Dismiss Notice
Join Physics Forums Today!
The friendliest, high quality science and math community on the planet! Everyone who loves science is here!

Mathematics = Arithmetic

  1. Jan 15, 2007 #1
    The problems with mathematics education cannot be fixed untill the general public stops using these terms synonymously. Today the news (Good Morning America - ABC) reported an autistic savant who, although he is mentally disabled in many ways, could "solve complex mathematics". I was very interested untill I saw that "solving complex mathematics" meant to this network news outlet "multiplying large numbers mentally"!

    Mathematics is the science of theorems. It is true that some theorems pertain to arithmetic, but this does not mean that arithmetic (the basics of which everyone agrees that everyone should learn) should be considered as part of mathematics any more so then writing is considered part of mathematics.

    Arithmetic (including U.S pre-algebra) should be made its own subject, beginning and ending in elementary school, with no mention of mathematics being made (since the students are not doing any).

    Synthetic and Analytic geometry, trigonometry and general precalculus should all be put under the heading "Computer Science", since that is exactly where the domain of application for these things begins and ends. By getting students to write a program to draw a circle we address their lack of motivation and sense of perceived uselessness of the material.

    Calculus belongs to Physics, these subjects should be studied together as old classics for the same reason that literature is studied.

    English should be correctly labeled "Literature and Creative Fiction", and rhetoric (as a means of persuasion) should be ridiculed.

    All mention of critical thinking, expository writing (clarity of communication) and reasoning(logic) belongs to mathematics. Mathematical Calculation should take on the generalized meaning of writing out ideas clearly and carefully so as to infer conclusions.

    In my opinion these things have not happened because:

    1) The English department has too much power, and they don't want to lose their monopoly on "writing" (which belongs to math at least as much as does arithmetic).

    2) The computer science department enjoys not being associated with algebra/precalculus, because they receive more funding and more students. Very few freshmen going into computer science realize they will be doing more of what they think of as math (precalculus) then will be the freshmen going in to mathematics.
     
  2. jcsd
  3. Jan 15, 2007 #2

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    You're either joking, or, well, being deliberately provocative for no good reason, right?

    Same comment applies.
     
  4. Jan 15, 2007 #3

    Math Is Hard

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    You'd better keep it down... English professors could be reading this right now and reporting back to their departments. Make too much noise, and they'll send some of the boys around to take care of you. :wink:
     
    Last edited: Jan 15, 2007
  5. Jan 15, 2007 #4

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    I'm going to take a deep breath, a strong drink, and not say a word!

    I've already gotten into trouble for repeatedly pointing out that mathematics is not physics!
     
  6. Jan 15, 2007 #5
    It seems that some of what I said is objectionable, and I would like you all to make your objections clear, so that I can address them. I stand by everything I said, I am not trolling (but I am proud of that I drove Ivy to drink :).

    Does something in my post suggest that I think mathematics is physics?

    In fact, I advocate seperating the two properly, that is by including the method of basic physics (freshman calculus) under the label "physics", so as not to confuse it with mathematics, the science of theorems.

    I think that finding an antiderivative relates more closely, in concept and appplication, to finding the force/charge/mass etc. than to showing that a function is integrable if it is bounded and continuous. The former is arithmetic (studied for application), the latter is mathematics (studied for aesthetics).

    Edit: Matt - I guess I could have said "direct domain of application", but I still think what I said was true and implore to share your reasons for disagreeing.
     
    Last edited: Jan 15, 2007
  7. Jan 15, 2007 #6

    DaveC426913

    User Avatar
    Gold Member

    Actually, I was going to say the problems with mathematics cannot be fixed until people stop looking to Good Morning America for their education.

    Wait. They don't. :biggrin:
     
    Last edited: Jan 15, 2007
  8. Jan 15, 2007 #7

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    You have said that you only wish for mathematics with application to the real world to be taught, and only in the context of its application to the real world. If you truly believe in what you said, that geometry should be taught only in computer science, because that is its only application, then you're missing the point of mathematics, not to mention seemingly being ignorant of some of its uses. Calculus (whatever you mean by it) certainly does not belong 'to physics', either as a subject in its own right, or as a subject to study for its own merits.

    You complain that people are stereotyping mathematics unfairly as mere arithmetic, then go and make the same mistake yourself.
     
  9. Jan 15, 2007 #8

    JasonRox

    User Avatar
    Homework Helper
    Gold Member

    Well said, and I'm quoting it to be said again.
     
