Regarding foreign languages: I took three years of French in school, then had no contact with the language for 40 years. Then, when traveling to France for the first time, I was amazed how much of the language came back from somewhere in my memory. Not verb tenses or declensions, but simple vocabulary. It was enough to keep me out of trouble.
Try John C. Calhoun.
Although there have been people going from VP to President (John Adams, Van Buren,…) no one has done it in the opposite order.
Duck and cover.
I have to say that I thoroughly enjoyed wood shop. I also learned to sew a seam, sew on a button and I have used all those skills. Nothing I learned in school has been totally useless. I wish I had learned enough French to become totally fluent, ditto German, but that’s my fault. I certainly can count to ein Tausend in both languages.
Oh, come on now! That hurts! LOL
My 2 years of German have been useless. Haven’t used it überhaupt.
The year of Latin, OTOH…
I’m seeing two themes in this thread:
- Teachers are told they have to teach a subject they themselves are ill-prepared for, so they drop back and punt.
- Especially in languages and shop, a lot of students desperately need not just the course material but how to learn it; they need someone to tutor them in the unspoken basics that more proficient people take for granted. For example, there should be a pre-Shop class on “how to not be clumsy”.
Sorry, got turned around – Tompkins was VP under Monroe.
A tie between square dancing and short division with remainders. Of the latter, I recall being ticked off to learn we spent all that time on it and it wasn’t even real math.
Girls can’t…
I’m not even sure what a Quadratic Equation is but later in life I took up, as a hobby, scale modeling. Often I would have measurements (perhaps in feet as in 6.6 feet or even meters) of a real thing and would have to come up with a measurement in inches or fractions of an inch. Eventually, I’d come up with a “conversion factor” (as I called it), a single number, usually a decimal, that every measurement would be multiplied by to get the measurement in scale. Sometimes, I be working off JPEGS and would have to go from pixels to measurement of real thing to measurement in scale. Then I’d pick up the plastic and the real fun would start.
I kept one on my desk when I was designing roads and running out materials lab. Got some interesting looks.
Thread 
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Simply, as in @lobotomyboy63 's link to real life examples, any equation that involves multiplying some unknown quantity by itself, so you get an x², with or without other stuff.
ETA: okay, technically it means an equation that the highest exponent it involves is ^2.
Our shop teacher only had two full fingers. We built a chess board, mine was functional but slightly crooked. In university, we had a Machine Tool engineering course where we used milling, numerical control and dozens of other machines. We built a vice. We built a strobe light in electronics, and an engine in Auto Mechanics as a group. Not to take home. None of these things were useless, exactly, but I cook more than I weld.
Arrowsmith and its complete turd of a protagonist.
Or, if the equation has two variables, it could have an xy term. Thus, for example,
xy = 4 is also a quadratic.
I do not know how you define “quadratic”. But I really think it needs a “^2” somewhere to qualify.
I think “2de graads” (what we call them in Dutch) equations are a useful tool in teaching basic maths skills. As a stand-alone skill I’ve found little value in them.
We could all use some more numerical skills.
Educators have a love for “neat” models that you can “solve”. In reality that only works in geometry.
As a result most people can’t figure out the most simple strength calculations, Electrical systems are a complete mystery and thermodynamics is like black magic. Learn people to ballpark stuff.
For most calculations 2.5 is an adequate placeholder for pi.
You should get a passing grade in physics, chemistry and maths if you are in the correct order of magnitude and use the correct dimensions.
I think my economics classes where the clearest waste of time. That shit uses numbers like they mean something. Some of the theory behind them have some merit, but doing actual sums in macro economics is just pretending to be something that it is not. My wrong answers based on a typo have as much chance of being correct as the “models”we used being applied “correctly”.
I imagine that’s how these formalized relationships start…people notice a pattern and try to make predictions based on data.
From the web:
The quadratic equation in its standard form is ax2 + bx + c = 0 , where a, b are the coefficients, x is the variable, and c is the constant term. The first condition for an equation to be a quadratic equation is the coefficient of x2 is a non-zero term(a ≠0).
The ax2 should be shown as ax squared, i.e with a superscript. We did tons of problems like factoring ax2 + 5x + 6 =0. That factors to (x+3)(x+2)=0, so one of the terms in parentheses must equal zero. x = -3 or x= -2.
I have a photo of my mom’s third grade class, waaaaay back in the day. If I had a time machine, I’d go back to that moment and ask the little boy toward the end of the row in the front what he wants to be when he grows up. I wonder if he knew he was going to be a doctor—our family doctor, in fact.
That probably explains a lot of the things we learned and ended up not using. Educators give students a start in a lot of things because young folks often have no idea what they want to do with their lives. My mom didn’t need the science class like our doctor did, but you don’t know who’s going to do what later so they all learn some of it.
I hated square dancing (they made us do it in P.E.) but I knew a girl in the class one year ahead of mine who started her own dance studio. And as posted upthread, sometimes the intent isn’t manifest—they had us square dance probably at least in part to teach us to interact appropriately with girls. So was it “useless” because I haven’t square danced since, or did it remove some of the boys’ rough edges?
We boys all took wood shop in middle school. That’s partly where I learned how handy I am NOT. But I took senior foods in high school and learned that I really like cooking. So for electives at least, it’s a buffet system of sorts…leave what you don’t like and go back for more of what you do.
I’ll grant that you maybe could’ve made that argument about my younger self back when said self said it seemed unutterably stupid to have to take a year of French instead of studying stuff that seemed more useful as well as more interesting. Oh, sure, in my case, it apparently did turn out to be exactly as big a waste of time as I’d figured — but, okay, putting aside the kids who would’ve chosen to study it, let’s assume for the sake of argument that some subset of kids would’ve chosen to study something else entirely but (a) got forced into this, and then (b) wound up realizing they had a knack for it and an appreciation of it, such that they went on to get some use out of it.
I can maybe see that. But: multiple years of it?
Hence my question: how long should it be, for that subject, before we let a student decide to leave it there and get something else entirely?