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Michael Froemmcke

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What does the average citizen need maths for?

I had a conventional education. In school and later at other educational institutions I was always just mediocre - but I became excellent at this - and as the years went buy I asked myself why the educational systems around the world seem to be promoting the same subjects.

WHY?

Topics: curriculum
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Closing Statement from Michael Froemmcke

I can understand that people, especially those who spent long years learning maths, are very passionate about the subject. Yet I am still not convinced that the actual outcome justifies the effort and, in some cases, pain associated with this subject. There seems to be widespread reluctance to even contemplate any alternatives, which reinforces my suspicion that most people are indoctrinated in believing that there is no good education without maths. I think the understanding of certain principles is far more important than an intricate knowledge of mathematics.... But this is just my opinion. Thanks to all the participants in this minor debate.

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    Jan 24 2013: To be able to understand the meaning of 'average', for example... :o)
  • Jan 24 2013: "G.V. Ramanathan, a professor emeritus of
    mathematics, statistics and computer science at
    the University of Illinois at Chicago, writes in the
    Washington Post that although a lot of effort and
    money has been spent to make mathematics
    seem essential, unlike literature, history, politics and music, math has little relevance to
    everybody's daily life. 'All the mathematics one needs in real life can be learned in early years
    without much fuss,' writes Ramanathan. 'Most
    adults have no contact with math at work, nor do
    they curl up with an algebra book for relaxation.'
    Ramanathan says that the marketing of math has
    become similar to the marketing of creams to whiten teeth, gels to grow hair and regimens to
    build a beautiful body, but even with generous
    government grants over the past 25 years,
    countless courses, conferences, and books
    written on how to teach teachers to teach, where
    is the evidence that these efforts have helped students? A 2008 review by the Education
    Department found that the nation is at 'greater
    risk now' than it was in 1983, and the National Assessment of Educational Progress math scores
    for 17-year-olds have remained stagnant since
    the 1980s (PDF). Meanwhile those who do love math and science have been doing very well and
    our graduate schools are the best in the world. 'As
    for the rest, there is no obligation to love math
    any more than grammar, composition, curfew or
    washing up after dinner. Why create a need to
    make it palatable to all and spend taxpayers' money on pointless endeavors without
    demonstrable results or accountability?'"
  • Jan 28 2013: Math to me, proposes analytical thinking, discipline, weighing options and giving balanced arguments. It's not really the end product of a mathematical solution that helps me, but the thought process that gives me the ability to rationally process my thoughts.

    In my eyes, I am an average citizen.
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      Jan 29 2013: Spot on! The good old fashioned way of getting those little grey cells working.

      Sometimes I hear that kids are allowed to use calculators in class, even scientific ones that process complicated equations. At that moment I guess any slight advanced math gets useless for the average citizen.
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    Jan 24 2013: Developing the thought process while doing math is lot more essential for people than just the subject alone. I guess you didnt watch Donald in Mathamagic land?

    http://www.youtube.com/watch?v=YRD4gb0p5RM
  • Jan 22 2013: Two basic reasons why everyone should learn math.

    First, to learn how the universe works.

    Second, to understand how others understand how the universe works.

    Math is a powerful tool. If you do not know math, you not only deprive yourself of a tool, but you will not understand how others are gaining advantage by using it. When you understand statistics others cannot use statistics to fool you.
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      Jan 22 2013: With all due respect understanding the physics of the universe does not necessarily equate to understanding society which, in my opinion, is far more important.
      • Jan 23 2013: I was referring to the entire universe. Society is part of that universe, and so are you and me.
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    Jan 22 2013: Here is a link that might help: http://mathforum.org/dr.math/faq/faq.why.math.html

    One more thing also. Those trying to sell products or points of view often take advantage of people's innumeracy and insecurity about math or science to mislead them. They know that most people "check out" once mathematics is used in argument (or once someone says something about (supposed) recent findings in neuroscience or quantum physics).

    The default for people without the background to understand what is being presented tends to go in one of two ways that I have noticed. One is just to assume that anyone who talks about math (or neuroscience or quantum physics) is probably smart or at least knows what he is talking about. Maybe he knows, but maybe he actually doesn't, but without any background you can't tell.

    The other default is the anti-intellectual one of assuming that those who are experts in these areas must be frauds (the reasons vary for why this must be so).

    If you know enough math actually to review arguments critically that involve math or enough science to review arguments critically that involve that, you won't be tempted to adopt one of these default views.
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      Jan 22 2013: Good point! What is considered essential knowledge?
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        Jan 23 2013: There would be some dispute over this, in part because it isn't like there is a fence separating not enough from enough.

