Eighth grade algebra
I took Algebra I in 8th grade. Algebra I and typing were the two classes I took in junior high that I can say I have used regularly for the rest of my life (so far).
In the school system I was in, there was tracking. Some kids got to take 8th grade Algebra I. The rest took regular math. The ones who took Algebra I in 8th took Geometry in 9th, Algebra II and Trig in 10th, advanced pre-calculus in 11th and Calculus in 12th. I got off that bus after 10th grade and took regular pre-calculus in 11th grade, then probability and statistics in 12th, along with a full year of computer programming.
I took four quarters of calculus in college and never used any of it outside of the exams for the courses. I took college physics that didn’t use calculus. I took physical chemistry in college and it didn’t use calculus. Basic algebra was as advanced math as I needed to make my career as an academic scientist.
Apparently, some school systems have decided to deal with the fact that many students are not prepared for 8th grade algebra by not offering it to anyone in 8th grade. The concern, it seems, is equity issues, and the answer was to level down. How this is good for the students who are bored by the lack of challenging curriculum escapes me. Happily, some schools are returning to a two-track system.
Not everyone is going to learn calculus. The reality is that college calculus is mostly a badge, not life preparation. And not everyone who takes Algebra I in 8th grade goes on to take high school or college calculus. But for those who embrace the challenge, and for those who actually need it for a career (e.g., engineering, physics, economics), holding them back for the hypothetical social benefits of leveling seems unfair to everyone.
Restoring 8th grade algebra
In the school system I was in, there was tracking. Some kids got to take 8th grade Algebra I. The rest took regular math. The ones who took Algebra I in 8th took Geometry in 9th, Algebra II and Trig in 10th, advanced pre-calculus in 11th and Calculus in 12th. I got off that bus after 10th grade and took regular pre-calculus in 11th grade, then probability and statistics in 12th, along with a full year of computer programming.
I took four quarters of calculus in college and never used any of it outside of the exams for the courses. I took college physics that didn’t use calculus. I took physical chemistry in college and it didn’t use calculus. Basic algebra was as advanced math as I needed to make my career as an academic scientist.
Apparently, some school systems have decided to deal with the fact that many students are not prepared for 8th grade algebra by not offering it to anyone in 8th grade. The concern, it seems, is equity issues, and the answer was to level down. How this is good for the students who are bored by the lack of challenging curriculum escapes me. Happily, some schools are returning to a two-track system.
Not everyone is going to learn calculus. The reality is that college calculus is mostly a badge, not life preparation. And not everyone who takes Algebra I in 8th grade goes on to take high school or college calculus. But for those who embrace the challenge, and for those who actually need it for a career (e.g., engineering, physics, economics), holding them back for the hypothetical social benefits of leveling seems unfair to everyone.
Restoring 8th grade algebra
College physics—all 2 years—required calculus.
Then thermodynamics—1 year—required differential equations.
I can’t remember what math fluid dynamics—1 year—used.
And I took Advanced Calculus for some reason.
You take a lot of math for an engineering degree.
@Dave,
I guess I took college physics for dummies. No calculus required.
The one quarter of biophysical chem I took was thermo: Carnot engine cycles; adiabatic expansions. Again, no calculus required.
My dad was an MIT-trained chemical engineer. My freshman year in college, I was an engineering student. When I came home for Christmas, my dad asked me “Have you learned how to use the slide rule?” I said “no.” He replied “You will never be an engineer.” He was right. I switched to A&S. I’ve certainly done my share of genetic “engineering,” but no calculus was required and no slide rules were harmed.
When I learned about Carnot cycles, the whole point was about the area under the curves. You didn’t necessarily have to do calculus. You just had to understand the concepts. In medicine, the difference between the glucose level and the A1C measure is basically about calculus.
@Kaleberg,
“In medicine, the difference between the glucose level and the A1C measure is basically about calculus.”
Not sure what “about calculus” means, but I’m 100% confident that neither the physicians, PAs nor nurses who discuss glucose levels and A1C have the slightest clue about calculus. Nor should they. I say this as someone who has been a medical school professor for 37 years.
Look, calculus can tell you the trajectory of a baseball when it comes off the bat, but the fielder who has to catch the ball can be very successful without doing the calculations.
