Posted on 02/11/2025 4:13:51 AM PST by MtnClimber
Unless young students learn the predicate mathematics for calculus, our nation will grind to a halt.
While Democrats focus on the liberal arts, which train students to be leftist activists beginning in grade school, it is the STEM studies that keep America functioning. As students ascend that ladder of mathematical logic, calculus becomes central to their ability to maintain our systems and invent new ones. Sadly, though, our schools are failing students, not just in teaching calculus but in teaching everything preceding calculus.
It is widely recognized among today’s undergraduates that the STEM field is at once among the most rewarding and the most challenging, promising well-compensated employment in the future while also demanding devotion and consistent concentration in the present.
A principal source of the demanding nature of the STEM curriculum is its solid mathematical core, the centerpiece of which is calculus, a cause of both delight and frustration for generations of college students.
Calculus, the mathematical analysis of change of continuous functions, was invented in the late 17th century by both Isaac Newton and Gottfried Leibniz, who were working independently of each other. Because Newton’s notational system was awkward and inconvenient, whereas the Leibniz notational system was intuitively appealing and easy to use, it is the Leibniz notation system that is in use today.
Because of the hierarchical structure of the topics in STEM, in which mathematics explains computer science and physics, physics explains chemistry, and chemistry explains biology, calculus finds itself cast in the role of the gatekeeper to STEM. And with that gatekeeper role in mind it would be highly illuminating to be a mouse in the corner of the first quarter college calculus classroom as the professor brings the daily class to a close.
(Excerpt) Read more at americanthinker.com ...
My college calculus teacher said you had to have good algebra to master calculus.
I guess I did, because I got my credits for 15 semester hours of calculus without the struggle some had and graduated with a minor in math.
Algebra is manipulation.
Back in my day, the folk that were good at algebra were good at common fractions because the four basic operations in fractions requires manipulation.
Don’t have much first hand observation with young folk today but I’d bet they aren’t good with common fractions because the teachers aren’t good enough at math to properly teach them and I guess calculators and computers can do the problems without being able to do them manually.
I was fortunate to get a great public school education.
By the time I got to high school I had mastered common fractions (algebra was strictly a high school course), could diagram sentences, and could find most any major capital, major country, and major river on a map.
That may be more education than many folk with college degrees today.
But you get what you pay for as most college is free isn’t?
Joey saw to that didn’t he?
I was tortured by math growing up.
My mother, for several years when I was in 2nd and 3rd grade, spent many summer hours with me (when, with six kids, I know she must have wanted some precious time all to herself) trying to teach me the Times Tables using flash cards while all my siblings were playing outside. I remember how torturous it was for me to think of everyone else having a good time, and here I was, my mother trying desperately to help me catch up in school, simply unable to learn no matter how she tried. My heart aches for her even now, thinking what must have been going through her head.
I was her “premie” born early at 2lbs 11oz back in the Fifties, and that was no insignificant thing. When I was six, they found out I was extremely nearsighted and immediately got me glasses, but I was far behind at that point. But she never gave up. What a woman she was.
Had to go to summer school for several years, my parent hired a tutor for me (some poor sailor off of a ship) and my 5th grade teacher Ms. Lang (who was a former nun who was also good friends with my mother) even tutored me on her own time, to no avail. I used to go to her apartment on the base at night. But it was no good. I just could not do math.
When I was in 7th grade in Subic Bay (George Dewey Jr-Sr High School) and Miss Shippen, my math teacher, was a young and attractive woman with very short cut blonde hair in the “Twiggy” fashion of the day, but with a very angular face, blue eyes, and a cool, forbidding countenance that very nearly made her...unattractive. But she wasn’t.
She had a very nice and trim figure, and wore very short (though not mini-skirt short) shoulder-less dresses, and wore heels. I remember thinking when she sat down, that she had really good looking legs which she always crossed professionally.
These were the impressions by Miss Shippen to this 12 year old boy who hated math with a passion, and went to summer school for a few years because of it.
Man.
Summer school was pure, unadulterated torture to me. It is one thing to be miserable in school knowing all other kids were there too, undergoing their own tortures.
But it was quite another thing to be in a classroom on a beautiful summer morning, having the thing you hated most in life being stuffed down your throat while all other kids were out swimming in pools, playing baseball, snorkeling at the beach, or doing whatever 12 year old American kids would want to do on a base in the Philippines.
In spite of all that-I think back to Miss Shippen. I do think she was a little bit gentler to me than she was to other kids. I was one of those anxiety-ridden, desperate kids who simply could not fathom mathematics, and when in class would just put his head down on the desk in abject despair, resting his forehead on his crossed arms. She had given up trying to engage me, but when she had to, I thought I noticed less of an edge to her. I don’t recall her being a mean woman, but she could be quite short with her students. And I thought she...took pity on me, as odd as that sounds.
Not enough for anyone else to notice. But I noticed.
In High School, I just gave up. When I graduated from High School, I couldn’t add or subtract fractions.
It was awful. I went straight into the Navy out of High School. But when I was in the Navy, I worked on a special project with a Tech Rep from Detroit Diesel Allison, and he was also teaching college level math courses to crew members.
At that point, I was determined I was going to get out after my enlistment and go to college, but as I wanted to get into STEM fields...my inability to learn math was a real problem for me.
But as we had struck up a friendship, he offered to tutor me at no charge. He got me to the point I was able to do entry level algebra, which was a huge thing for me.
