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posted by Fnord666 on Sunday December 25 2016, @09:36PM   Printer-friendly
from the do-you-speak-math? dept.

When one of my daughters was in high school, a student in her math class stood up in disgust and exclaimed "Why do we have to learn math for 12 years when we are never going to use any of it?" You might think that as a mathematics educator I would find this statement upsetting. Instead, the student's question got me thinking about the fact that she saw no connection between the mathematics and her future, even though her curriculum was full of story problems that at the time I would have called "real-world problems." Every mathematician has probably encountered an "I'm not fond of math" confession. Choose any subject and you can probably find someone who dislikes it or does not care to practice it. But when I have talked with strangers about my experience teaching English and shop and history and physical education, I rarely (if ever) have encountered a negative response. Because math can be a pathway to many careers, the problem seems important to address.

Mathematics in its purest forms has incredible power and beauty. New mathematics is key to innovations in most science, technology, engineering and mathematics-related (STEM) fields. Often at the time new mathematics is invented, we don't yet know how it will relate to other ideas and have impact in the world. Mathematical modelers use ideas from mathematics (as well as computational algorithms and techniques from statistics and operations research) to tackle big, messy, real problems. The models often optimize a limited resource such as time, money, energy, distance, safety, or health. But rather than finding a perfect answer, the solutions are "good enough" for the real-life requirements. These problems can be motivating for mathematics students, who can relate to mathematics that solves problems that are important to them.

To solve modeling problems, mathematicians make assumptions, choose a mathematical approach, get a solution, assess the solution for usefulness and accuracy, and then rework and adjust the model as needed until it provides an accurate and predictive enough understanding of the situation. Communicating the model and its implications in a clear, compelling way can be as critical to a model's success as the solution itself. Even very young students can engage in mathematical modeling. For example, you could ask students of any age how to decide which food to choose at the cafeteria and then mathematize that decision-making process by choosing what characteristics of the food are important and then rating the foods in the cafeteria by those standards. The National Council of Teachers of Mathematics (NCTM) is providing leadership in communicating to teachers, students, and parents what mathematical modeling looks like in K–12 levels. The 2015 Focus issue of NCTM's Mathematics Teaching in the Middle School will be about mathematical modeling and the 2016 Annual Perspectives in Mathematics Education will also focus on the topic.


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  • (Score: 3, Disagree) by stormwyrm on Monday December 26 2016, @01:29AM

    by stormwyrm (717) on Monday December 26 2016, @01:29AM (#445918) Journal

    The girl who is complaining is correct; she will never use this stuff.

    And be worse off for not being able to use mathematics to solve everyday, real-world problems. Basic numeracy would go a long way towards getting people to understand their finances and manage them properly for one. It would help prevent people from getting taken in by scam artists, and understand the pointlessness of gambling. Reasonable numeracy would help people to understand science better, and help keep people from getting deceived by people with vested interests in obscuring scientific issues. For instance, this article [ucsd.edu] uses some pretty simple physics and maths that can demonstrate that anthropogenic global warming is a reasonable hypothesis. As the article says:

    But before anyone gets the impression that I claim this method offers irrefutable proof that climate change is real and expected, let me clarify that such a cursory analysis cannot constitute an airtight case. Leave that to the IPCC (which has, incidentally, concluded that anthropogenic global warming is an airtight case). But I find it personally persuasive, understanding the broad outline of the problem. Such simple analysis makes it easy to adopt a default position that climate change is real and expected. It would take a lot of convincing evidence of complex masking (conspiratorial?) mechanisms to destroy these pillars. Not impossible, but not easily done.

    But no one below a certain level of numeracy will be able to comprehend the article and its use of maths, and it hardly uses anything beyond elementary school arithmetic, though the physics is university-level.

    Sure, leave the algebraic geometry, cohomology, and non-Euclidean geometry to the people who are actually interested in that kind of thing. But everyone ought to have at least a grasp of the basics.

    --
    Numquam ponenda est pluralitas sine necessitate.
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  • (Score: 1) by Ethanol-fueled on Monday December 26 2016, @01:40AM

    by Ethanol-fueled (2792) on Monday December 26 2016, @01:40AM (#445920) Homepage

    Just what we need, for math to be politicized so that people who don't think they need it will be even more turned off by it.