        It depends what you want to be able to understand.

        There would be good argument for a couple of years of algebra because real flexibility with the understanding of variables, parameters, and models is valuable in many settings and applications. Geometry is usually the easiest way to introduce the idea of deductive proof, which forever changes a students' thinking about whether a conclusion has actually been tightly defended. It can be done with number theory also, but geometry has its own additional value in understanding spatial problems.

        There is a lot of science one cannot understand without the concepts of calculus, though the calculations would not be as vital.

        John Allen Paulos, author of A Mathematician Reads the Newspaper, argues that inferential statistics is the most important part of literacy- that is, not the calculation of means and correlation but rather understanding what conclusions can be drawn legitimately from a sample or study design and what the threats are to what are called "internal validity," "external validity," and "construct validity." These are mostly logical issues and assessments that give a person who masters them lots of leverage.
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    Jan 29 2013: As for the used of the word "average", I referred to the concept (fell free to re read the 1st post).

    It's a mathmatic concept even before math was formalized as a science. Math describes how things are, doesn't create them.

    Average was a math concept before math, english or any language had a word for it ;). English just happened to pick average.
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    Jan 24 2013: i would need higher math for my hobby project. sadly, i'm not good enough. i'm getting insecure when it comes to doing integration in a 3D polar coordinate system.
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    Jan 23 2013: Education is a powerful tool and I believe it is allways used by the powerful to exploit those at the bottom. Erroneously I had assumed that education was meant to enable people to claim ownership of their own destiny. Now, as an old man, I realise how stupid I was and still am. But I can certainly say that maths didn't help me to achieve anything. But having said that, not many other subjects were more useful. Humankind with all the mathematical and other knowledge has managed to lead us to the edge. Most scientists are in agreement about the poor state of our planet's atmosphere. Has this knowledge brought about change? This very fact is evidence enough for me that something went wrong in the educational systems that has deeply affected us.
  • Jan 23 2013: As Ken Robinson says, the ultimate goal of math in schools is to teach students calculus.
    In reality, just a few percent of us need to know calculus, but everybody needs to know statistics.
    Without an understanding of statistics and basic math you can be decieved about everything from how much you are being ripped off by interest rates on your mortgage to organizations that are lying about the significance of a change in the occurrance of something to suit their own agenda.
    In this world, without basic math and particularly statistics you are the mercy of every con artist and shyster with something to sell
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      Jan 23 2013: I once checked the interest I as charged on my mortgage. I had been overcharged. What a surprise! Not by much but... So I went to the bank and after talking to the manager who was keen to get to the bottom of the mathematical nuances and after a few calls and conversations with the service in charge of working out the amount. None of us was wiser. I had wasted an hour of unpaid time. From the point I realised how inadequate my education was. I had only given me the mean to work out by how much I was being ripped off.
    • Jan 24 2013: I think you've touched on a good point Gordon. I'm not sure, but I suspect the whole imperial measuring system, as opposed to the logical metric one, was designed to confuse and cheat the lower classes, who probably never benifitted from many years of formal maths education.
      A modern example would be trying to compare deals between different telco/ electricity providers. Nearly impossible, and I have university level maths education.

      The other benificial aspect is the way it teaches you to think. It is teaching you how to compare numerically. How could I work out whether the S2.50 jar of 500g pasta sauce is better value than the S3 750g jar.
      I use maths everyday.
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      Jan 29 2013: sorry but no. average is a word borrowed by math. it is much older and broader. if average would be a math term, tell me what "average citizen" would mean? add up all the citizens, divide by the number of citizen, and you get an average citizens? how to add two persons?

      if one wants to be witty, wit is required.
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        Jan 29 2013: Not really,

        You are referring to arithmetic mean.
        Average is a typical value or central tendency in a set.

        Many other ways to found an average.

        "Many different descriptive statistics can be chosen as a measure of the central tendency of the data items. These include the arithmetic mean, the median, and the mode. Other statistics, such as the standard deviation and the range, are called measures of spread and describe how spread out the data is." - Wikipedia, of course.

        So the average citizen would be a citizen who represents the typical or the central tendency in the set of all citizens. He might not even exist in a physical form!

        Math isn't really about numbers.

