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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.
(Score: 0, Informative) by Anonymous Coward on Monday December 26 2016, @02:35AM
Well, here is what it says there:
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.
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":
https://www.skepticalscience.com/postma-disproved-the-greenhouse-effect.htm [skepticalscience.com]
(Score: 0) by Anonymous Coward on Monday December 26 2016, @03:23AM
It seems that your link [skepticalscience.com] does not support your position and rather supports Tom Murphy’s initial simplistic modelling approach.
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
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
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
(Score: 0) by Anonymous Coward on Monday December 26 2016, @07:59AM
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
So yes, it is significant.
(Score: 0) by Anonymous Coward on Tuesday December 27 2016, @01:22AM
(Score: 1, Insightful) by Anonymous Coward on Tuesday December 27 2016, @01:53AM
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
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.