  10. Jan 15, 2007 #9
    Ah, a typical forum misread.

    In my post when I say "no mention of mathematics", I am refering to (in the sentence) elementary school. Obviously, if we are to seperate mathematics and arithmetic, then we much teach arithmetic without making mention of mathematics! The kids in elementary school aren't ready to think they are doing math! Then they don't respect it!

    Later I bring up mathematics as the science of theorems, teaching students to think, write and reason clearly as well as to read other's writings with depth. This subject is central (as English is now) to all students. This kind of (true) mathematics should be required and the "applications" math track be relegated to the Accounting/CS/Physics electives.
     
    Last edited: Jan 15, 2007
  11. Jan 15, 2007 #10
    I kinda agree with this. :approve:

    But, does that mean Applied Mathematics is not mathematics and should be thrown out of math departments worldwide? :grumpy: I think we need to strike the balance between pure and applied, and make it clear to the students that they need to have a fair amount of exposure to both to get a good appreciation of mathematics. Over concentration in either extreme is not a good idea.

    I dread math books with tonnes of applications and calculations with formulas pop up from nowhere without proper proofs or at least the sketch of the ideas behind the theorems. But that is not to say that we completely ignore teaching applications to students and let the other department do the job.
     
  12. Jan 15, 2007 #11
    Take a slice of a calculus class: a cs major, a bio major, an econ major, a phys major and a math major.

    The problem comes when we force these people to study calculus from each other's intended realm of application. For the science majors, this leads to a dislike of math, and for the math majors it leads to a dislike of applications.

    That makes the case for not studying applications in the math department (i.e. students elect to take the applications they are interested in at the departments they are interested in). But I propose something stronger: that calculus (of real functions of a single real variable) no more belongs to the math department than to any of the others! They should all teach their own brand of calculus tailored to be relevant an interesting to their students, then people wouldn't dislike math so much.

    Now the guards will call me away for taking on the calculus cash cow :smile:
     
  13. Jan 16, 2007 #12
    ill say what feynman said: physics is to maths what sex is to masturbation :)
     
  14. Jan 16, 2007 #13
    but feynman was a physicist. he is supposed to be biased towards physics. :)
     
  15. Jan 16, 2007 #14

    Gib Z

    User Avatar
    Homework Helper

    Richard Feynman was an excellent physicist, and if he wasn't he would have been an excellent Number Theorist. One of the most profound people to ever live. But I would reverse that quote.
     
  16. Jan 16, 2007 #15

    HallsofIvy

    User Avatar
    Staff Emeritus
    Science Advisor

    You said "Calculus belongs to Physics". Are you unaware that calculus is used in Biology, Economics, Meteorology, etc., etc.?
     
  17. Jan 16, 2007 #16
    Here is what I said three posts above this:

    And then I argue that calculus is no more a part of mathematics (mathematicians use it as a topic about which to prove theorems) then it (calculus) is a part of physics, bio, econ, meteorology, geology etc.
     
  18. Jan 16, 2007 #17
    That's right! Also, writing shouldn't be taught by an English professor, because so many other people besides English professors write.

    History should not be taught by historians, because history involves so many non-historians.

    Phys. Ed. shouldn't be taught by athletes because so many non-athletes like to do sports.

    Biology shouldn't be taught by biologists, because so many non-biologists use biology (on a daily basis, no less).
     
  19. Jan 16, 2007 #18

    morphism

    User Avatar
    Science Advisor
    Homework Helper

    I think it is you who has no idea what mathematics is.
     
  20. Jan 16, 2007 #19

    Hootenanny

    User Avatar
    Staff Emeritus
    Science Advisor
    Gold Member

    :rofl: I love this post, it gets my nomination for post of the year! :rofl:
     
  21. Jan 16, 2007 #20

    matt grime

    User Avatar
    Science Advisor
    Homework Helper

    IN AN AMERICAN UNIVERSITY:


    Don't judge the rest of us because of your education system.
     
Know someone interested in this topic? Share this thread via Reddit, Google+, Twitter, or Facebook

Have something to add?



Similar Discussions: Mathematics = Arithmetic
  1. Modular arithmetic (Replies: 5)

  2. Arithmetic progression (Replies: 2)

  3. Arithmetic Sequence (Replies: 4)

  4. Modular arithmetic (Replies: 7)

Loading...