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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, Interesting) by maxwell demon on Monday December 26 2016, @10:07AM

    by maxwell demon (1608) on Monday December 26 2016, @10:07AM (#446025) Journal

    Since they are missing from the summary, here are the reasons:

    1. Solving rote problems is boring. Modeling involves making genuine choices.
    2. Nobody likes to be wrong. Modeling problems have many possible justifiable answers.
    3. Contrived story problems can be mind numbing. Modeling problems matter to the end-user who needs to understand something or make a decision.
    4. Math is hard and requires practice. Modeling presents problem solving as a creative, iterative process.
    5. The “mathematician as solitary genius” myth discourages almost everyone. Modeling is inherently a team sport.
    --
    The Tao of math: The numbers you can count are not the real numbers.
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  • (Score: 2) by Dr Spin on Monday December 26 2016, @12:01PM

    by Dr Spin (5239) on Monday December 26 2016, @12:01PM (#446043)

    Solving rote problems is boring. Modeling involves making genuine choices.

    This is probably true, however, I found out by experiment that, no matter how much I detest
    doing large numbers of similar problems to learn a new maths concept, it really does make
    it stick in the mind better and for longer.

    --
    Warning: Opening your mouth may invalidate your brain!
  • (Score: 1) by Francis on Monday December 26 2016, @07:15PM

    by Francis (5544) on Monday December 26 2016, @07:15PM (#446123)

    I used to like applications right up until I realized how broken they were. The applications are often written by mathematicians to isolate a concept giving something that is completely useless for anything else. For example, doing parabolic motion in terms of horizontal displacement rather than time.