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    Should Well-Educated People Know Math and Science?
    By Michael White | August 6th 2008 05:18 PM | 18 comments | Print | E-mail | Track Comments
    About Michael

    Welcome to Adaptive Complexity, where I write about genomics, systems biology, evolution, and the connection between science and literature,

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    A physics professor, writing in Inside Higher Ed, asks why intellectuals think it's ok to be ignorant of math and science, but not of art, music and literature. When among intellectual company, humanities professors can confess, without a trace of shame, their complete ignorance of science, one of humanity's most important intellectual achievements. But in our culture, a science professor had better not admit to a similar level of ignorance about art or music. This physics professor quotes another blogger to illustrate the phenomenon:
    Is it worth considering that perhaps there are even some smart people who aren’t great at math and/or science?.. [A]re we to force every peg, round or square, into that hole at the expense of forcing students, who may be gifted in other equally important subjects, to drop out after a long series of demoralizing failures?
    To which he replies:
    This is the exact same chippiness I hear from physics majors who are annoyed at having to take liberal arts classes in order to graduate. The only difference is that students seeking to avoid math or science classes can expect to get a sympathetic hearing from much of the academy, where the grousing of physics majors is written off as whining by nerds who badly need to expand their narrow minds.
    I'm sympathetic, but really, there is a difference between math and the humanities. There is a reason, I think, that being literate and appreciative of the fine arts has always been considered an important trait of educated people in general, while being competent in math and science has instead been viewed as the province of whizzes and geeks whose minds are somehow abnormally suited to equations (but not to other social graces) . You don't have to be able to play music or produce art in order to appreciate it. But to appreciate math, and to a lesser extent science, you have to be able to do it. Think about it: there is obviously a huge difference between Art 101 (even when you assume a very rigorous, challenging Art 101) and Algebra 101. You simply can't appreciate math without being able to solve equations. You can look at a work by Rembrant or Cezanne or Marden Hartley and appreciate what it's trying to express, the techniques behind it, the culture context, without being able mix colors yourself, but you can't look at a 3rd order polynomial equation and admire its structure or its significance, without actually being to solve polynomial equations. This is not completely true of science, but unfortunately, science and math have been linked together in cultural circles. While students today who are science majors need lots and lots of math to be successful in today's computer-based scientific world, all other students don't need most of that math - but they do need an appreciation of science. What we need, to change this culture of shameless science ignorance, are more classes designed to teach science to people who will never have to practice it. Scientists might learn from the humanities professors who have to teach complicated subjects, like philosophy, in general ed. classes. This way, humanities students won't be dropping out of science classes "after a long series of demoralizing failures."

    Comments

    Gerhard Adam
    I have to disagree with your general assessment, since to appreciate the arts requires some sense of what it takes to produce the work. This is precisely why so many humanities professors have strange notions of what is important. In my freshman year, I had a humanities professor that was trying to introduce a piece of music to the class by demonstrating the time signature changes in the music. As a musician, I could see that this was complete nonsense, since there weren't any time signature changes at all. The only thing changing was the tempo during each of the intervals. It seems that the only real difference between the humanities versus science/math is that the humanities can be faked since they are almost completely subjective and therefore above scrutiny. The problem with math/science is that you can't just fake it. Students are perpetually assaulted with an individual professor's sense of what is important or legitimate, which is simply an attempt to elevant the humanities to a science of sorts. If it were simply a matter of appreciation, then there wouldn't be a need for "experts" in the field. If my personal appreciation is all that is needed, then why insist on a class? In the end, the only way to appreciate anything is if you actually have a sense of how it works and how to do it. You may not do it well, but without that involvement, its incorrect to suggest that you have any knowledge of it whatsoever.
    Mundus vult decipi
    adaptivecomplexity
    I have to disagree with your general assessment, since to appreciate the arts requires some sense of what it takes to produce the work.

    Maybe it is more a matter of degree. In college I was a music major, and my rigorous Freshman music theory class was every bit as challenging as my first calculus class.

    But when it comes to music, there is an in-between level of education, more than just subjective personal appreciation, but less than full analysis of say, harmonic progression, or use of 12-tone rows, or the form of a piece. You may be able to understand the historical context of a piece of music, the aesthetic aims, and what sonata form is, without being able to actually read a musical score and identify in detail the formal and harmonic elements. I don't think that's really possible with math.

    It is possible, to some degree, with science. You can pick up the bigger concepts without being able to work them out yourself, or apply them in a detailed situation.

    Mike

    Mike
    Gerhard Adam
    Once again, I have to dispute your assessment regarding math. The problem isn't that math requires so much effort, but rather than most teachers (throughout elementary and high school) are so bad at teaching it. As a result, they lack the ability to provide the type of insights you're alluding to and resort to simply generating huge homework assignments which leave students mystified. There are many cases where books have been written to reflect advancements in mathematics ranging from the history of PI, to chaos theory, which are all well within the range of most people's ability if they hadn't been so turned off by math at an early age. Learning the concepts of math and developing an "appreciation" of it doesn't require knowing how to do differential equations any more than appreciating music requires that you be able to orchestrate a piece of music.
    Mundus vult decipi
    adaptivecomplexity
    Gerhard, I apologize for the delayed reply; I've been away from my computer for much of the last 2 days.