    • (Score: 0) by Anonymous Coward on Monday December 26 2016, @02:28AM

      by Anonymous Coward on Monday December 26 2016, @02:28AM (#445933)
      The last time science was heavily politicised was in the days of Trofim Lysenko [wikipedia.org]. He had his own theories of biology that were in accord with Soviet ideology, and the fact that they didn’t reflect reality resulted in disastrous agricultural policy for the Soviet Union that caused famines which killed millions. What will this next politicisation of science yield, I wonder?
    • (Score: 1, Touché) by Anonymous Coward on Monday December 26 2016, @03:15AM

      by Anonymous Coward on Monday December 26 2016, @03:15AM (#445949)

      Except here, the definition of "politicized" is "I don't agree with the results, therefore it can't be true".

      • (Score: 1) by Ethanol-fueled on Monday December 26 2016, @03:42AM

        by Ethanol-fueled (2792) on Monday December 26 2016, @03:42AM (#445954) Homepage

        Math is like any other language, you can frame your argument and set everything up to make your point, but there are always a few assholes out there who not only know that language but can use it to argue against you.

        The barrier to argument is a bit more high, but the idea remains the same.

        The mathematical argument might be more effective to the layman if it were titled "a survey of statistical data with regard to geophysics and climatology" rather than "Man causes climate change because Leftist Faggots Told me so."

        Knowing math doesn't make people smart anyway - as a technician who's worked with more than his share of autistic retard engineers, I speak with authority in these matters. That a retard like me can see a thinly-veiled mathematical political rant is a testament to that.

  • (Score: 1, Insightful) by Anonymous Coward on Monday December 26 2016, @01:55AM

    by Anonymous Coward on Monday December 26 2016, @01:55AM (#445924)

    Everyday "numeracy" is not worthy of the description "Mathematics"; that is not what we mean here. Mathematics is about encoding and then manipulating thoughts; most people don't need such generality in problem solving, and can get on just fine after being taught simply to follow a few a simple magical, habitual rituals that Just Work (e.g., calculating what the price of shoes are after that 40%-off sale is applied).

    • (Score: 1) by khallow on Monday December 26 2016, @08:14AM

      by khallow (3766) Subscriber Badge on Monday December 26 2016, @08:14AM (#446001) Journal

      Everyday "numeracy" is not worthy of the description "Mathematics"; that is not what we mean here.

      It is what the original article was speaking of and probably the grandparent. So there is plenty of "we" who do mean just that.

      most people don't need such generality in problem solving, and can get on just fine after being taught simply to follow a few a simple magical, habitual rituals that Just Work (e.g., calculating what the price of shoes are after that 40%-off sale is applied).

      Someone still needs to come up with that magical ritual. Most people have the raw brainpower to do that without requiring a helper. But they need to know some math first.

  • (Score: 0, Informative) by Anonymous Coward on Monday December 26 2016, @02:35AM

    by Anonymous Coward on Monday December 26 2016, @02:35AM (#445937)

    this article uses some pretty simple physics and maths that can demonstrate that anthropogenic global warming is a reasonable hypothesis

    Well, here is what it says there:

    The law for thermal radiation is that a surface emits a total radiative power of A·σT4, where A is the surface area, σ=5.67×10−8 W/m²/K4 is the Stefan-Boltzmann constant, and T is the surface temperature in Kelvin. For instance, a patch of Earth at the average surface temperature of 288 K (15°C, or 59°F) emits 390 W/m² of infrared radiation. To figure out the temperature of the Earth, we demand that power in equals power out, and radiative transfer is the only game in town for getting heat on and off the Earth. If we did not have a balance between power in and power out, the Earth’s temperature would change until equilibrium was re-established. Hey—that’s what global warming is doing. But let’s not get ahead of ourselves…

    While the Earth intercepts a column of light from the sun with area πR², the Earth has a surface area of 4πR² to radiate. Considering that 70% of the incoming sunlight is in play, we have an effective influx of 960 W/m² onto one quarter of the Earth’s surface area (why not half? much of the Sun-side of the Earth is tilted to the sun and does not receive direct, overhead sunlight). So the radiated part must work out to 240 W/m², which implies an effective temperature of 255 K, or a bone-chilling −18°C (about 0°F). Incidentally, if the Earth were black as coal, absorbing all incident solar radiation, the answer would have been a more satisfactory 279 K, or 6°C, but still colder than observed.

    http://physics.ucsd.edu/do-the-math/2011/08/recipe-for-climate-change/ [ucsd.edu]

    This treats the earth as a 1 dimensional object (ie ignores latitude, rotation, and day/night), all sorts of misconceptions have resulted from its near ubiquitous presentation in introductory-level books. It is off in estimating the greenhouse effect by a factor of ~3. See section 3 of this paper: https://arxiv.org/abs/1303.7079 [arxiv.org]

    Please stop spreading long-recognized misinformation.