        Don't mistake all math for arithmetic.
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          Jan 29 2013: one more time, the last time: average is NOT a math term. it is a common word in english language. math also uses it. but when we say "average citizen" we are NOT referring to the mathematical meaning.

          http://www.thefreedictionary.com/average

          av·er·age (vr-j, vrj)
          adj.
          1. (Mathematics) Of, relating to, or constituting an average.
          2. Being intermediate between extremes, as on a scale: a player of average ability.
          3. Usual or ordinary in kind or character: a poll of average people; average eyesight.
          4. Assessed in accordance with the law of averages.
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        Jan 29 2013: As for the used of the word "average", I referred to the concept (fell free to re read the 1st post).

        It's a mathmatic concept even before math was formalized as a science. Math describes how things are, doesn't create them.

        Average was a math concept before math, english or any language had a word for it ;). English just happened to pick average.
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        Jan 29 2013: Do I get to get an F in the good company of all the positivist philosophers?

        Mind you, I also find quantum physics terribly exciting and eagerly await to see where Schrodinger's cat will take us next!

        I just wouldn't simply fail someone for grounding arguments in a school of thought that gave us so much.
        • Jan 29 2013: ....where Schrodinger's cat will take us next!

          To 'non locality' and it's the end of the very notion ' next'
          Welcome ! :)
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        Jan 29 2013: Thanks! Now you got me busy again :)
  • Jan 29 2013: well undoub"TED"ly maths is one of the most if not the most important subjects u will study. think of a situation your parents send you to the supermarket with cash and u do not know how much u have shopped in case there is a mistake in the bill. we see numbers everywhre. starting from ur bank acc number to the amount being credited or the tax being deducted.. if u have basic idea in maths all dis u will get. else ur payslip will look like a chinese magazine. beautiful but useless!!
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    Jan 29 2013: I thank you for all your comments, but I cannot escape the suspicion that many of us will just retrospectively justify the time invested in studying maths and other subjects. I am still waiting for the convincing argument.
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    Jan 28 2013: Not for the math itself. For logical thinking.
    Or more. Maybe the same reason like art or music.
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    Jan 28 2013: A kettle of water will maintain its' heat longer than a cup of water - maths
    A 2 for 1 offer is only half the saving it seems - maths
    This account offers you 2% aer before tax - maths
    This credit card will charge you x interest on x - maths
    How long will it take to get to edimburgh by car as aposed to train?
    Is this deal really a deal and am I getting good value for money?
    Can we realistcly afford a child?
    How are other people able to work out these magic things and I can't?
    Why do we call the 1600's the 17th century?

    -DC
  • Jan 25 2013: I think math are definitely not useless, it's just that the "random citizen" (if it even exists) usually does not findd a use for the rather advanced math he learned. But one cannot deny the benefits it has on the big picture (ex : reasoning, logic, objectivity).
    So the problem is not that it's useless it's more in the way it's teached and how some children feel bad about themselves because they do not succeed in math (and therefore in the conventional educational system which is largely based on math -in France at least-). And those children are not "bad" at math they just have trouble learning it this way. I am one of those children and I feel a bit sad that I dropped out of math class when I was offered to because I felt It could bring me something. But I just couldn't learn it that way.
    So yes there is a problem with the place that is accorded to math in our system because it lures some children into thinking they are "bad" and won't do well later on anyways. (I always remember the joke about a math teacher giving macdonald's emplyment forms to the students which failed the test.)

    So I think math Is definitely a good thing to teach but that other ways of succeeding should be given more importance.
    And as always watch more Ken Robinson to have faith in a change of our educational system.
  • Jan 25 2013: It’s not a result of societal peer pressure, but I’ve noticed that those who are dismal at basic math, have a low opinion of themselves, even though they are precious, warm, caring, nurturing, giving, hard-working and creative souls. Where a person is dismal at math, questions at length have uncovered the fork-in-the-road being a primary "teacher" who did not really want to "be there", along with parents who refused to apply themselves and help their own children.

    I had the wonderful opportunity to home-school my son beginning at age 13. As established curriculums were weeded out, adding to history, literature, creative writing, positive interactive approaches, piano, search and rescue, rappelling, martial arts, just a wide variety... I was teaching him trig and medical anatomy when he was 14. He and I were at a retired teacher's home where I was working, and she curiously checked out his assignment. She loudly exclaimed, "THAT'S TRIGONOMETRY!! THAT GAVE ME SUCH A HARD TIME IN COLLEGE!" My son looked at me with complete despair in his eyes and spoke "Daddy!?" with a slight question in his voice. I said, "Don't worry Jake. Sine, cosine and tangent are merely words of a different language. Each word has a specific meaning. Once you understand what each word means, it will be simple... and I have more patience to teach you this, than you have fears that you won't learn it. Relax son", and I gave him a kiss on the brow as I embraced his head.

