On math

Please excuse this non-anime article.

A New York Times article has been making the rounds on the Internet recently.  In it, a retired professor of political science says that algebra should not be taught in schools, and that math in general has very few real-world applications.  He goes on to say that knowledge of math is used as a deciding factor in otherwise un-mathy environments (college applications, for example), and that this bars brilliant people from achieving their full potential.

These arguments hinge on two key claims:

  1. Math in school is useless.
  2. Math is not a good measure of intelligence (brilliance, etc.).

As I said on twitter,

Come September, I’m going to be a third year in college.  I’ve only just entered the world of upper division physics, so I haven’t had the decades of experience others might have.  But even I know that math is not useless.

Firstly, the more minor reason: math inspires.  Science is the single most important field of study in all of human history, to the point where we equate knowledge with science.  And to just imagine somebody proposing we cut out the very foundation of science from education… it’s infuriating.

Math is a subject that makes children interested in STEM-related fields.  And if not that, it’s an Honest-to-God prerequisite for everything in science.  Biology, medicine, physics, chemistry, engineering, computer science, and more.  Without algebra (or calculus), students would be denied the opportunity to move into these fields.  And in the middle of a technological revolution, these jobs represent the future of white-collar employment.

Secondly, subjects like math and science give students invaluable tools to handle all sorts of problems in life.  This ranks up there on the list of overused cliches, but it’s really true.  The mathematics/science courses I took in middle school and high school were:

  • Algebra 1 and 2
  • Geometry
  • Calculus
  • Statistics
  • Physics
  • Chemistry
  • Biology

Now let’s omit the extra courses I took, since I ended up majoring in physics.  The required courses to graduate from high school were:

  • Algebra 1 and 2
  • Geometry
  • Chemistry or Physics
  • Biology

Algebra covers things like equation solving, polynomials, trigonometry, systems of equations, everything Excel can do, exponents and logarithms, and more.  Geometry covers the laws of basic shapes, with a focus on circles.  It also has a lot of table-ish proofs, or at least my class did.  Biology is the study of living things, and Chemistry is the study of atoms, molecules, elements, compounds, and the interactions between them.  Physics is a very broad term, the science of matter itself.  In high school, mechanics (and sometimes electromagnetism) is taught, and this focuses on the laws governing motion of macroscopic objects.

Okay, flomu, what’s your point?

What do all of these subjects have in common?

Yes, it’s their structure.  There’s a well known term called the “scientific method” that generally refers to objective techniques for conducting scientific research and experiments.  This is similarly reflected in mathematics, where proofs and conjectures serve a similar purpose.  These are in stark contrast to subjects like Literature, English, etc., where persuasion is more important than documentation.

Learning this structure allows students to view the world from an objective viewpoint.  First, set up a hypothesis.  Next, test to see if it’s true.  If your results contradict your hypothesis or previous results, then something is up.  Now apply this to the real world.  Presidential elections.  Your friend’s stories.  A New York Times article.  This is a format that is completely different from the ideas of “voice” and “audience” that we all learned in English class, but is very complementary.

The goal of education is to create a well-rounded society, capable of thinking critically and weighing facts against opinions.  Classes like English and History allow students to voice their own opinions on matters, whether it be in a class discussion or in a term paper.  These subjects nurture students’ voices, helping them develop into people who can speak their mind and do it in a coherent way.

On the other hand, Math and Science classes force students to learn the system and abide by the system.  This kind of iron fisted objectivity helps students see the difference between fact and opinion.  It allows students to stop and think back to the basic axioms that they believe in, and derive their own result from there.  This ensures that whatever comes out of a student’s mouth isn’t garbage, that they have mulled over their opinion before shouting it out.

Thirdly, let me fight a dumb article’s opinion with my own dumb argument: What would you replace math with?  There is nothing that could take its place.  You want science courses?  Oh, you don’t know algebra?  Too bad.  You want more down-to-earth math courses?  Too bad.  You need algebra to understand the very basics of Statistics.

So what are we left with?  English, Foreign Language, and Physical Education.

Mankind has declined.

10 Comments on “On math”

  1. Trollkastel says:

    Math created philosophy. Descartes, Plato, Wittgenstein — they all owe everything to the discipline of mathematics. It is a system of logic, a way to argue for one’s beliefs.

    To destroy math is to destroy philosophy. And therefore, destroying every hint of civilization.

    Clearly, we are going headfirst into the apocalyptic setting of Jinrui wa Suitai Shimashita.