    But no one below a certain level of numeracy will be able to comprehend the article and its use of maths

    Using the wrong average (ignoring Holder's inequality) like at your link is an example of innumeracy... Even skeptical science calls it an "algebra lesson" and "simple educational tool":

    I will say that I do not particularly like this model as a suitable introduction to the greenhouse effect. It is useful in many regards, but it fails to capture the physics of the greenhouse effect on account of making a good algebra lesson, and opens itself up to criticism on a number of grounds; that said, if you are going to criticize it, you need to do it right, but also be able to distinguish the difference between understood physics and simple educational tools.

    https://www.skepticalscience.com/postma-disproved-the-greenhouse-effect.htm [skepticalscience.com]

    • (Score: 0) by Anonymous Coward on Monday December 26 2016, @03:23AM

      by Anonymous Coward on Monday December 26 2016, @03:23AM (#445951)

      It seems that your link [skepticalscience.com] does not support your position and rather supports Tom Murphy’s initial simplistic modelling approach.

      But, in actuality, the globally averaged solar re-distribution approximation is not bad when we use it to describe the temperature for planets like Earth or Venus. These planets have an atmosphere or ocean that transport heat effectively, especially Venus with virtually no day-to-night or pole-to-equator temperature gradient.

      Yes, Tom Murphy’s model amounts to the proverbial spherical cow moving in simple harmonic motion in a vacuum, but if such a simplistic model already produces results that support hypothesised global warming, then it will, as he himself notes, take plenty of complex masking to undermine the simple model’s basic conclusions. But no, the scientists who have spent their lives studying this phenomenon have rather shown that the higher-order effects not accounted for by the simple analysis do not serve to disprove global warming.

      • (Score: 0) by Anonymous Coward on Monday December 26 2016, @07:13PM

        by Anonymous Coward on Monday December 26 2016, @07:13PM (#446121)

        The link says exactly what I said it says... whatever else you are talking about doesn't make this model less nonsensical. Stop using it!

    • (Score: 1) by tftp on Monday December 26 2016, @05:35AM

      by tftp (806) on Monday December 26 2016, @05:35AM (#445975) Homepage

      radiative transfer is the only game in town for getting heat on and off the Earth

      Which is a wrong assertion, and no math will help you once you throw enough garbage in. Earth has a hot iron core [phys.org], heated by radioactive decay and other causes:

      Although we crust-dwellers walk on nice cool ground, underneath our feet the Earth is a pretty hot place. Enough heat emanates from the planet's interior to make 200 cups of piping hot coffee per hour for each of Earth's 6.2 billion inhabitants, says Chris Marone, Penn State professor of geosciences. At the very center, it is believed temperatures exceed 11,000 degrees Fahrenheit, hotter than the surface of the sun.

      • (Score: 0) by Anonymous Coward on Monday December 26 2016, @05:50AM

        by Anonymous Coward on Monday December 26 2016, @05:50AM (#445978)
        And just how much of that heat at the earth’s core actually makes it up to the surface where it can actually warm the atmosphere? It seems to be a drop in the bucket compared to solar radiative heat transfer, even if you are talking about enough heat to make 200 cups of hot coffee for everyone on the planet. Is it enough to heat 5.1480×1018 kg of air to an appreciable degree? From the looks of things, barring a catastrophic volcanic eruption not seen for at least 100,000 years, the answer is no. Tom Murphy is trying to get a big picture here, not dwell on tiny details that may not matter very much in the grand scheme of things.
        • (Score: 0) by Anonymous Coward on Monday December 26 2016, @07:59AM

          by Anonymous Coward on Monday December 26 2016, @07:59AM (#445997)

          Well, how many cups of coffee is 5.1480×1018 kg of air? Therein lies your answer. That's why we need math.

