should I offer overtime or comp time?' etc. As [for] salespeople and lawyers, effective negotiation require[s] them to be able to say: 'I can't drop the price any more but I can do X' (which costs us less), etc.

"Graphic[...] designers often use a lot of math directly when working out layouts and things. An intuitive understanding and lots of effort can help compensate, but it's a significant loss if they can't do simple math on how tall / wide things are when you scale them."

Is that written poorly enough to take the time to passive-aggressively call someone stupid on the internet?

> If it had been read to you out loud, you wouldn't have noticed an issue

Maybe someone should start working on a text-to-speech app for HN with built-in meaning detection, then? Without one, onemoreact's posts unfortunately were not read out loud to me, and I had to do double-takes for "vary", "preform", and "incite" (all real words pronounced differently than what was intended). The missing punctuation also made it difficult to parse the text given the absence of verbal pauses or tone changes.

I'm not saying that I like to read emails like that, I'm saying that to accuse somebody of having difficulties thinking when they have difficulties in grammar and spelling is a low blow. The brother of an ex of mine is a dyslexic PhD geologist who uses a combination of text-to-speech and assistants to do a lot of important research work. English orthography is weird, and is largely used as a class marker to dismiss people with no regard to the content of what they're saying. In addition, it's not at all unlikely that English is onemoreact's second or third language.

It'd be different if the argument was incoherent, or took a huge amount of effort to understand.

I'm not saying insulting intelligence is acceptable when laziness is a more likely cause, but you can't say the the post was "extremely clear" then go on to rewrite it, adding several written language features that aid clarity greatly.

English is my second language, and I sorta know a couple more and could have a nice rant about English orthography and phoneticity or lack thereof and the root causes of this unfortunate situation. English as a second language issues might cause one to confuse "vary" and "very" but will not be the cause of pluralizing with an apostrophe. The lack of quotation marks is also at best a laziness issue, not a dyslexia issue.

I really struggle to see why someone would go to the effort of posting a comment and not bother to correct at least the spellcheck-catchable typo "extreamly."

I just corrected the grammar for illustration. I didn't have any problem understanding it.

Pluralizing with an apostrophe or not using quotation marks are even common with people who have English as a first language, and are signs of discomfort or lack of practice with English writing, which could be the result of dyslexia, English as an eighth language, or any other reason. Could even be stupidity, but when the ideas are coherent, to jump to that just seems to be a way to feel superior to someone.

Seemed like an intelligent enough comment to me, even though I would extend it to the reading comprehension that the author of the subject of this thread must lack to fail a 10th grade reading test with 62%, then further extend it to become a belligerent attack on management in general. The school boards in America are still debating evolution every single year. I add, of course, that school boards have nothing to do with teacher's unions, and break them more often than they support them.

I wish you luck in your struggle.

Why wouldn't quotation marks be a dyslexia issue? Dyslexics have no intuition whether written language "looks right." That includes punctuation.

That writing reminds me of a friend of mine who is dyslexic. I always have to sound out his writing to make sense of it.

I find those that think in such general terms also tend to think poorly ;-) My personal experience is the best writers rarely have much to say, but I have probably spent to much time in the consulting world where saying something meaningful is far less important than saying something well. Still, I try and avoid generalizing to much because incite rarely comes from generalities.

This is very valuable insight.

That applies in general, not just in the corporate world. Lazy writing implies lazy thinking.

Yes, but... Lousy spelling and punctuation are not necessarily lazy writing.

What else would you call them?

Dyslexic. An ex-girlfriend of mine is very bright and gifted at logic (majored in philosophy), but her spelling and syntax are terrible.

Disabilities don't count, I'm talking about people who can write better if they cared to try, not those who can't.

Negatively motivated writing.

Managers, lawyers, graphics designers, salespeople, the list goes on.

For salespeople, sums, differences, multiplication and division of fractions might not be the best example; calculus might be more appropriate. Some of the best salespeople I've ever worked with could effortlessly modify the deal numbers in their head on the fly during a negotiation. For example, it could entail working out a seemingly big "cash discount" number and offering it on the spot, knowing full well that it won't take so many points off the margin that the pricing team will throw a fit nor impact their commission such that they care. These are fairly simplistic one or two decimal place fractional arithmetic that are only moderately more complex for the layperson than tallying up the tip at a meal, but it puts a lot of pressure on the customers when they are told, "if I have to walk out of this meeting without closing, I won't ever get the authority to offer that discount again".

I get that math can be a valuable skill, but you're suggesting that it is the only valuable skill. That anything that does not make use of high school math is inherently worthless. That is a very strong statement.

Take a look around and I think you'll find many, many incredible things that were done and made without the aid of trig and algebra. Specialization is pretty much the foundation of modern economics after all.

Everyone (irrespective of their profession) should be able to master basic math.

> If simple math isn't valuable to your profession, it might at least be worth a think about how valuable your "profession" might be in the first place

I don't think the requirement for maths is a way to judge the value of a profession. I think it's essential for every day life, but not necessarily for work.

Simple math? What? Who said 'simple math' and how do you define it? I know my GP probably couldn't 'simple math' his way out of a paper bag, neither could a lot of valuable professionals who don't use math on a daily basis.

There's more to life than knowing how to do math. And the people ruining the world are generally not the ones that suck at math.

For starters, people should at least try to master enough maths to be able to master their own personal finances. That most people chose to neglect to do so and instead gave 100% trust to their bank advisers might be one of the causes for recurring economic crisises(es).

Also while I can think of several jobs you might be able to conduct without knowing maths, performance in most of them could nevertheless improved a lot by knowing maths. I imagine running your own business without knowing maths is also a recipe for disaster, so by deciding against maths, you automatically settle for loan slavery for your life.

> If simple math isn't valuable to your profession, it might at least be worth a think about how valuable your "profession" might be in the first place.

I regularly end up doing simple math for people who cannot, including those in management. And that's not even counting the programs I have written.

Apparently, a lot of people have forgotten how to deal with simple fractions, to say nothing of simple 2D geometry. Most of you probably have no idea how many windows have ended up screwed up or back ordered because of this...

That is exactly what I was thinking! I don't care if the simple arithmetic isn't necessary in one's profession (if it's 10th grade, I'd guess that it's either Algebra 2 or Trigonometry/Pre-calc), it's still shocking to know that someone who has a B.S. degree doesn't know it.

The test-taker seems to be making excuses.

The problem is too much focus on 'simple math', and not enough on numeracy.

> simple math

The point probably is your and other people's definition of what "simple math" is and should be...

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