    You wrote:

    [Teachers] resort to simply generating huge homework assignments which leave students mystified.

    There are many cases where books have been written to reflect advancements in mathematics ranging from the history of PI, to chaos theory, which are all well within the range of most people's ability if they hadn't been so turned off by math at an early age.

    Maybe this is the problem: even assuming that you have competent teachers, there is a certain level of math that people really do need to master, instead of just appreciate - the math we're all supposed to learn in elementary or middle school. This is enough to turn some people off early, for whatever reason (say, a bad teacher). People who are turned off early put up a mental block that prevents them from being interested in exposure to more advanced concepts like diff. eq., even if they don't have to master them.

    You bring up a good point about popular books on math - I think I would agree then that such math books are effective at developing an appreciation of the concepts - Pi: A Biography (math, obviously) is probably very comparable to The Rest Is Noise (music). We need more general education courses that treat math that way, as opposed to courses that are just a continuation of more math that students need to master.

    Mike

    Mike
    Gerhard Adam
    Thanks for your reply. Consider this scenario ... Let's separate math from arithmetic so we don't confuse the issue. In elementary school we're taught the basic manipulation of numbers called arithmetic. For the sake of argument, let's treat that as a separate subject and consider it the province of elementary school alone. From this point on the student will begin to be exposed to mathematics proper, but let's imagine instead of math, we taught students music in the same fashion. First, we introduce them to a bunch of notes, key signatures, and scales. We make them endlessly do homework that consists of writing out scales (ie: major, diminished, augmented, etc.). Then we throw modes in there, maybe even make them write a piece of music (but never let them hear it). After years of this, we suddenly decide that if they're qualified we'll let them learn an instrument. What do you think the results would be? Instead of spending time teaching algebra and geometry to middle school students. How much better would the time be spent in teaching them the history of math? Giving them a sense of the problems that were addressed and solved? Following through with the development of "pi", or logarithms, or the invention of calculus. All without doing problems, but illustrating and demonstrating concepts. How would the student's attitudes be different? I may be wrong, but I've found that when students are given the time to "appreciate" math, they suddenly discover they no longer have a problem using it. This is why I placed such a burden on the teachers, because if you don't have enthusiasm for your subject and think of creative ways to present it to students ... can we really be surprised when students blow it off as something to be endured?
    Mundus vult decipi
    adaptivecomplexity
    I like the music analogy - it's true that we would never think of teaching students music the way we teach them math.

    Perhaps much of the problem is that we don't conceptually separate arithmetic from the rest - once students learn how to do arithmetic in elementary school, they then move on to the next subject, which is treated in the exact same way, another basic skill that just has to be mastered without the larger picture.

    We teach kids to read in elementary school, and then take that as a given, and move on to a survey of bigger ideas in literature, for example. Maybe we should do the same thing with math - kids should master arithmetic in elementary school, and then move on to learning more than just the mechanics of geometry and algebra later on.

    My favorite example of teaching math is in the Feynman Lectures on Physics - the lectures develop various mathematical ideas, from differential equations to complex numbers, as the need arises, instead of leaving it to a context-less math class. (That's not to say that math classes can't be taught without context, but, as you point out, often they are).

    Mike

    Mike
    Gerhard Adam
    I agree completely. As you well know, when you listen to music one of the things that is such a great experience is when you hear something that completely surprises you and you have to marvel at the musician or composer for having thought of it in the first place. It would be great if we could teach that kind of enthusiasm to students regarding math. I know what thing I've told every student I've ever tutored (and it always makes a difference): Math is a new language which can't be acquired by memorizing any more than reading is achieved by memorizing words. It seems that once they realize that math is a language, they begin to understand that the failure to solve a problem isn't a deficiency of their mental abilities, but simply a failure to understand the "sentence". It opens up a whole range of possibilities then for filling that gap.
    Mundus vult decipi
    adaptivecomplexity
    You've changed my mind about what I originally wrote, regarding doing math and appreciating it. I have read a few popular math books, which I didn't really have in mind when I wrote the post, but those books prove you can convey an appreciation for the concepts without having to be able to solve homework problems.

    I did have one fantastic math teacher, who hit the right combination of bigger concepts and problem-solving skills. I loved his class - and then I went on to major in music...

    Mike

    Mike
    Gerhard Adam
    Well it seems the only thing left to do is to simply revamp the entire educational system in this country. Ah well ... maybe next weekend.
    Mundus vult decipi
    adaptivecomplexity
    It's good that you're not overly ambitious.

    Mike

    Mike
    Jim Myres

    Teachers are the problem

    Gerhard Adam has it exactly right.  I have eight children, unfortunately none of them has ever had a math teacher that enjoyed the subject they were teaching.