      • (Score: 1) by khallow on Monday December 26 2016, @05:54PM

        by khallow (3766) Subscriber Badge on Monday December 26 2016, @05:54PM (#446107) Journal
        To put some actual numbers on this, the average heating due to geothermal activity is estimated to be 0.09 watts [wiley.com] per square meter. The average heating due to elevated greenhouse gases is estimated (by NASA) to be 0.8 watts [nasa.gov] per square meter.

        So yes, it is significant.
        • (Score: 0) by Anonymous Coward on Tuesday December 27 2016, @01:22AM

          by Anonymous Coward on Tuesday December 27 2016, @01:22AM (#446212)
          And average solar radiative heat transfer is, as Tom Murphy’s article says, 960 W/m2, and the fraction the planet radiates out back into space is something like 390 W/m2. 0.09 W/m2 is several orders of magnitude smaller than the radiative heat transfer component, so for the very rough model that he is trying to construct it will not matter that much. Remember that Tom Murphy’s goal in constructing the model was to see whether global warming was a reasonable hypothesis or not based on the fundamentals. As I have said elsewhere, his is a spherical cow in a vacuum model. He isn’t out to fully demonstrate the reality (or otherwise) of global warming: that’s the IPCC’s job, so he is fine with ignoring such relatively tiny contributions to overall planetary heat transfer. The IPCC’s model must (and does) incorporate it though, because they are trying to fully quantify just how much the planet is supposed to be warming. Yes 0.09 W/m2 is important for a more sophisticated model because it can be involved in feedback.
          • (Score: 1, Insightful) by Anonymous Coward on Tuesday December 27 2016, @01:53AM

            by Anonymous Coward on Tuesday December 27 2016, @01:53AM (#446215)

            The model is useless for demonstrating anything. It gets the greenhouse effect wrong by ~60 K, how can it tell you anything useful about changes on the order of 1-2 K?

          • (Score: 1) by khallow on Tuesday December 27 2016, @09:28AM

            by khallow (3766) Subscriber Badge on Tuesday December 27 2016, @09:28AM (#446282) Journal

            0.09 W/m2 is several orders of magnitude smaller than the radiative heat transfer component

            And net CO2 growth is a couple orders of magnitude slower than seasonal changes in CO2 concentration.

  • (Score: 2) by driverless on Monday December 26 2016, @05:05AM

    by driverless (4770) on Monday December 26 2016, @05:05AM (#445969)

    The girl who is complaining is correct; she will never use this stuff.

    And be worse off for not being able to use mathematics to solve everyday, real-world problems.

    You're conflating basic arithmetic with the mountains of mathematical junk that kids get stuffed into them at school. Basic numerology, the sort they teach for the first few years of school, is pretty essential. Anything beyond that is useful to only the tiniest subset of a subset of the population. For example I did calculus through university level (I'm a scientist). I have never, ever, ever used or needed any calculus, ever. It was ten years of utterly wasted effort that I could have put into learning something that's actually useful.

    The one form of maths that I think people should be given a more advanced knowledge of is statistics, because they'll actually need that, along with critical thinking skills, to defend against the mountains of bullshit that marketers and politicians throw at them every day.

    • (Score: 0) by Anonymous Coward on Monday December 26 2016, @06:08AM

      by Anonymous Coward on Monday December 26 2016, @06:08AM (#445980)
      Then your only quibble is about where the basics should be. And well, I’m an electronic engineer, and yes, I did use calculus a fair bit, though I did use discrete mathematics far more. And calculus I think is really needed for a proper treatment of statistics, though you can probably get a lot of useful bits already with just high school algebra. The error function is defined by an integral, for instance.
    • (Score: 2) by Dr Spin on Monday December 26 2016, @11:56AM

      by Dr Spin (5239) on Monday December 26 2016, @11:56AM (#446042)

      For example I did calculus through university level (I'm a scientist). I have never, ever, ever used or needed any calculus, ever.

      Whereas I learned it at A-level, went on to do it at degree level, and now, in my retirement, still use it to solve everyday problems.

      I am not talking about exact numerical solutions using Fortran programs, but using an understanding of the behaviour of the underlying
      equations to anticipate the phenomena that govern everyday life.

      The answer to the girl in question is however:

      "Cos if you dont understand maths, you will be ripped off the moment you go to buy something online!"

      --
      Warning: Opening your mouth may invalidate your brain!