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I'm really shocked that somebody who is an engineer would be asking this question.
When children are in elementary school--and even when they are in high school--their future college major, as well as the career area that they will eventually choose to enter, are both unknowns in any real sense.
If you don't teach algebraic skills to kids who might later decide that they want to enter the field of engineering, or chemistry, or economics, or business administration, or other fields that require mastery of algebra and the more complex math courses that require a foundation in algebra, then you will essentially block kids from those career paths.
In my case, algebra is something that I never used beyond my undergraduate studies, but if I had chosen a different career path, it is entirely possible that I would have been severely handicapped without the mastery of algebra.
OK, I'll tell you really why. In the wake of 1980-s, one guy was sitting in a hidden well-guarded facility in the USSR, near Moscow, watching the screens that were monitoring the world for the possible nuclear weapons launching. At some point, he saw on his computer screen that from a certain point in the US several nuclear missiles were deployed and were flying to the USSR. His next step - as his orders dictated - was to launch Soviet missiles in response. The picture on the screens was clear - USSR was under American attack. He had several minutes before it would be too late. He hesitated to fulfill the orders and started THINKING. He figured out that all the launces were from the same point that was strange because US had many areas where these missiles were located. He had a couple of minutes left to make a decision. He analyzed the situation and did not hit a button. Now we all are alive. He, as Wiki says, is still with us, too. If he didn't have a well-trained brain, we would not be here today. Ave, human intellect. Go study differential equations, and all gods bless us all.
The point is not that we should not teach Algebra. We should.
The point is we force algebra into simple problems and needlessly complicate them. Then when a average kid is 25 they can't do any simple math. Instead of having the right math for their intelligence level given to them they have had a bunch of stuff they will never have a need for clouding their minds. I don't know how many people I tutor who say "I have been through pre calc or algebra II. but then don't understand simple concepts.
There is no reason to solve for x in 97% of simple problems. We shouldn't have to "set up" anything for a problem this simple or to figure out how many feet you travel in 1 sec at 80 mph.
This is said case: Kids sit there and go okay... part over whole equals.... or no it's times or wait... no it's whole over part times... no equals... it's equals. variable over 100... yeah okay that's it. I watched my son do this for 5 minutes to figure out 40% of 200. I thought my son was trying to figure out something like a constant substitution kind of thing where he was solving for a variable. When I came over there and saw him floundering over figuring out what 40% of 200 I had to laugh. I just said to him. What is 40% of 100.. he answers 40. So what is 40% of 200. He immediately said 80. Then I look at his notes he has 4 pages of notes on percentages but he is solving for x each time. As I read the notes I understand why he's having trouble. The teacher was writing all of this on the board and he was having trouble keeping up writing, and most of his notes looked incomplete.
My son is not the smartest, or quickest to grasp concepts but he is not dumb, both of his parents are "educated" (we have the paper, the definition of "educated" is debatable) and we can solve the problem much faster.
To us 40% of 200 is a no brainier. I wouldn't have even thought to set the problem up like the teacher was having her students set it up.
We were not driving, we were in a break room arguing over braking distance and reaction time on a motorcycle vs. in a car.
The most complicated thing I have ever had to do as an engineer was figure out a bunch of radii not on a blueprint. Everything else I can find at engineering tool box, or solve with a simple algebra triangle, maybe a constant gets thrown in.
An old school slide rule, vernier caliper type engineer was arguing with me ( he is my boss). He said to me "I feel bad that you new guys have to rely on technology so much." I knew where it was going, because old engineers like to flaunt their superiority and offer backhand humble brags in the form of concern. And I responded. "Oh you mean how you guys used to rely on a thousand page book full of tables, and that not having the book is the exact same as not having the internet or software." He said "No I mean you can't solve problems without the software." (which is not true at all.)
I said "what is the locked rotor current of a 3 hp 3 phase SCM motor at 460v" he just laughs and walks off. Why because he knew he need to look it up in a table he didn't have on hand. No one remembers every formula or algebra triangle, everyone know simple ones like PIE and EIR maybe power vector triangles, but beyond that your going to have some sort of reference and these days companies don't even want you remembering things. So what if the software is a shortcut, its not the 60s where you could scrap titanium pieces and say oh well. Everything is lean and there is no room for error, hell I get requests daily to shave 3 or 4 seconds off a process because it means 30 more widgets at the end of a day.
haha this debate has been going on for a long time. Forty years ago in high school I had a job as a lackey at a small business. I had been accepted to college and was planning to major in econ.
