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Thread: Why are we still teaching algebra?

  1. #76
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    Quote Originally Posted by Andrew Pitonyak View Post
    ...
    Why do doctors learn calculus and similar? So that they can calculate dosage. Reality, they do not calculate dosage, they look at a chart created by someone else who knows calculus. OK, the resesarchers probably do it themselves.
    Try giving medicine to llamas - there's no chart. Although it's basically a simple ratio calculation, since there are no meds dosed by the mfgrs specifically for llamas they are all "off label"and it gets tricky. In using meds labeled for sheep or horses you have to convert from the label dose in milligrams or the number of "clicks" for gun dispensers for the weight of the other livestock, then take into consideration the guidelines on a llama's physiology needs compared to the other livestock, then calculate the dose based on the weight. It can get SO confusing unless each step is written down and combined into one equation to give the # of clicks or milligrams to give for the llamas weight. Someone without math skills has to call the vet and ask. Then how can they possibly check the vet's advice for accuracy??

    I've mentioned this thread to several people. They all had the same response: it would be irresponsible to drop or reduce math instruction; what's desperately needed is MORE math in public schools.

    JKJ

  2. #77
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    "It would be irresponsible to drop or reduce math instruction; what's desperately needed is MORE math in public schools."

    Agree completely, but let's stick to useful math. An engineer must be fearless when it comes to math and many other subjects. But is is not practical to teach every subject in extreme depth. Most engineers must be jacks of all trades so we can get things done. Specialties (including arcane math) should be developed in advanced degree programs, personal passions or as the job requires.

  3. #78
    Quote Originally Posted by Bob Glenn View Post
    When was the last time you used algebra?
    You know, I happen to be very good with algebra. So stop picking on one of the few things I've mastered. I'm getting a complex.
    “Travel is fatal to prejudice, bigotry, and narrow-mindedness..." - Mark Twain

  4. #79
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    Quote Originally Posted by Dave Anderson NH View Post
    Now the 4 semesters of calculus and one of differential equations are a different story. I haven't used those since I graduated engineering school.
    I use algebraic principles all the time and I expect many do without even knowing it. However, I have not used Diffy Qs since my exam on them, I think I mave have used calculus a couple of times but it is extremely rare.
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  5. #80
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    Why do doctors learn calculus and similar? So that they can calculate dosage. Reality, they do not calculate dosage, they look at a chart created by someone else who knows calculus. OK, the resesarchers probably do it themselves.
    The knowledge math could likely set off an alarm in a doctor's mind if a chart had a misprint or typo.

    As was mentioned earlier it helps students to learn how to use their brain as much as it teaches a useful tool.

    But is is not practical to teach every subject in extreme depth.
    True, should we let bureaucrats decide when to direct students away from the path of higher learning to a path of low on the ladder wage slave for the rest of their lives?

    Math skills come in handy in everything from shopping for groceries and planning meals to paying bills and home maintenance.

    Reading, writing and arithmetic are the foundation of all education. With a meager beginning of engaging the human mind with the "three Rs" all else can be explored, learned and put to use.

    jtk
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  6. #81
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    Quote Originally Posted by Jim Koepke View Post
    Math skills come in handy in everything from shopping for groceries and planning meals to paying bills and home maintenance.
    And making life decisions based on more than hope. Math came in handy when I was trying to decide when to retire - for a given expected lifetime, for a given retirement age what is the break-even age considering a reduced income and the trade-off between reduced work-related expenses vs estimated increased avocational expenses, also considering the private insurance and Medicare numbers. After careful calculations I decided to retire at age 56. Best decision I ever made (besides the choice of life partner!)