My major was Chemistry, and boy, if it wasn’t for Jerry Wouters, I would have never made it. One of the prerequisites for my major was taking Physical Chemistry, which has a huge amount of calculus in it (huge for me, at least) and it nearly gave me a nervous breakdown, but I passed it!
That was 45 years ago, and I am pretty good at every day math now, and all these years, I wished I could have seen Jerry Wouters again and shake his hand in thanks. If not for him, I could have never made it through college.
I found what I thought was his address some years back after the advent of the Internet and wrote him a long letter of gratitude, but...he never answered, and I figured he probably never got it.
Point is, I had plenty of help along the way. I Thank God for those people...Ms. Lang, Jerry Wouters, and that poor Petty Officer trying to teach the XO’s kid (me) who would just put his face down on the table in frustration and refuse to listen...all of them.
Sigh. I wish I could have had the opportunity as an adult to thank them. I was so fortunate, even if it didn’t help me, that so many were willing to try. I wish there were better ways to teach math.
Now? I would have been SOL today, and no doubt, they would have pumped me full of Ritalin or something else. I am so glad I grew up then, in the circumstances I did.
>>It’s somewhat analogous to our predecessors using calculus to prove the Pythagorean theorem, so now we can apply it with simple arithmetic and a little algebra.
Umm.. I’m fairly sure the Pythagorean Theorem was proved WITHOUT calculus (Euclid’s Elements, Book 1, proposition 47, iirc).
One of my jobs in college was being a math tutor tor the VA. I tutored students who were going to college under the GI Bill and were having trouble with math, mostly algebra. I hope I did some good.
You hire out someone who can, or send the kids to a community college.
There’s also Saxon Math, probably the best math curriculum I’ve ever seen.
I used it with my kids and earned a lot as I went. I’d have to read the prepare the lessons ahead of time and because of how they cover and explain the material, I finally learned all that math that the public schools made so confusing and after decades of thinking I was bad in math, found out I was actually good at it.
They also have math from K - 12 but the place to start is with math 54, fourth or fifth grade. You can find much cheaper options for teaching the basics of skip counting,
addition, subtraction, multiplication, and division.
I find it difficult to get an audience on this topic, yet it is terribly critical that people pay attention. Very little of the faults in schools these days rest with the teachers. It is my experience that the students themselves and their parents are the problem. Students, as a general rule, don't care about anything but communicating on their phones. They do not apply themselves to the learning process, and then parents descend upon the teachers when their beloved little darlings get bad grades. Parents do, indeed, take these cases to court and usually win. That forces the schools to lower grade standards, provide an infinite amount of time for makeup, and no handle on classroom discipline. It even forces schools to allow the rabble to keep and use their phones during class.
I taught a technical class in high school for three years following retirement. That gives you an inside perspective most self-righteous outside observers never see.
I told my kids early on, YOU are responsible for getting an education, not the teachers. There are plenty of resources out there to learn the things you need to outside of the school.
Captain Obvious alert on the headline. Cucumbers, condoms, and conflicted sexuality have taken priority over STEM.
I can understand that.
The data shows that the testing for basic skills among teachers is sorely lacking.
Not exactly surprising since the job pool of teachers comes from the society at large which tests out much lower than most so-called developed nations.
But maybe I'm misinterpreting the objective data, nevertheless I'm sticking with my self-righteous opinion.
Excellent solution. Once I retired, I got very bored. Unusual circumstances put me into a local high school teaching Embedded Computing under a provisional certificate. (I had to get a certificate within three years.) I really enjoyed teaching; but, I saw the actual causes of public failure: Students and parents.
My class was well outside of the box for students. In a school of 3600 students, 25 joined the class. No matter how hard I tried, about 10 scored 95 or above and everyone else below 30. Students either engaged, or didn't. Parents of the low scored students often berated me for their child's low scores, even when I showed them how many were knocking out 100s.
I taught for three years. The school gave me everything I wanted anytime I asked. That amounted to over $30,000 worth of lab gear. Students routinely told me that the class was their most favored in all of high school; and, many selected college courses and career based on that class.
Getting a teaching certificate at the ripe old age of 72 seemed pointless, so I left after that three years. They were confident that they could continue the class; but, it turns out that deep subject knowledge was indeed necessary.
I tried to find private schools who would want such a course, but was ghosted following any attempt at contacting them.
I was at a church picnic last summer....the youth group (junior high school kids) were selling hotdogs and sodas....the kid couldn’t make change for a $10-bill...I don’t think calculus is the problem...
They were confident that they could continue the class; but, it turns out that deep subject knowledge was indeed necessary.
It is a mixed bag, for sure. Educators have the lame-brained notion that teaching skills can overcome lack of subject matter knowledge. I witnessed that as well.
I recommend addressing both sets of problems in order to discover meaningful solutions. A lot of work goes into the destruction of the school system. ;-D
Exactly!! I don’t think I learned anything truly meaningful in college. I bought four six-foot shelves of technical books over the span of my career. Education should never end; and, do-it-yourself is the premium method.
My son has completed Calculus I, II, III, and IV at ASU.
= 36.74 minutes
A wonderful solution is for schools to make it easier for old farts like me to serve as a teacher at retirement. They have to face facts: Anyone who settled for teacher’s pay did so because they couldn’t make the grade in engineering. Right now, I’d teach without asking for pay. I bet I’m not alone.
I’d teach without asking for pay. I bet I’m not alone.
Calculus is simple. If you can calculate and apply the expression nx^(n-1) then you are a calculus expert. The rest is math.
Thx!
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