    My thoughts - there is an solution to this problem in mathematics:

    Assume:
    Let us assume that one Science/Math student  is equivalent to one Humanities student 

    Let:
    Science/Math student be represented by “x”
    Humanities student be represented by “y”

    Then:
    x = y

    If this is true, as we assume, then we can multiply both sides by “y” because what you do to one side of an equation you have to do to the other.

    xy = y(to the second power (y∧2))

    For lack of something better to do why not subtract x∧2 from each side.

    xy - x ∧2 = y ∧2 - x ∧2

    Now this is too big, so just factor both sides.

    x(y - x) = (y + x)(y - x)

    Still too big so divide both sides by (y - x)

    x = y + x

    Conclusion:
    This proves that one Science/Math student is equivalent to one other Science/Math student and at least one Humanities student.

    This is about as simple as math gets, if you are a Science/Math person it will be obvious to you what the problem is here.  If you are a Humanities person and don't see the flaw in this math you probably bought Enron stock.

    adaptivecomplexity
    Jim, you crack me up. That's great!!

    Mike

    Mike
    Gerhard Adam is right when he says that the humanities can be faked, but wrong in assuming that science can't. Bad teaching and bad scholarship exist in all subjects. Real humanities work is just as rigorous as real science, I know that from having both ends in my research career. And there are plenty of professors out there who fake the sciences and math, too. I've been taught by some of them.

    I think there is a problem in how and why we teach science and math. Most of the time it has an outcome. It serves a purpose, but that's always someone else's purpose. It makes money. We don't make appreciation or self-elevation our main goals. It's always "You can use this to build bridges or cure cancer". In other words, you can use this as a tool, because I'm teaching it as nothing but a tool, and I have no motivation except to train you into a tool for someone else to use, just like I'm a tool for whoever runs this institution and makes up the curriculum.

    If science and math were taught for their own value, like art history, maybe they would be recognized as culture, not just as servile tools for some engineer or technologist to use for something that really matters.

    And, frankly, you can't get everything out of a painting with no prior knowledge. Just like you can't get everything out of nature. You go in with what tools you have, and in art history, most newcomers have already mastered enough basic tools to get started. That's where science runs into trouble. Hardly anyone masters those basic tools in grade school and high school, and they're just taught as tools to help you do your shopping and operate your bank account, not as part of being a human being. I think that's also why so many big-name intellectuals focus on art and music in culture. It's because they don't know how to look at nature. They never mastered the basics in grade school.

    Gerhard Adam
    "We don't make appreciation or self-elevation our main goals. It's always "You can use this to build bridges or cure cancer". In other words, you can use this as a tool, because I'm teaching it as nothing but a tool, and I have no motivation except to train you into a tool for someone else to use, just like I'm a tool for whoever runs this institution and makes up the curriculum."

    I'm not sure what other purpose teaching has.  I'm going to step out on a radical limb here, but it seems that the whole point of the education system is to produce "useful" individuals.  It is obvious that one can't create genius, or aptitude, or curiosity.  While exposure to various topics may certainly allow a student to connect at one of those levels, that is hardly the overall purpose of education.

    The simple reality is that whether it be an art/music school or a science class, the vast majority of people passing through will never be more than average.  It isn't likely that someone will produce a Da Vinci, Mozart,  or an Einstein by the educational process.

    I agree that it is the "appreciation" element which is sorely needed in most people, but I don't believe this is something that an educational system can produce.  I would argue that without this desire or interest being sparked by parents, I don't see how much of this would change at all.
    Mundus vult decipi
    Stellare
    Well-educated people should know math and science. I have mentioned this on several occasions earlier, that it causes a problem for our society as a whole that it is even fashionable to be ignorant of these topics while the modern world is founded on its principles and applications.

    And, come on, math and science isn't that hard to learn. Who came up with that idea in the first place? :-)
    Bente Lilja Bye is the author of Lilja - A bouquet of stories about the Earth
    Not only the modern world, but every societies of the World know mathematics since the earliest times. That is natural. Even... mammals like dogs ans wolves know to count. That is approximate, but wolves can estimate the number of members of another pack , hidden by a wood, only by the number of howls... ( I heard it on Radio France Internationale ).

    The primitive tribes also use maths and parts of their bodies to represent number. Over 10... all is approximate.

    And what about ancient people who built temples and roads ? and what about Hipparque (190-120 av JC) and Ptolemy (90-168 ) who try to represent the Earth on maps ?

    Also, for contradicting Michael, I will say that arts need mathematics and sciences to be realized... ( May be to follow)...

    Basic math + basic science= general knowledge. History too for that matter. Thanks for this blog.

    Dubious Virtue
    "You can look at a work by Rembrant or Cezanne or Marden Hartley and appreciate what it's trying to express, the techniques behind it, the culture context, without being able mix colors yourself, but you can't look at a 3rd order polynomial equation and admire its structure or its significance, without actually being to solve polynomial equations."

    What about a Ingre or David or 12th century alter piece? Without understanding the symbolic language of the artwork you miss out on the significance of the work.

    I suspect my appreciation of science is similar to yours of art ;]