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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: 2, Insightful) by Booga1 on Sunday December 25 2016, @11:19PM
The vast majority of math that matters to the average person isn't calculus or any advanced maths. Basic arithmetic will do for 99% of your day to day problems(percentages, price per unit, etc...). Maybe if you really get into understanding long-term planning, compound interest would be important. Still, by the time the average student has enough earned/saved for that to matter, they'll have long forgotten it.
I'm not saying it's not important to teach more advanced concepts. After all, we do need to identify those students who WILL use it in their careers, so just ignoring advanced math courses would be stupid. Where to strike the balance is more of an interesting question for me. How far down the rabbit hole should students be forced to go?
(Score: 0) by Anonymous Coward on Sunday December 25 2016, @11:33PM
How much of anything does anyone need to know? You can live in most Western countries with almost no skills. Rudimentary arithmetic that kids know by age 6 and reading are helpful but that's all you *need* to know. It's a pointless argument - yes kids, you don't need to know anything to be a voting member of society.
(Score: 1, Insightful) by Anonymous Coward on Sunday December 25 2016, @11:35PM
By age 9. an above arverage student is probably above average in all the population.
(Score: 0) by Anonymous Coward on Sunday December 25 2016, @11:54PM
Why is it pointless? It may well show that we shouldn't squander too many of our resources trying to teach absolutely everyone things that the average person will not use. I think that making sure people know how to teach themselves is a more valuable skill. Too often people vote based on shallow things like a candidate's charisma or how likable they are, rather than policy. Too often people say that they don't know how to do X but do not have the motivation to learn how to do it.
(Score: 0) by Anonymous Coward on Monday December 26 2016, @01:58AM
The right solution isn't to improve the electorate; rather, the right solution is to abolish "Democracy".
Only the Free Market makes sense; in order for good decisions to be made, the weight of your future "vote" must must be based on outcomes of your past "votes".
(Score: 2, Funny) by Scruffy Beard 2 on Monday December 26 2016, @02:32AM
According to many economic theories, people (rational actors) behave as if they know calculus.
Put that in you pipe and smoke it.
(Score: 1) by khallow on Monday December 26 2016, @08:18AM
(Score: 0) by Anonymous Coward on Monday December 26 2016, @11:58PM
You just keep thinking about it, Einstein.
(Score: 1) by khallow on Tuesday December 27 2016, @09:30AM
(Score: 5, Interesting) by AthanasiusKircher on Monday December 26 2016, @03:18AM
The vast majority of math that matters to the average person isn't calculus or any advanced maths. Basic arithmetic will do for 99% of your day to day problems(percentages, price per unit, etc...). Maybe if you really get into understanding long-term planning, compound interest would be important. Still, by the time the average student has enough earned/saved for that to matter, they'll have long forgotten it.
Failure to understand compound interest has an ENORMOUS impact on people's financial lives... Probably more than any other math concept. It's the reason poir people don't understand how bad carrying balances on credit cards is compared to other loans. It's the reason stupid people make bigger payments on a mortgage (because the balance is higher) rather than paying off smaller credit card debt. It's the reason people suck at planning for retirement. It's a major reason how people get suckered into really stupid loan terms. Arguably, it was a major contributor to the financial crisis of the past decade.
This is NOT a small matter... This one concept easily ruins the lives of thousands (perhaps millions) every year when they make stupid decisions that a little knowledge of compound interest could fix (and result in vastly significant financial outcomes a decade or two later).
And if we as a society were at all responsible in the US, we'd spend a lot less time in high school math worrying about parabolas and hyperbolas and roots of some bizarre forms of equations... and more time doing stuff relevant to financial math until students can make reasonable life choices. (I say this as someone who taught high school math for a couple years.)
The basic algebra, exponential stuff, etc. to deal with truly basic financial strategies is an essential life skill for anyone trying to understand their finances.
Beyond that, another "more advanced" math topic relevant to everyday life is stats. Developing some sense of basic statistical intuition is nececessary to spot bad argumentation anywhere (whether from a politician or a distorted chart or graph in the newspaper or when your boss is throwing out "some figures" in a misleading fashion).
A lot of these topics doesn't have to do with technical fluency in doing the math in detail as much as intuition about how these things work... But it's hard to attain that intuition without at least some experience with the underlying math.
(Score: 2, Interesting) by Booga1 on Monday December 26 2016, @03:55AM
I get that, and I agree with you. I'd say the most valuable college course I ever took was statistics. It's just that, we were taught simple interest, compound interest, etc... in school.
I just don't think it's sticking in people's minds. Maybe people's financial lives would be better we drove those lessons home a bit harder instead of pushing calculus, trigonometry, and advanced algebra.
(Score: 2) by driverless on Monday December 26 2016, @05:13AM
Failure to understand compound interest has an ENORMOUS impact on people's financial lives... Probably more than any other math concept.