As someone who has used enough calculus for work to see calculus in every day examples, I am dismayed at people who feel they have not used the math they learned.
Explaining the difference between inflation and price levels is trivial for someone with calculus. It is clearly confusing to a large part of the electorate.
The Laffer Curve actually displays an important result for those who have calculus. If you are near its top, it is hard to see which way is up.
How to think about the trade-off between fuel economy and travel time.
I had basic and advanced algebra in high school, never did calculus at all. Programming back then included a lot a algebraic notation, so I guess I used it, but I was in my middle forties before I ever needed to dredge up simultaneous solving for multiple unknowns. The analyst specified the method for the program, but I still had to verify the numbers during testing, and that I did the way I had been taught.
@Arne,
“The Laffer Curve actually displays an important result for those who have calculus. If you are near its top, it is hard to see which way is up.”
LOL! You don’t have to learn calculus to know the Laffer Curve is complete rubbish. I learned in junior high that every graph has to label the ordinate and abscissa and have units on both. The Laffer Curve had neither. There was never any way to know where you were on the curve. Calculus had nothing to do with it. It was purely a propaganda tool for the gullible.
You missed the point. The Laffer Curve was used as propaganda, but the idea that it discussed a relationship that can be described by an inverted U would lead to the fact that at its top the slope is zero. In real life, in which calculus is ever present, finding the top of the curve is difficult. (In the case of the Laffer Curve difficult = impossible)
@Arne,
You don’t need calculus to see that at the top of the curve, the slope is zero. It is obvious on casual inspection.
And yes, in real life, finding the top of the Laffer Curve is impossible, but that also doesn’t require calculus. Casual inspection of the graph makes that obvious.
I have no doubt that calculus has many important applications. Falsifying the Laffer Curve isn’t among them.
I did choose the Laffer Curve example to provoke commentary, but I would still hold that understanding differentials is important to many problems that actually have data.
@Arne,
Yes, of course. Important to many problems and irrelevant to many others. Just like any specialized methodology. Nobody is saying otherwise.
Joel:
I was aware you were beyond myself early on in education. The high school system when I was in it probably 6-10 years earlier than you offered 2-years of Algebra to which I engaged. Then it was a year of Geometry and one semester of Trigonometry. It was not till fresh year of college did I touch Calculus and zoomed through it after the military. We were young and I was in a hurry to earn a degree. We had planned a family. Switched from engineering (a dearth of jobs then) to business and economics.
My high school years of drafting gave me a skill which became obsolete due to CAD CAM replacing it in later years till there was a need for some to draw a plate and no CAD CAM was nearby. The ability to draft fades into history the same as the ability to splice rope and tie knots which my father taught me. Lost skills . . .
@Bill,
LOL! My dad, who was a Naval officer in the ’50s, taught me knot tying. I still tie bowlines every now and then. He also taught me Morse code (CW). He had an advanced class license, which he got in college, and could handle a semi-automatic key. I managed to get up to 5 wpm on a standard key to get my novice class license in 8th grade, but it wasn’t renewable and I never got up to the 13 wpm for a general class. My dad also taught me basic circuit theory and how to strip and solder wire. Who does that now?
actually algebra is beautiful: enough reason to learn it. so is calculus, though a good deal more difficult for some. still, a good enough reason to study it. the same reason to get what they call a liberal education. though both can be wasted on most people. i have my doubts that people who only know how to operate computers or program them can remain human in the long run.
back in the day of sailing ships, the word was that officers were pretty good at navigation and stuff, but hopeless at knot tying. there is a moral there. somewhere.
Well, calculus is good for calculating slopes and areas under curves anyway.
Otherwise, it was very challenging and I had to take two years of it while I was in college. Never found any use for it afterwards. Algebra has always found uses.
@Fred,
Calculus (and geometry and trigonometry) is good for many things. Nobody needs to tell me that and the point is irrelevant to the point I make in my post.
We apparently had similar experiences. I found calculus was useful to pass calculus exams, but for nothing else after that. I found algebra useful throughout my professional and personal life.
joel
it seems to me that our whole approach to education is wrong.
just as a place to start, there should be no “tracking.” students should be allowed to “take” anything they want. the teacher’s job is to inspire them to take things of value to them, either as humans, or as people who will need a job. then to encourage them to work through difficulties, or even dislike. “encourage” = teach them courage, which means lead them to teach themselves courage. and for those who have a special love (we call it talent) for something,”teach” them to fly…but not like Icarus.
