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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: 4, Interesting) by Aiwendil on Monday December 26 2016, @09:12AM
They're teaching it wrong. The issue is sixfold (ime).
*) They don't explain how/why something is the way it is (peano axioms would have been nice to learn).
*) They fail "the deserted island test" (ie - having us using a calculator or a lookup table and not teach us how to create the lookup table)
*) Grind it until you hate it - if you get the concept on the first or second time round, prepare for months or weeks of tedium.
*) Never look back - no repetition after you've been doing something else so you won't havy any reinforcement, nor checking for gaps
*) All tests are announced in advance - so you can just put a a review of the last couple of months in short term memory and skip actual learning (also - tests are "never look back", so only covers recent stuff and not testing for gaps)
*) On the first twelve years they don't really teach you math nor tries to make you understand it (what they do is the equal of teaching MS Office for twelve years and calling it CompSci), after twelve years of basic math I still can't even read actual math. (As a friend of mine put it once "if it has numbers it isn't math")
[Do note that "grind it until you hate it" and "never look back" has a partial common solution]
So, in the first twelve years of math I had exactly one class that tried to teach us to understand math (a teacher showed why N^0=1) [just like in PhysEd - in twelve years one class was theoretical and the rest was only 'run around'. They didn't even try to teach us to take proper strides, hiw to breathe, give us excersices to help with posture, how to do proper lifts... so I expect the issues in teching are systemic]
And while griping - why don't they start each course with a surprise test consisting of last year's final exam?
(Score: 3, Touché) by maxwell demon on Monday December 26 2016, @09:58AM
If they did that for each course, it hardly would be a surprise test, would it?
The Tao of math: The numbers you can count are not the real numbers.
(Score: 2) by TheRaven on Monday December 26 2016, @12:54PM
Grind it until you hate it - if you get the concept on the first or second time round, prepare for months or weeks of tedium.
Worse is the focus on performing the mechanical steps. Understanding what kind of mathematical building blocks you need to solve a particular problem is an important skill. Transforming the problem into a mathematical form is an important skill. Understanding why the tools that you're using work is an important skill. Spending six months going from being able to solve a particular kind of equation 0.001% of the speed that a computer can do it to being able to solve it 0.01% of the speed that a computer can do it is not a useful skill.
sudo mod me up
(Score: 0) by Anonymous Coward on Monday December 26 2016, @04:16PM
This is along the lines of my first thought, too. Given the number of high school graduates that have to take remedial math classes in college to get up to high school graduate level, they need to figure out how the teach basic math before they move on to adding mathematical modeling to the curriculum.