    JKJ

  7. #82
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    Quote Originally Posted by Jim Becker View Post
    That's an example of what I mean about how math is being taught these days...useless operations. And it's not about algebra...it's about the strange thought processes they are teaching that make things more complicated in my mind. The fact that this is labeled as an algebra problem and the initial equation looks like one masks the reality that this "problem" is part of the "new-new-new math" methodology being taught in elementary schools in recent times.
    Nothing "new math" about that. The foundation of algebraic solving is that you simplify equations by performing identical operations to both of two equal things (the opposite sides of the equation) until you have a simple form that answers your question. That's what was being demonstrated there, with a very simple example. The real value comes when the equation starts more complex, but you start with simple to learn the techniques.

  8. #83
    Quote Originally Posted by Kev Williams View Post
    Here's why I failed algebra... below is a screenshot of a 'kids introduction to algebra'..,

    ================================================== ==

    ================================================== ======

    In what universe should I find it necessary to cancel out a +5 with a -5 and 'have a go at subtracting 5 from both sides', to end up with a 9 character equation to get to another 5 character equation-- I mean, what does +5 and -5 equaling 0 have anything at all to do with "what plus 5 equals 12"? The SIMPLE equation change is x=12-5 ...! THAT I can understand!
    Quote Originally Posted by Rod Sheridan View Post
    Kev, you can't simply move the 5 to the other side of the equation.

    You can do the same thing to both sides of the equation, and keep the validity of the equation.

    In other words you can add -5 to both sides of the equation, or subtract +5 from both sides. Obviously that's the same result, a different "visualization" is all.

    It's pretty obvious to you because you've mastered the skill and don't have to write it down, however what you are really doing is adding -5 to both sides of the equation............Rod.
    To begin, I didn't say anything about moving the 5 to the other side, the puzzle said that!

    Second, my calculation to get at the answer uses simple SUBTRACTION! Which for some reason doesn't get drilled into kids heads in school like addition and multiplication... example, off the top of your head, who here doesn't know what 7x9=, 6x8=, 3x5= --- or 2+2 or 5+8, etc... but how many of us have to THINK was 8-5 is, or 9-3, or 7-4? Easy enough, but me, I don't have subtraction memorized like addition or multiplication, simply because I was taught my basic addition, and then came the times-tables until they were second nature (and still are!) But while they taught us how to subtract, we were never taught to memorize any 'minus tables', at least not in my time ('72 grad)...

    My whole point here, is that I think a kid would likely find it much easier to understand that figuring out what X is involves nothing more than subtracting 5 from 12, and ESPECIALLY if kids had basic subtraction memorized. Maybe kids know subtraction better these days, I don't know, but what I do know is x=12-5 \ =7 makes perfect sense, but x= x+5-5=12-5 \ x+0=7 \ x=7 is complete nonsense!
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  9. #84
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    I use algebra all the time in my work, and not infrequently outside work. Calculus less often, but still shows up in both. Ditto statistics.

    But to answer the original question, we still teach algebra because many people WILL need and use it. We taught both our children algebra and higher math (they were home schooled). One is now a history professor, and probably uses any of it rarely if at all. One is a research scientist who uses higher math literally every working day. He wouldn't have had that opportunity had he not learned algebra first.

  10. #85
    Quote Originally Posted by Kev Williams View Post
    Maybe kids know subtraction better these days, I don't know, but what I do know is x=12-5 \ =7 makes perfect sense, but x= x+5-5=12-5 \ x+0=7 \ x=7 is complete nonsense!
    This might be nonsense to you, but my experience in teaching algebra to students of all ages indicates it is not nonsense. When I start with a simple equation, such as X + 5 = 12, and tell the students the process starts by isolating the x term, I usually have blank stares because they don't have any idea where to start. What you find obvious is not obvious to all. From a mathematical point of view, there is no such thing as moving a term or value from one side of an equation to the other. The "moving" is accomplished by performing identical operations to both sides of the equation in order to eliminate the unwanted variable or value.

    In the case of the equation above, isolating x starts with subtracting 5 from both sides. In my experience with students new to algebra, this has to be shown in detail, with every step clearly defined, so the student can understand the process and build on it as the equations become more complex. Crawl, walk, run. In time everyone understands the process, and some steps in isolating terms can combined as you described.

