Algebra

Sunday, February 2, 2020

In the vernacular here at Yonder Mountain, I been a thankin’…

An’ a readin’…

An’ a watchin’…

An’ a listenin’…

An’ a wonderin’… why is it that every time the subject of educating our precious progeny comes up, some folks begin advocating we eliminate tried and true basic elements of the learning process?

It’s long been known that cursive writing aids development of fine motor skills. The over educated geniuses to whom we’ve delegated administering the education of our precious progeny have been trying to eliminate it from the curriculum for decades… with no real reason other than it takes time and practice to master the skill.

Fine motor skills? When IBM built a humongous campus in Charlotte, N.C. there was talk about expanding, perhaps even moving, some of their mechanical assembly manufacturing to Charlotte from up north. In the end they decided against it because, as was explained to me at the time, there was no ready workforce capable of assembling the intricate mechanisms. Fine motor skills… but some genius with an EdD is more capable of telling the community what our children need to learn in order to be successful, taxpaying adults.

Another favorite is math. Oh, they feign advocacy that math skills are necessary, but their actions state otherwise… unless, of course, our children need only to know how to cook rice and grits… perhaps flip burgers at the local greasy spoon. That needs to be put in the same stink-hole as the old adage that women have smaller feet than men so they can stand closer to the stove and sink while they’re cooking and washing dishes.

And the geniuses to whom we delegate administration of educating our children continue their attempts to be paid more for less…

Education, by its very nature, is foundational. Before advancing to the next phase, the previous subject matter must be conquered. Conquering must include understanding, not merely performing operations by rote. Doing otherwise is nothing more than setting students up for failure. Exempli gratia; before studii can understand why women leave dents in flooring with high heels they must first understand force multiplication, that if we take a little bitty 100 pound girl, put her in spike heels, that relatively small weight is concentrated on a very small area, the area of her heels, and can be significant. It’s easy to calculate the magnitude if we understand simple math.

In his Notebooks of Lazarus Long, Robert A. Heinlein attributes to ol' Laz; “Anyone who cannot cope with mathematics is not fully human. At best he is a tolerable sub-human who has learned to wear shoes, bathe, and not make messes in the house.”

If we stop and think about that a little, just a little, it really isn't too far from wrong is it.

A favorite example of geniuses on the wrong track is algebra. We have some teachers who’d have us believe most of our precious progeny will never use algebra, so they ask why it's even taught. To be sure, algebra can be difficult to master, but only because by the time we’re capable of understanding the underlying concepts we’re used to doing all our ciphering with numbers, not letters… used to working with specifics, not generalities. Properly introduced, that’s nothing more than a speed bump someone’s saturated with diesel fuel… a couple of knocks and the barrier falls to pieces. Algebra is a transitional subject, like the concrete block laid between the footings and wall plate of a house, it’s somewhat useful on its own but is absolutely necessary as the foundation for other subjects.

As a practical matter, will any particular studii need to know that (3x^2 – 14x + 127) is a prime polynomial? Probably not, but it isn’t a matter of understanding a specific operation. It’s that foundation dealie, the process of getting from one level to the next and to throw out such an illustration is a prime example of using information, or an example, out of context.

Will every studii need to know 127 (decimal), 01111111 (binary), 01000000 (Gray, a specialized binary code), 177 (octal), and 007F (hexadecimal) are all the same magnitude? Probably not, unless she’s going into one of the pocket protector fields, and possibly not even then. But there are also those situations when flipping a binary 2 or 4, depending on the hand, at some idiot who desperately needs it is a must… except the flipp-er also needs to be good with his hands in other respects in case the flip-ee takes offense.

One might believe accountants don’t need to understand anything but addition and subtraction, debits and credits. I once had a company controller explain that he made 3 percent on his money by paying me in 60 days instead of 30, even if he paid a 1.5 percent late fee. “I offer a 2 percent prompt payment discount if you pay in 10 days” said I, and he repeated that he got 3 percent by paying me in 60. So I asked if he would agree a 2 percent discount would be the same as investing money at 2 percent interest. He agreed. So we had a lesson in the time value of money, and compounding, using algebra, in which he learned that investing his money with 2 percent interest paid every 10 days his money would double in 37 periods… 370 days to double his money… a 100 percent effective annual percentage rate or APR. He started paying our invoices in 10 days and asking other vendors to give him a similar prompt payment discount.

Won’t use higher math after high school? There certainly are those of us who must use relatively complex math each and every day. Not just the pluses and minuses but the timeses, gazintas, and more; powers, roots, functions, sets, transforms. And those funny little Greek hickiebobs. Math is the basic language of the universe, of thought. We use math for triangulation, calculating roof geometries, the slope of a road or incline, calculating distances with only basic tools, phase relationships, vector forces, mapping coordinates, playing pool, writing, writing poetry, music, and timekeeping. Some of us even work with other than 1s and 0s, outside of the digital world… sometimes with pi on paper and pie in the other hand.

