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In almost all countries all over the world, mathematics is a main subject in school. Maybe the subject bringing trouble to families with kids.

It is clear that scientist, engineers, etc. need mathematics as a part of their higher education at colleges. This is maybe the biggest argument (Since after finishing school everybody should be able to study whatever he or she wants, they have to know some basic mathematics). But there are also many subjects unrelated to mathematics (law, language studies, etc.) and young people heading to such subjects (being bad in mathematics) are frustrated.

What are the arguments I can give to a school kid, to his parents or general to anyone why mathematics is so important - apart from the above argument?

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  • $\begingroup$ I had a similar feeling during writing (and by selecting appropriate tags). However, I think that this is a very interesting question a lot of people have to cope with. $\endgroup$ – Markus Klein Mar 14 '14 at 19:49
  • $\begingroup$ This question should be a community-wiki. $\endgroup$ – Ittay Weiss Mar 14 '14 at 23:06
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    $\begingroup$ The title question is arguably too broad, but I believe the actual question in the text, "What are the arguments I can give to a school kid...why mathematics is so important," is a specific enough question to warrant not being put on hold. $\endgroup$ – jpd527 Mar 17 '14 at 4:29
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    $\begingroup$ You never hear this question asked in art class (not by students, anyway). You know why? Because they're enjoying the art class. I think the most fundamental cure is to teach in a way that the student has fun in the class - then it becomes a moot point. Of course, that's very easy to say from the comfort of my armchair. $\endgroup$ – Jack M Apr 22 '14 at 12:36
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    $\begingroup$ See the July Edit to my answer at MESE 8052 and, in particular, the link to: Is Math Important? (with panelists Jo Boaler, Jordan Ellenberg, and Steven Strogatz, among others). $\endgroup$ – Benjamin Dickman Jul 10 '15 at 18:07
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I really like this answer given by John Green:

https://www.youtube.com/watch?v=x78PnPd-V-A

"School is not about you! School does not exist for your benefit or for the benefit of your parents. Schools exist for the benefit of me. The reason why I pay taxes for schools even though I don’t have a kid in school is that I am better off in a well-educated world. Public education isn’t a charity project; I pay for your schools because I want you to grow up and make my life better. I want you to make me beautiful books that will bring me pleasure and consolation; I want you to make me cooler cars for me to drive in, drugs so I can live a longer, healthier life. I’m paying for your education in the hopes that you invent a microwave pizza with actually crispy crust and that you’ll spread the availability of the internet so I can get more youtube views in Zambia. Your education isn’t just about you; your nation is making an investment in you because they believe that you are worth it."

To that I'd add, the world is a better place when people understand each other, and understand the full scope of humanity. I want to live in a world not only of mathematicians and engineers, but one where the poets and the journalists and the waiters and the doctors and the nurses and the truck drivers value and understand mathematicians. (And writers. And historians. And construction workers. And etc.)

Kurt Vonnegut said that we need more writers who were trained as engineers, and that's exactly right because we need fewer things keeping us from empathizing with each other.

One more thing: if you're looking at human progress, it's easy to look at the extremes, the Newtons, the Eulers, the Shakespeares, the Twains, and yes, those people obviously helped progress humanity. But human progress doesn't primarily come from geniuses and the famous -- it couldn't, because there are so few geniuses and so many nots. Real, sustainable human progress comes from the broad swath of humanity that is just trying to learn and appreciate the ideas of others. When we learn we are committing a creative act as important and vital to humanity as Einstein's accomplishments. Without us, where would Einstein be?

If we understand an idea or a perspective, we have the ability to pass it on to others. Sometimes that passing on happens formally -- you're trying to teach something -- but just as often it happens informally. You talk about an idea and someone happens to over hear it, they run off and think it themselves. You raise a kid and accidentally make them smarter than you were.

For better or worse, ideas spread. It's our job to fill our head with as many good ideas as possible so that we spread the right ones.

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    $\begingroup$ I feel that this is an argument for why we have schools and why we teach maths, not a reason for why we teach you maths. $\endgroup$ – user1729 Mar 20 '14 at 10:05
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From "What is Mathematics For?" by Underwood Dudley (Notices of the AMS, vol. 57, no. 5, May 2010):

So that there is no confusion, let me say that by “mathematics” I mean algebra, trigonometry, calculus, linear algebra, and so on: all those subjects beyond arithmetic. There is no question about what arithmetic is for or why it is supported. Society cannot proceed without it. Addition, subtraction, multiplication, division, percentages: though not all citizens can deal fluently with all of them, we make the assumption that they can when necessary. Those who cannot are sometimes at a disadvantage.