    To further complicate the teaching, some students don't understand the order of precedence in arithmetic operations, which can produce incorrect results in solving equations. In these cases, a few steps backwards for the class, or extra help for the individual, is required.

  11. #86
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    Quote Originally Posted by roger wiegand View Post
    How can you get through a day without using algebra? ie, i have a board 8 ft long and I need a one 49" and one 18", can I get them out of my 8 ft board? Answering that question by calculation is algebra, whether you like it or recognize it or not. Yes you could use a story stick and get a geometric solution, but I'll bet most of you take the calculated (algebraic) approach when staring at your wood pile. I use algebra 100 times a day, whether it is calculating angles, figuring how long a piece needs to be, or deciding if I will have enough money left in my pocket for a hot dog if I buy a beer.

    Just think of the endless discussions on this site of how big a pipe or wire one needs to serve multiple air tools or power tools. The answer is almost always simple algebra. Algebra is basically the study of equations, so whenever you say x=y you are asserting a hypothesis that is subject to proof, so 2+2 =x represents a very simple, yet useful, algebraic equation, 2+x=4 a slightly more interesting one. Ability to use a symbol for a number (x in this case) opens up a whole world of possibilities for doing calculation as well as describing general solutions to frequently encountered problems, like area=pi*radius squared for a circle. Isn't it nice to have algebra so that you can either know the radius and find the area or know the area you want and calculate the radius?
    I don't consider 2 plus 2 as algebra. 2 plus 2 is basic math as are most "daily calculations". Anyone can make something complicated, it takes some thought to make things simple. You don't need an algebraic equation to figure out if you have enough money in your pocket to buy something or if your board is long enough to cut two pieces pieces to length. That, sir is simple math.
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  12. #87
    Yes, but you do need Algebra to determine which package of crackers is the best buy at the grocery store w/ without coupon.

    If folks want to be ignorant, that's their choice --- certainly society still has lots of ways to punish such willful ignorance --- you get charged more at the grocery store for not finding the best buy, folks waste money on lottery tickets because they don't understand probability and odds, folks don't properly save for and invest in retirement, or they choose the wrong time and interest rate to refinance their house.

    But as a society, we have an obligation to offer future citizens the best opportunities which we can, and that includes an education which will make it possible to learn anything which they might wish. I've experienced both the best and the worst of what U.S. school systems can offer, and any school system which does not offer all possible subjects at all possible levels matched to each student's ability is a dis-service to those students, and society because the students with greater potential, who are not offered such opportunities will not get the best education which they can.

    We've got legislators who want to know why NASA has to launch weather satellites, when all one has to do to get the forecast is check the TV forecast --- we need better education which includes mathematics which is the fundamental language of science.

    This pretty much sums it up:

    http://matt.might.net/articles/phd-school-in-pictures/
    Last edited by William Adams; 09-02-2018 at 3:50 PM. Reason: add visual guide to a PhD

  13. #88
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    Quote Originally Posted by William Adams View Post
    What an interesting way to illustrate!

    JKJ

  14. #89
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    That is better than how a PhD was explained to me as something being Piled higher and Deeper.

    jtk
    "A pessimist sees the difficulty in every opportunity; an optimist sees the opportunity in every difficulty."
    - Sir Winston Churchill (1874-1965)

  15. #90
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    Quote Originally Posted by Kev Williams View Post
    Second, my calculation to get at the answer uses simple SUBTRACTION!
    How do you know what to subtract from what? You know because you have an intuitive grasp of algebra. Teaching algebra creates that grasp, and puts it on a firm foundation so you can do more complicated computations for which the answer isn't immediately obvious. How many sheets of OSB and how many bundles of shingles at 4 bundles per square do I need to reroof my semi gable-roofed house with attached lean-to roof, and how does the cost of that compare to the cost of a steel roof? There is a bunch of basic algebra to get the answer, even though you may never actually write an equation with an "x =" in when doing the calculation.

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