That's more than just a math problem, there's an overall failure to understand how loans work, period. For example a friend of mine who worked for a large bank dealing with mortgages (well before the GFC, so not ninja mortgages) had people calling up complaining that the tenants in their mortgaged rental property had moved out but the bank was still charging them interest, and how could they do that given that the rental income had stopped? There was a complete lack of understanding of basic financial issues, nothing to do with maths.
The solution in this case is to teach people money management. Teaching them abstract theories about compound interest calculations isn't going to help much.
(Score: 0) by Anonymous Coward on Monday December 26 2016, @07:29AM
You realize that when Trump's rental properties stop producing income he stops paying the banks? Sometimes before.
This is how all rich people operate - if they are not making money on it, no one does. And that is what the seminars at places like the discredited Trump U teach.
So average people are understandably confused and angry when this system of wealth 'creation' is not extended to them.
To quote the president-elect. "When you owe the bank a million, that's your problem. When you owe them a hundred million, that's their problem."
No wonder the Chinese are worried about President Trump. He is about to reveal to them that they have hella billions of problems!
(Score: 0) by Anonymous Coward on Monday December 26 2016, @08:09AM
When Trump's rental properties stop producing income he gets the secret service and foreign officials to rent them out.
(Score: 1) by khallow on Monday December 26 2016, @08:55AM
You realize that when Trump's rental properties stop producing income he stops paying the banks? Sometimes before.
Sounds like he's got it all figured out. Yay Trump.
So average people are understandably confused and angry when this system of wealth 'creation' is not extended to them.
I wouldn't use the term, "understandably". Average people don't have the competence or assets to back a $100 million loan. And a loan that big can threaten the long term health of the bank while no similar problem exists for a small loan. It's not magic why banks treat different loan amounts differently.
To quote the president-elect. "When you owe the bank a million, that's your problem. When you owe them a hundred million, that's their problem."
Perhaps Trump said that paraphrase of the quote, but it long predates him. It's attributed [barrypopik.com] to John Maynard Keynes at least by 1945 who at the time called it an "old saying". Assuming that's true, of course.
It's interesting how often quotes get misattributed. It's to the point that if you can't show the written work that the quote came from, then it's probably not true.
(Score: 2) by AthanasiusKircher on Monday December 26 2016, @06:52PM
Absolutely agree. I wasn't advocating for "abstract theories about compound interest," but rather essential applications of it first and then relevant theory/abstraction to begin to develop a deeper intuition. When I was teaching high school, one of the other teachers completely revamped the "general math" elective (what student who chose not to talk Algebra II took in order to graduate) to involve a huge amount of practical math, especially financial math. By the end of the course,they couldn't do symbolic manipulation for a great variety of algebra problems (that wasn't the point), but they knew equations to deal with loans, investments, etc. in depth and could answer detailed questions about how changing parameters would likely alter the outcome.
(Score: 2) by driverless on Tuesday December 27 2016, @03:08AM
Interesting, were they even allowed to do that? Here you have to teach whatever the gummint tells you to, using approved textbooks, typically whatever was trendy a few years ago when the last reshuffle in the education department was carried out. And that's another issue, the way the stuff is (required to be) taught. If they used Sylvanus Thompson's "Calculus made Easy" then many students would find it a lot less tough going.
(Score: 2) by stretch611 on Monday December 26 2016, @06:53AM
I don't agree that only the basics are needed for most people. And not just algebra and stats as some people have mentioned.
Believe it or not, even Geometry has uses for many people.
When you are a painter you use geometry to determine how much paint you need. You need to determine the area of the walls you are painting... as well as removing the piece of the wall that has a window. So help you if their is anything oddly shaped like a bay window or anything circular (OMG!!! pi!!!) You may suggest that it doesn't matter if they go over... but if you see the price of good paint in the hardware store, a gallon difference can be the difference between you or a competitor bidding on the job getting it. (also, custom paint colors can not be returned, and you want them all to be mixed in the same batch to make sure the color is even.)
Architects, artists, and practically any type of design people need to know it as well. You need to calculate the cost of materials on area and sometimes even volume of the items you design.
Even some gas station attendants need to know some geometry. Back when I worked for a gas station while in high school, I needed to measure the amount of gas left in the storage tanks underground. It was measured by sticking a wooden ruler into the tank and seeing how many inches of gas was in there. You can't determine the volume of gas without knowing how to calculate the volume of a cylinder. Admittedly, many places do this with electronic equipment and computers now... But, there are many smaller older mom and pop stations throughout the US that do not have the volume to completely modernize.
Not to mention how many times a use for the pythagorean theorem comes up...
Now with 5 covid vaccine shots/boosters altering my DNA :P
(Score: 2) by TheRaven on Monday December 26 2016, @12:49PM
sudo mod me up