High school was the sixties …
I did a year of calculus at university, never used it (in computer science*). Algebra I still use everyday and used it to teach community college basic programming as a process example: pick which parts need to be solved first and work your way out from there. Most students taking introductory courses from me were also at the introductory levels of math and because the math and computer science depts were the same dept it made for good cross-pollination
*I think often of arcs and tangents and arc-tangents; cusps, parabolic curves …
Unfortunately today government schools have become a social job system for most of the teachers (statistically the lowest IQs of licensed professionals) and a baby sitting service for the students—( test scores are still trending lower ) What has caused this? What changed since these commenters were in school? (What killed Rome —Free bread(welfare) and Circuses (video games)
@Jackson,
What are “government schools?” West Point? Annapolis? The Air Force Academy?
Probably these:
@Fred,
Then why call them “government schools?” They’re public schools. They’re funded by local citizens and overseen by school boards consisting of local citizens elected by local citizens. I guess you could call them “peoples’ schools.”
The same reason they call it ‘guv’mint cheese’?
‘Government schools’, the ones with all races & creeds, is meant to be pejorative.
@Fred,
” . . . is meant to be pejorative.”
That’s what I suspect, too.
Still the master of inane remarks.
You can blame the outcome on whatever you want and you quote the most common misconceptions. It has little to do with IQ when teaching. It has to do with being able to relate. If you can not get the simplest message across with your notable high IQ, you are a failure and your IQ was a waste.
Stop with the baseless remarks. you are attempting to foment and even at such an attempt you fail. Stop with the silliness.
I was in HS in the early sixties, I was also ‘tracked’ at least for awhile.
Algebra was no doubt my favorite HS math course. Did not enjoy geometry at all. Calculus was not offered in my HS in those years. (It may have been, to those who were still tracked.)
But I loved physics, and so that became my college major. I had some catching up to do when it came to calculus. Because it was not offered when I was in HS, I did not appreciate it was essential for physics. Since Newton invented it, it turned out to be very important. I should have guessed that would be the case.
You and I are of approximately the same age if you were in high school in the early 1960s. I studied algebra in HS, as well as calculus, and went on to study engineering in college. My main interest was fluid mechanics and thermodynamics but my university had us studying the Schrodinger wave equation for our introductory college level chemistry course, which was mandatory for all students planning on graduating. How does one understand the Schrodinger wave equation if you don’t understand calculus? If one goes on to study nuclear and solid state physics, how does one understand the various wave equations if you don’t have some grasp of calculus. Even fluid mechanics and thermodynamics require a fair understanding of calculus to begin to understand the equations used for entropy and enthalpy. The same could be said if one is studying electromagnetic field theory. Algebra, particularly linear algebra and matrix manipulation, would certainly be generally adequate for use in computer sciences, although when developing spline fitting algorithm it probably helps if one can recognize how the technique compares to calculus.
By the time I graduated with my BS Physics, I certainly didn’t love physics any more. I came back to it later on, as something I liked to read about, not necessarily to understand. I was taken by a comment made, perhaps by Richard Feynman, that nobody really understands quantum mechanics, they just learn how to use it. And I had one intro course in QM, as a senior, and I never had occasion to use it.
Praha,
yes, you never can tell ….who will need calculus, and who will emerge as a genius from the crowd.
Michael Faraday regretted his “lack of mathematics” but he invented the science of electricity and magnetism. had to leave the math to Maxwell.
as for me, i took a lot of math. was supposed to be pretty good at it. but not world class, found little use for it in my work, beyond simple arithmetic, but i was better at solving problems than the graduate engineers and accountants i worked under. i am pretty sure the math i had studied played a role in that, more in the nature ot “thinking” than knowledge of math facts or algorithms. surprised me because that is exactly the reason the old days teachers gave for studying math. new days teachers teach a lot of high end jargon (“associative law of addition”) and nothing about arithmetic, so we have engineers who can’t tell when their calculators give them answers off by orders of magnitude…and bounce million dollar apace probes off the surface of Mars because they mixed English and Metric numbers in their equations.