    • flomu says:

      I don’t know if I’d go that far, but it’s definitely intertwined with things like logic and philosophy. The methods used there are very similar.

      On Twitter, Numberss_ suggested that Logic and Philosophy should have a larger role in education. While I can’t argue with that, it’s definitely not a replacement for Math, which has so many more practical applications in addition to teaching students the “system of logic.”

  2. CorbanSaezer says:

    Math is important for people who:

    1. Want to compare mortgages and living expenses
    2. Want to know whether to spend more money to reduce a miniscale risk
    3. Plan large anime convention groups, and need to divide expenses

    Those who have no need of these things don’t need math, but they also don’t sound very ambitious.

    • flomu says:

      4. Splitting the bill at a restaurant.

      That seems to be a very large point of concern among me and my college friends (even though we’re all math/science majors…).

      But yes, sometimes everyday things like keeping track of payments requires algebra, not just arithmetic. Math isn’t absolutely necessary for people to live their lives, but it does allow them to live more fulfilling ones.

      Including going to anime conventions.

  3. Taka says:

    I just took Multi-variable calc and found myself wishing they’d focused more on multivariable stuff in earlier classes. Hell at least introduce the three dimensional plane and talk about some basic vector equations.

    • flomu says:

      The split between Calculus and Multi-variable is definitely messy, but necessary. Trying to visualize things like curl is so much harder than visualizing Riemann sums. And trying to find a tangible example for something like Stokes’ Theorem… ugh. There’s a large psychological barrier there, I think.

      It’s much like the leap in physics from down-to-earth Mechanics to abstract E&M.

  4. Mushyrulez says:

    Higher-level math/science is great. But I hope you haven’t forgotten what high school science was like, yet.

    At least where I’m at, everything we learn in lower-level high school math/science classes are straight from the book. There’s no exploration, no room for creativity, nothing but memorization of formulas and tables in math to prepare for some stupid provincial exam.

    “Sure,” you might say, “That’s because math doesn’t need creativity as their foundation. Besides, this is all in preparation for higher-level scientific fields, where a solid foundation is mandatory!”

    Yes, that is true.

    But how many students enter science/math in university? In fact (actually, this isn’t a fact, it’s a question), how many students even manage to graduate high school? I even ask my parents, accountants (who manipulate numbers on a daily basis) simple things like calculating the height of a mountain 20 kilometres away at an angle of 5 degrees and they don’t know what function to use. That’s not even calculus, that’s basic trigonometry, which they haven’t used for so many years in their life that they’ve absolutely forgotten how to use it.

    And lower-level high school science is even worse. Instead of teaching us to test data rigorously, of the benefits of repeated experimentation, or even of objectivity, lower-level high school science tells us to memorize these facts stated on this textbook and regurgitate it on a test.

    Isn’t that the exact opposite of science? Furthermore, the facts we learn can’t possibly serve as any foundation, either, since we don’t get Biology/Chemistry/Physics streams until grade 10.

    It’s not about university math/science. It’s about high school math/science, things that are taught so perversely that they not only DISSUADE prospective math/science majors from pursuing their interest but also ruin the very basis of the scientific method by their ‘believe-what-the-textbook-says-because-it’s-always-correct’ methodology.

    There is an alternative. In fact, there are dozens of alternatives by making math electives and not mandatory, as well as by focusing on practical, real-life examples in (mandatory) arithmetic classes and focusing on the proper use of the scientific method to give people the means of objectively viewing the world – on their own. Not only would this root out the students who would rather (and actually do) skip math courses, but would also encourage greater creativity, independence, and ultimately [insert something here I’m too lazy to continue writing please don’t respond to this comment]

    • flomu says:

      The fact is: it’s hard to teach math. Algebra, especially. Arithmetic is easy to link to real-world situations (what is your wallet minus the price of this meal, etc.), but algebra is more subtle. What’s the point of learning trigonometry or geometry or plotting quadratic functions? I’m not quite sure I can give a satisfactory answer to that, besides “wait and see.”

      And unfortunately, there’s no way around algebra to get into Biology, Chemistry, or (especially) Physics. Introductory science courses like the ones you describe are more or less fact regurgitation for higher level courses. The hope there is that once you get into the specialized Biology and Chemistry classes, you’ll remember some facts so you aren’t distracted from the real science.

      It’s about high school math/science, things that are taught so perversely that they not only DISSUADE prospective math/science majors from pursuing their interest but also ruin the very basis of the scientific method by their ‘believe-what-the-textbook-says-because-it’s-always-correct’ methodology.