Algebra, though, is another matter. Almost all citizens can and do get through life very well without it, after their schooling is over. [...]

Jobs do not require algebra. [...]

Even those who are not burdened with the error that algebra is necessary to hold many jobs support the teaching of algebra. Everyone supports the teaching of algebra. The public wants more mathematics taught, to more students. The requirements keep going up, never down. The reason for this, I am convinced, is that the public knows, or senses, that mathematics develops the power to reason. It shows, better than any other subject, how reason can lead to truth. Of course, other sciences exhibit the power of reason, but there’s all that overhead—ferrous and ferric, dynes and ergs—that has to be dealt with. In mathematics, there is nothing standing between the problem and the reasoning.

Economists reason as well, but sometimes two economists reason to two different conclusions. Philosophers reason, but never come to any conclusion. In mathematics problems can be solved, using reason, and the solutions can be checked and shown to be correct. Reasoning needs to be learned, and mathematics is the best way to learn it.

[...]

What mathematics education is for is not for jobs. It is to teach the race to reason. It does not, heaven knows, always succeed, but it is the best method that we have. It is not the only road to the goal, but there is none better. [...]

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What goes into the school curriculum is to a huge extent a political decision backed by ever-changing research 'evidence' pointing here today and there tomorrow.

What goes into the math curriculum is like-wise supported by 'evidence' about the superiority of this or that technique, that piece of mathematics or the other. It is to a huge extent random.

So, there are (at least) two questions here. What does one gain from the discipline of mathematics, and what does one learn from the specific topics covered. I'll address only the latter.

Typical off-the-shelf answers seem to be: learning mathematics will enhance your problem solving abilities and your logical thinking. Who doesn't want to be a better problem solving and logical thinker? The problem is there seems to be little evidence to support these claims.

So, looking at the evidence, the best reason to learn mathematics is that if you are good at it, it impresses people. And when people are impressed by you, they tend to give you better jobs with more money. Of course, some may argue that an even better reason to learn mathematics is if you like it.

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    $\begingroup$ Exactly the reasons put forward to teach Latin and Greek... ;-) $\endgroup$ – vonbrand Mar 16 '14 at 16:36
  • $\begingroup$ @vonbrand: Yes, but skill at Latin and Greek no longer causes people to give you better jobs with more money, at least not often. It worked better in the U.S. in the 19th century. $\endgroup$ – user173 Mar 20 '14 at 19:04
  • $\begingroup$ @MattF., while "getting a better-paying job in the current society" is certainly a worthwhile goal, we are trying to find out if it is useful in itself, not as a means to an end. My guess is that the time devoted to math (or greek, or whatever other "teaches how to think" subject comes along) would be more fuitfully used to "teach how to think" in the area where said thinking is to be applied. $\endgroup$ – vonbrand Mar 20 '14 at 19:14
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    $\begingroup$ @vonbrand: here's a quote from Stefan Banach (from my memory): Mathematics is too sharp a tool to be given to children. If one wants to teach them logical thinking, teach them Latin instead. $\endgroup$ – mbork May 11 '14 at 17:35
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    $\begingroup$ @vonbrand: so I guess I won't convince you... I love Latin grammar, and (as I said) German comes close. And in case of "school" maths, most students also don't see the point. Frankly speaking, me neither: if we want to teach logical thinking (and perseverance, and being systematic, and perhaps other things), we might as well teach them chess & bridge (even though I strongly dislike those games...) instead of maths. Or, to be less controversial, say, graph theory instead of (pre)calculus. $\endgroup$ – mbork May 13 '14 at 6:55
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Because math helps rewire your brain. Most people wont become scientists or engineers, but the part of the brain math helps exercise is the piece that works on problem solving. One can claim that it's a rare job that never needs to solve any kind of problem at all. The school years of exercising that part of the brain will help the adult in whatever they wind up doing.

If math classes are structured so the students have group time for solving, this time isn't all about math, per se, but about the skills needed to function in any group doing any job.

Update - The article must have been a paper one I can't find, not one I tagged or bookmarked. In the interest of keeping an open mind, an article supporting a somewhat opposite view - Is Algebra Necessary?

