Why does no one in elementary and highschool education bother to explain formulas to kids...

Why does no one in elementary and highschool education bother to explain formulas to kids, they are just forced to memorize it and work by it like a machine , never realizing what they're doing. This is actually a major problem in education.
How are you supposed to be interested in mathematics if you don't actually know what you're doing and why it's done that way.The only way is if you work through the formula yourself.

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it's true, one article said that the US public school math curriculum is "a mile wide and an inch deep" in this very sense. meanwhile chinks learn fewer concepts but in far greater depth, and perform better as a result. it's really just a "less is more" thing, but for some reason there's this obsession in western education about drilling math as computations. but the conceptual stuff starts to become more important as early as "precalculus" material i.e. trig and algebra, and particularly in calculus, which is why the US/canada have so many people flunk out at that level, despite being fairly conceptually simple math.

on another note, i'm an undergrad math major, and in any math course i've taken with math education majors present, their averages are consistenly 10-20% lower than that of the group of math majors. so it could also be a question of badly qualified educators. also, a lot of primary educators simply give up trying to teach math because they lack even basic math skills like adding fractions.

Is there any material closer to the "Chinese" approach rather than the US approach?

>yourself

there ya go

i meant asia in general. if you want material closer to that find literally any older textbooks. but honestly if you really care you can learn it yourself, there are tons of online resources. pretty much every basic math thing has been proven in depth somewhere on youtube or stackexchange

I don't know about others, but when I got older I realized that many of my math teachers growing up were brainlets who learned some sesame street version of "how to teach math" in teacher's college. I'm not sure that their understanding of the math was much deeper than what they were trying to impart on us students.
I went to allegedly good public schools in ontario btw.

The US cares more about the idea of education rather than its purpose. Schools care more for numbers in tables and charts than encouraging students to ask and understand. Schools are contempt with producing educated idiots who can find the area of a circle but do not know, or care to understand, why.

this is very true and pisses me off in hindsight

what are the best math textbooks for elementary - calculus range?
want to get my future kids prepared with textbooks that actually teach why math works and not memorization.

maa.org/external_archive/devlin/LockhartsLament.pdf

because most teachers don't care about the kids' understanding, they just want them to pass so they can keep their job and make more money.

After a few years of college I realized that the majority of my high school teachers were actually full fledged idiots. I always suspected a lot of them were stupid but it is a little disconcerting to understand how they stack up against the people at my school. It is especially clear when I consider the people in my majors only math classes that wanted to be teachers.

There is a reason people say that those who cannot do teach.

To be fair, I did have about two teachers in high school that were actually quite competent. My calc teacher and my chemistry teacher.

better pic showing area of a circle. As you infinitely divide the circle into more and more pieces, the rearrangement becomes a rectangle with area l*w=pi r^2

I lost all faith in reforming education when I went to college and saw who were the education majors. It all makes sense now.

Probably because a lot of "basic" formulas can not be fully proven without "advanced" methods and would essentially amount to a bunch of hand-waving by people who can't even construct the real proof themselves. It isn't, and won't ever be, practical to have someone with anything but a teaching/liberal arts degree in the public school system.

What are some good books that DO actually teach instead of just doing the formulas bullshit?

Because if you can memorize it there is literally no point in proving it. Math majors try to use being able to prove things as a point of superiority, when it is literally useless for engineers, chemists, biologists, architects, etc you get the point.
>"B-but I learn better if y-you prove it!"
This is why a math major is the brainlet path opposed to engineering.

>Probably because a lot of "basic" formulas can not be fully proven without "advanced" methods
this you fucking brainlet, you prove most of the "elementary" formulas that you are talking about with calculus, try explaining that to your average 6th graders
Well, I found out when teacher put the proofs for the formulas as a side material but not required for the exam that I understand that concept the easiest because a mathematical insight makes things "fit" together for example in physics and physics related subjects like those we use in engineering.
Just memorizing things by heart is for your dorky girls that get straight 100 in any theoretical subjects but struggle in practical works.

Where does the /pi come from tho

Pi is the diameter over the circumference of a circle

duckduckgo.com/

Because teachers arent smart enough to know shit.

The thing is you're going for this intuitive, visual explanation that works great BUT you have to pull a greek letter out of your bum. And basically, it's assumed that pi*r*2 is the circumference as an implicit first step.

Because the instructors don't understand them. They generally just read the textbook aloud

Circumference / Diameter =: Pi

Circumference / Diameter = Pi
Circumference = Pi * Diameter
Circumference = Pi * ( 2 * Radius )
Circumference = 2 * Pi * Radius

Arithmetic and elementary dimensional analysis should be intuitive before introducing elementary geometry.