We can talk about calculators, computers, iPads and fast internet service, how they’ll make doing school or work work easier. How do any of these contribute to understanding? Isn’t education all about understanding? I keep thinking back to my calculus instructor in college telling us “We’ve spent the last semester and a half learning how to do things the hard way. That was so you understand the concepts. Now we’re going to learn the easy way.” In the previous class she’d given us a test with only one (1) question on it… one question that took 6 or 7 sheets of paper to work out, and required us to show our work.

Studying math teaches us to follow a process toward a goal. Nothing we do can be performed without following some sort of process, at least in the beginning and before we’re slapped with an epiphany about the subject at hand. We can’t build a house beginning with the roof, or the walls with no foundation.

Understanding math enables us to evaluate life and the world around us, eliminate superfluity, and focus on the necessities. Administrators of our education systems don’t like it because we might begin asking questions.

Processes… some time ago I was swapping war stories with a Semper Fi Bro. To keep things in perspective; the difference between a fairly-tale and a sea story is that fairy tales begin with “once upon a time” and sea stories begin with “now this is no bull.” War stories are worse, generally with a soldier involved.

Back when he was a crewleader on a piping project out west in the middle of BuFu, Nowhere they were pressure testing a ¼ mile section, seriously behind schedule due to a number of unforeseen challenges, like metamorphic rock where pipe was supposed to go, and in their rush to get back on schedule they opted to use compressed air instead of non-compressible water because either was allowed in their test plan. They had a weld on the end of the pipe fail. “Man, the flange on the end of that pipe blew off and landed 5 miles away. Where it landed looked like a bomb went off.” “That’s a lot of force,” said I. “Not really. We were only working with 750 PSI (pounds per square inch).” I disagreed about the force, and knowing where he’d been we ciphered it out... after some discussion. There might have been adult beverages involved, and cigars, so we weren’t necessarily in a big hurry… but I’ll admit to nothing on the off chance one of Speaker Pelosi’s understudies gets wind and tries to take away the EGAs (Eagle, Globe, and Anchor) we earned all those years ago for violating some imagined law. Those folks are diligently trying to take away anything people have worked hard to earn aren’t they… Presidential authority, assets we deplorable working stiffs have accumulated, anything and everything they can get a grubby Mitt on.

In order to determine the force applied across a surface by a pressure we must know the area of the surface. They were working with a 36 inch round pipe. There are at least 2 methods to determine the cross sectional area, the area of the open end of the pipe that was capped off. First would be to take a string, run it around the inside of the pipe, then lay it on the ground in a parallelogram and multiply the length of the base times the height. The second, and easier, method would be to use a formula developed by those ancient GreekGuys, Pi times r^2 (the circle radius squared). Much, much easier and more accurate. We can get out to better than 3 decimal places with that baby. Both methods were actually developed by those ancient GreekGuys, and each requires algebra.

So we have Pi (3.1416, rounding to 4 decimal places) times 18 inches (½ of 36) squared = 3.1416 x 324 = 1,017.8784 square inches of surface area.

750 PSI means we’re applying a force of 750 pounds to each square inch of surface area of the cap across the end of that pipe, which gives us 750 pounds (force) x 1,017.8784 square inches (surface area) = 763,408.8 pounds of force pressing against the capped end of that pipe, ignoring insignificant zeroes and the process of cancellation of units. If we consider they had a ¼ mile of compressed air, in effect a ¼ mile long compressed spring, exerting that amount of force, they had a serious amount of stored energy and it isn’t inconceivable the landing zone of the cork in the end of their pipe might have looked like a bomb exploded, because that’s exactly what they had when the setup blew… a bomb.

Okay, so it might have only landed 2 miles away. The airborne distance and potential damage was still significant, and if it was legal here in Tennessee I’d wager he’s still requiring his welders to calculate the force applied during a pressure test when they do one… lowly welders… lowly in the eyes of some, that is.

So what happens when we aren’t taught algebra, and geometry, in school? There could be serious safety issues, for one, each and every day on each and every job no matter if it’s a pipeline welder or a stock clerk at Wally’s because they don’t understand the potential hazards of their jobs. We use algebra every day whether we know it or not.

What happens to the kid with a driving interest in science, making stuff work, inventing stuff to solve a problem who doesn't have the tools to proceed? What about the kid who doesn't know what she wants to do in life, then stumbles onto something that flips a switch... and it's off the the races because the fire was lit?

Cutting basic, and necessary, elements of children’s education is just plain igner'nt for any adult to advocate, pure laziness when suggested by a freeloading “educator.” Freeloading educator? Not all of them but if the Foo Bird poops, ya gotta wear it.

Teachers charged with educating our precious progeny must have support from the system administration, and the community, to shield them from minutiae so they can teach those who want to learn don’t they. If those determining the curriculum don't know the subject matter and how it’s used, that's a problem too.

And then there’s ol’ Laz again; “Don’t handicap your children by making their lives easy.”

But what do I know. I was just one of those kids whose life was changed by an electrical spark, a high voltage arc actually.

Bzzzzzzt!

Royce Burrage, Jr.


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