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    $\begingroup$ I have never been able to find evidence for this claim. Does anybody have a link to a study or experiment that validates the idea that knowing math helps you in non-math areas? $\endgroup$ – Michael Pershan Mar 14 '14 at 20:33
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    $\begingroup$ I think I'm permitted to edit, post-close. I tagged an article suggesting this, not a blog post but scientific article. Will search for it this evening. I'm open to it being unproven. And I'm open to it being an unrelated high correlation, i.e. High problem solving people happen to be good math students, but studying math didn't make them so. Something conclusive would be great. The article I read was persuasive enough. $\endgroup$ – JTP - Apologise to Monica Mar 14 '14 at 20:40
  • $\begingroup$ @JoeTaxpayer, "high correlation" is not "causation," sadly. And I believe your reference hits it head-on. Probably much the same can be said about almost any subject included in the curriculum... $\endgroup$ – vonbrand Mar 16 '14 at 16:44
  • $\begingroup$ My first DV received here. Long after I'm dead, the data will prove my assertions correct. $\endgroup$ – JTP - Apologise to Monica Mar 25 '14 at 20:04
  • $\begingroup$ @JoeTaxpayer - To quote Clarence Comstock in his 1905 address to the NEA: "We begin to learn that the real worth of mathematical study is not the general training of the mind but the training of the mind in mathematical thought to the end that our ignorance of the phenomena about us may be lessened and our impotence in the face of the forces which surround us may be reduced." - page 791. He delivered this address as the "mental discipline" justification for mathematics in the curriculum was increasingly losing credibility. $\endgroup$ – JPBurke Apr 22 '14 at 13:04
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Mathematics is the language of number, pattern, and form. In our society that depends so heavily on technology and inventions, every educated person needs to be able to read and understand that language. Advanced studies in every field of knowledge, from history to politics to language to business depend heavily on mathematics. Not knowing mathematics limits what you can study and learn.

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Mathematics is an enormously powerful cultural achievement that (generally speaking) expands our ability to see the world and to act in the world. Mathematics education is our time-consuming effort to welcome you, the individual, into this culture.

It's not a passive effort, and it doesn't happen all at once. You have to engage with the world of mathematics, and you will do so gradually as you gain the ability to mathematize in the world (the ability to use math in how you see and think about your world).

Sidebar:

Take, for example, knowledge of ratios and proportionality. Assuming you already know some arithmetic, you can learn to read a word problem so that you place three numbers this way:

2/3 = ?/12

And you can use arithmetic to find the missing value. But people who have an understanding of ratios and proportion don't see this problem the same way. Those people see a relationship between two quantities becoming a property or quantity in itself (in mathematics, we call this an extrinsic property or quantity). In appropriate situations, this becomes a powerful thing to know. It's related to rate, and it can be used to think about and compare proportional situations in many contexts.

It's the difference between being able to follow instructions and just mix the ingredients of lemonade together so that you get the recipe right vs. thinking mathematically about how the ingredients come together to create the flavor of the lemonade.

When your view of the world changes it's as if you can see things that were invisible to you before. And once you can see things, you can make decisions based on them. Imagine being in big room in the dark, and the room is full of big obstacles. You want to move around, but you have to stumble around, feel your way around obstacles slowly, be careful not to trip. You can make progress moving around, but it seems pointless.

Now, turn the lights on. Not only can you see where the obstacles are, but you can see the opposite wall of the room, and doors. You can choose to walk directly toward them -- that's a goal you weren't even aware of before. Seeing the objects in the room didn't just allow you to move around more quickly; you can now move with purpose. There's a point to it.

Here's the most important thing: as the knowledge becomes your own, you are the one who answers the question what is the point of learning this mathematics? Math educators can only help turn the lights on. The rest is really up to you and what you want to do.

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I personally feel that this question, as posed, is a bit of an oxymoron.

But there are also many subjects unrelated to mathematics (law, language studies, etc.) and young people heading to such subjects (being bad in mathematics) are frustrated.

Is this not understandable? I, as a student, was heading from the start to mathematics. This meant that I was frustrated by nearly everything else: speeches on making apple pie, tests on government, 5-paragraph essays with lots of transitions, ...

There is no possible justification to give a student who knows they will never use math in their real life. And in fact, most people do not. Many of the most influential people in the world - politicians, lawyers, business people, artists - will never touch a single equation once they leave school.

The fact is that mathematics is not so important! It is important to those who love it and use it, to people like me. But the same goes for everything else - History is vastly important to those who use it, but not to people like me who would rather not read another history book for the remainder of our existence.

The worst possible choice would be to give them terrible reasons as to why they will need mathematics someday. Students are intelligent enough to know that is not true. You should just tell them that working hard and pushing themselves to complete tasks which may not be to their liking, are good life skills to have. But you should also encourage them to pursue what they love, no matter what anyone tells them.

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