The Mars problem had to do with metric <=> english units conversions.
If only we were able to get away from those pesky metric units! All it takes is one little slip up.
Interesting story in the NYT about why those lunar probes keep falling over lately. In the most recent case, they had to make the lander tall, for various reasons, and now they are pointing out that if only everything had worked right, there wouldn’t have been a problem. How about that?
Must remember Murphy’s Law. (And lunar gravity is 1/6 earth’s.)
(Tall landers tend to fall over more easily in lighter gravity. The planned lander for lunar astronauts is going to be ‘as tall as a 16-story building’.)
Why It’s So Challenging to Land Upright on the Moon
NY Times – March 4
Two spacecraft have ended up askew on the lunar surface this year. It is easier to tip over in the weaker gravity on the moon than you may imagine. …
What is the total charge stored in a capacitor with a capacitance of 30,000 uF, and a maximum safely rated voltage of 50V? The capacitor has an ESR of 30 milliohms and is allowed to charge directly from a voltage source with an output impedance of 10 milliohms?
Followup: A system uses an average power consumption of 15 watts and is rated to operate from 20-50V. How long will this capacitor be able to provide current to the system before it falls below 20V?
It is IMPOSSIBLE to solve this problem without calculus. Yeah, yeah, I get it. You do not have an intellectually challenging job so you don’t need “that fancy math”. But someone has to design and build your damn iAmusements for you.
One thing that you can absolutely count on is for the proud to denigrate, poo-poo, and minimize that which they cannot do. Pride proceedith the fall.
Pete:
Thank you for your comment. I think you need to understand something here as we all come here and have different backgrounds. Me, much of the time I did throughput analysis for manufacturing companies to discern the best way to lay out a facility and get the best capacity to pinpoint the bottlenecks. The hard part to all of this was convincing people they do not need tons of inventory to meet demand. It costs money to have Inventory. Spent a lot of time on the shop floor learning the processes.
Nobody said Calculus was not necessary. We do not use it or at least I did not. After you walk away from your design, it was up to me to find the best way to plan it and have the necessary capacity. Theoretically, I am a million-miler+, just not on one airline. I still have a few hundred thousand miles on Delta. My job took me to quite a few countries in Asia and Europe.
We are an eclectic bunch of disciplines here. And relax a bit.
@Pete,
“ You do not have an intellectually challenging job so you don’t need “that fancy math”.”
LOL! Yeah, I guess you’re right. I’ve been a biochemistry professor at a medical school for 37 years. I’ve authored or co-authored over 100 scientific articles since 1982 that have been collectively cited over 9200 times. No intellectual challenges for me, I guess.
“One thing that you can absolutely count on is for the proud to denigrate, poo-poo, and minimize that which they cannot do.”
Please point out where anyone here has denigrated, poo-pooed or minimalized calculus. Take all the time you need.
“Pride proceedith the fall.”
I think the word you’re looking for is “precedes.” Heh.
Y’know, I don’t think your acumen, etc are being challenged here.
I studied physics, it got so if there weren’t equations involved, the material couldn’t be that interesting. All the same, I struggled with math. Faraday was sort of my hero, at that time.
But, after graduation, I never had a job that required higher math, unless you count Boolean Algebra as such (& I kinda doubt you do.) Some jobs need higher math expertise, others don’t. (People at work used to come to me for help with their Boolean problems. Does that count?)
I like your comment about having had ‘physics for dummies’ in college.
That’s pretty much how I deal with the subject now. With one intro course in quantum mechanics, taught by a very esteemed physics prof, and later learning that mostly physicists studing QM were not meant to understand it, it would make them crazy. (But still use it, as the most successful scientific theory ever.)
I got into learning about entanglement, or trying to, and appreciating that it has a lot to do with how the universe works (weirdly), and how it drove Einstein crazy (figuratively), Niels Bohr having insisted that various phenomena in physics were not really present unless/until they were observed.
I just spent 20 minutes writing a post about some of the finer points.
Covering the Anthropic Principle, as well as getting into the Least Action Principle.
It was not accepted, and I’m not going to bother to try further explanation.
Suffice it to say that it is not uncommon for physicists to believe that the universe could not exist if we humans (or other intelligent life?) were not around to observe it. Unless God is really keeping it going, perhaps.