One day the accountant excitedly handed me a piece of paper with a percentage problem on it. It was something like say, what is 43 percent of 271. I told him I would just set up an equation: 43/100=x/271 and solve for x. "You see?" he said excitedly at the secretary at the next desk. "They're not teaching these kids today! They're getting this algebraic stuff!" Not exactly quotes, but I do remember distinctly that he used the word "algebraic," voice dripping w/ contempt.
Then he told me that I should just multiply .43*271.
Now I have to do conversions all the time (a la OP's example) because my hobby is distance running. Runners think in minutes per mile; treadmills give miles per hour, and to make it worse most races are in kilometers rather than miles. I have all the shortcuts down because I've done it so much, but I'm still glad I was taught the algebraic principles in high school.
But maybe you would've naturally gravitated to another line of work, one which didn't require high-level math...
Instead, I "gravitated" to a "line of work" where my advanced math skills could be put to good use. My "line of work" is one where a thorough understanding of advanced mathematical concepts is an absolute requirement to even be considered.
Now, had I been restricted to the basic mathematical concepts provided by a seventh grade education, sure - I would have had no choice but to "gravitate" to another "line of work."
The economic world runs on the point slope formula. If you don't cover your fixed costs you go broke. Algebra.
The economic world can ignore the depreciation of durable consumer goods for the last 60 years.
The Laws of Physics do not give a damn about economics. There were 200,000,000 cars in the United States in 1995. How many are still working today? What have economists said about the depreciation of all of that junk?
I guess the depreciation of all of the under-engineered junk sold to consumers doesn't count as a fixed cost.
Seemingly the issue is no one actually knows what math is anymore. All I keep getting from people referencing math is that all it is is a bunch of numbers and operations and such. Those things are only tools to mathematics. Mathematics is a study of logic and problem solving. Literally nothing in science can be done without logic and problem solving and building these concepts through rigorous exposure to manipulation. Surer you can know that 0.075 is 7.5% but what does that actually mean?
There is a big difference between an engineer and a mathematician in what you need to know and understand. this is teh primary reason I ditched my aerospace engineering training for pure mathematics. Math is the study of the logic, engineering is the application of formulas, generally in a plug and chug method. However both must at least be able to use the knowledge of not only algebra but basic calculus.
So that is why we need to be teaching kids things like algebra, it is logic, the numbers mean nothing, it is the understanding of how things relate and can be manipulated.
Algebra teaches logic as much as it teaches math. I haven't used algebra since I was a kid, but the logical thinking is used daily - although my wife would disagree with that last statement!
I agree. Logic is an intellectual skill that separates the men from the boys (and women/girls too, of course). Logic is used in other things than math or science. For example, you use logic in composition. You won't construct a concise coherent paragraph, or even develop your argument in a convincing manner without logical reasoning. Ironically, using logic in composition actually makes that essay a "plug and chug" thing to write. Foreign languages are very often logical, especially compared to your first language. Finally, you can't be taught verbatim everything you need or want to know. Many things, you'll have figure out for yourself and that logic you obtained from algebra will be your best tool.
However, math can be overdone, sometimes with the best of intentions. The biggest mistake my magnet high school science curriculum did was all that high algebra stuff they insisted on starting out with.....just to teach us Ksp's with that quadratic equation baloney or logarithmic expressions just to figure out complex stoichiometry in quantitative analysis. Turned out, in college or the MCAT or DAT, or GRE it was just that plug and chug thing you needed to know. All that other garbage was just a distraction and resulted in way more headaches than it was worth. Save that garbage for engineering school.
But for many it is necessary to master intermediate to higher math for math's sake - in order to understand numbers and how they "work." A good example is statistics - specifically, biostatistics. There is an "epidemic" of statistical ignorance, running rampant in part because people have limited knowledge of numbers and their operations and cannot discern the difference between the correct and incorrect use of statistical tests. I see it all the time. You really need good higher math ability to critique statistically-based conclusions. There are way too many people inept at this.
Basic algebra should still be taught even to those who may only need it to balance a household budget. No basic algebra, no HS diploma, not even in home ec.
In my work I use high-level math on a regular basis. If I had been restricted by someone who decided I didn't need any more math than what I had learned by the seventh grade, I'd probably be cutting lawns, flipping burgers, or washing dishes.
I tell my students that every subject you learn trains your brain to think in a different way and what you take away from that class is the brain you developed. However, algebra is one of the more useful maths to learn and I think geometry is the one that trains your brain in ways you'll use for the rest of your life in decision making.
I think geometry is the one that trains your brain in ways you'll use for the rest of your life in decision making.
Absolutely!
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I tell my students that every subject you learn trains your brain to think in a different way and what you take away from that class is the brain you developed. However, algebra is one of the more useful maths to learn and I think geometry is the one that trains your brain in ways you'll use for the rest of your life in decision making.