      The problem isn’t the science itself – it’s how it is taught. You can always teach by following the textbook and you can teach with lots of demos. Neither gives students a good understanding of science, nor do they excite students. There are equations behind every demonstration, and a teacher needs to be engaging and able to explain the science behind each step without getting too technical or too simple. And that is damn hard to do – much harder than lecturing at the college level, where everybody already has a background in math and science built from years of boring high school education.

      In my own experience, I went into a science field because I didn’t like writing essays. But after I got to college, I realized how valuable the classes I’d taken in high school actually were. For example, my college probability and statistics course went far, far beyond what I’d done in high school AP Statistics, even though the content is supposed to be similar/identical. We delved into the reasoning behind each method, using a combination of graphics, equations, and examples to keep interest up.

      And even for somebody who’s not going into a science-related field, math and science are invaluable. I described how the scientific method was worth learning in my main post above. And in addition, a basic knowledge of biology, chemistry, and physics is absolutely required to prevent perpetual ignorance. We can’t have a society where scientists are making groundbreaking discoveries and the populace just doesn’t care or understand. Or even worse, a society where the masses go against science, ignorantly citing opinions against proven facts and evidence.

      There is an alternative. In fact, there are dozens of alternatives by making math electives and not mandatory, as well as by focusing on practical, real-life examples in (mandatory) arithmetic classes and focusing on the proper use of the scientific method to give people the means of objectively viewing the world – on their own.

      So to get rid of standard math classes in favor of electives would be a terrible idea. People who aren’t exposed to math just won’t take math classes so there has to be a degree of tough love. While the system is broken in terms of bad teaching, students still /need/ to take math classes, if not only to prevent themselves from making stupid comments later in life.

      • Mushyrulez says:

        There is no way to get around algebra to get into advanced science, but people who aren’t interested in science in the slightest hardly need to go through algebra to get to somewhere they’re not going, right?

        A basic knowledge of chemistry, biology, and physics is definitely invaluable: and so is a basic knowledge of grammar, history, literature, physical health, cooking, psychology, law, French, woodworking, photography, etc. (What if you don’t know the inner workings of a cell? What if you don’t know the rate of deceleration due to friction? What if you don’t know how to cook simple pasta e fagioli? What if you don’t know how to perform CPR? What if you don’t know how to assemble a table?)

        The last paragraph can be substituted with any of those courses with similar meanings. Sure, math is definitely more important than most of them as a foundation for advanced studies, but in everyday life, I daresay even psychology is more important.

        But a clarification before the end: math is great. Math is awesome. The world would be a much better place if everybody understood even high school level math and applied objective reasoning with the scientific method in everyday life. But the way we teach it is definitely stupid, and as that article says, I still believe that we must make post-arithmetic math and all of high school science an elective to encourage critical thinking and destroy the misconception that math is difficult and boring.

        P.S. ‘It’s too hard’ has never been an excuse for anybody to not teach right.

        P.P.S. ‘It’s too hard’ is a valid excuse for the lack of posts on O-New recently

        P.P.P.S. ‘It’s too hard’ is not what a girl would say to me ever because nobody likes me

      • flomu says:

        I don’t want to put it like this, but… basically, science is more important than subjects like photography and woodworking. Thus, everybody is required to study it. To be a member of an educated society, a student needs to learn about at least math and science. This helps them understand the basics of scientific discoveries instead of having to Google what a cell is or what Newton discovered.

        This is all covered in a term called scientific literacy. And the name really fits. Because mankind as a race is getting more and more technologically advanced, we must require a certain level of scientific understanding from your everyday citizen. You don’t want normal people singing songs like this ( http://knowyourmeme.com/memes/fcking-magnets-how-do-they-work ) and then believing them too.

        So the point is that while an English major may never use physics when writing a news article, he or she is required to know a degree of math and science to function in the world. Scientific literacy doesn’t have as drastic an impact as regular literacy, but it is necessary to understand a news story or how your television works. I mean, you can’t just Google something like that and expect to understand everything from the Wikipedia article without any prior background in science.

        Another point I need to emphasize is: if we take out high school math as a required course, then all of the science courses should also become electives. Then we’d all be taking nothing but electives, English, and History. In that kind of environment, trying to “destroy the misconception that math is difficult and boring” would be even harder…

        but yeah math is awesome

        physics too. e=mc^2

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