    Grateful resolve settled back into his gaze and he refocused on the assignment I had given him.

    He hasn't used trig once in 17 years... but he knows that he can. He has no fears of learning anything... and THAT is a huge benefit in life. As well as learning, that lack of fear, nurtures honesty, objectivity and creativity. He is completely as ease in the company of men and women whose accomplishments eclipse his own, and he readily teaches with attuned patience and humility, those who know less than he does.
  • Jan 25 2013: Hey man, math IS taught for average citizens! ;-)
    ..I am an average citizen, since until when I was showed what can possibly be done with (advanced) math I didn't even think that something like that could be possible. After long training I can use these instruments well and understand them, and I've got all the opportunities of an average citizen to build upon my skills.. ..not only in my job, in my daily life too.. and how many hobbies today do not involve math, when hi-tech and knowledge are so pervasive and high-level? how else would you defend yourself from fraud people, just by being constantly suspicious?

    Imho, real non-average citizens can figure out their way even without being taught how to, that's how they managed to discover properties and prove theorems in the past, at least.

    Is it abstract? Yes.
    Is it difficult to create? Yes.
    Is it difficult to imitate/understand? No: Consciousness is Abstraction! Things become difficult only when you've become lazy enough to stop this abstraction process for a while, loosing the consciousness of the meaning underneath.

    To me how is taught today is good enough.
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    Jan 25 2013: Nicely said. Perhaps we should start by really looking at the parts of the world that are visible to the naked eye first. That you are blind is just your personal drama but that, despite all the collective knowledge, humanity's vision is decking and replaced by some strange illusions.
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    Jan 25 2013: Good point! I wish you luck. We need people who are passionate about life to make maths more palatable. If maths was taught seriously and accepted seriously and the logical consequences were drawn... Perhaps we could achieve more democracy.
  • Jan 25 2013: I want to rewrite math from scratch in such a way that not only is it highly learnable, it's so obvious how every single technique and concept is an analogy for real live things, that people who know it will use it in their lives all the time and thereby live smarter and better. Then a smarter and better society.

    The way math is written now, it's not important how concepts are analogous to real phenomena. We don't practice drawing those analogies. So naturally no one cares and no one really benefits. But math is "the discipline which compares the most diverse phenomena and finds the secret analogies that unite them" - Descartes. And it's powerful. So let's use it!
  • Jan 25 2013: To see the 'unknown' world.
    I often feel like being blind.
    I just want to learn more about it. It may open my eyes to see the bigger world through deeper understanding.
    That's all.
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    Jan 24 2013: For average level of analysis , critical as well logical thinking to apply in day to day life
  • Jan 23 2013: know where you are and sizes How can you compare things otherwise?
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    Jan 22 2013: There is not a day that goes by that I do not use math in some form. I would be quite lost without it. I wasn't very good with geometry so I had to go back and teach it to myself - only to discover how interesting it is. You can't survive in today's world without math. From budgeting your money to solving day-to-day issues, I use math far more than I thought that I would when I endured those classes and found the boring.

    Ken Robinson's talk about school killing creativity is not about dropping math. Hardly! More about making it more relevant and therefore interesting, so that curiosity is inspired and the student as well as all of humanity benefits

    Had I had ME as a teacher back when I was learning that boring geometry in school, I would have aced it, and might have gone on to be a physicist. Math is actually quite fun when you do it out of school. I do wish that it had been fun IN school.
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      Jan 22 2013: There some professions that use maths, but I am convinced that there are more that don't. I used maths as an example because educational systems seem to be obsessed with just a few subjects. I think it is time humanity reflected on their educational systems.
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        Gail . 50+

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        Jan 23 2013: With that I agree wholeheartedly. My REAL education began when I left school. Only then did I begin to learn how much information was being withheld. Only then did I discover the JOY of learning. Before then, education was punishment inflicted on powerless victims who had no say in the matter (children) - and beyond that, an ALLEGED avenue of success for those who had bought into the lies.

        I think that it is very sad that generations are graduating from various schools not even knowing how uninformed they are. And because they have been told that they are now "educated", they don't know that they are now "ready" to begin educating themselves.

        This applies even for those with a PhD. Their knowledge is so specialized that it excludes a LOT of relevant information that is considered part of another field. SAD