For what it's worth, I struggled with math in elementary school and especially high school -- I failed algebra I, then passed it with a D; then I failed algebra II before passing it* with a D. It wasn't until I was forced to take a business calculus class in my 20s that it started clicking, and I assure you the quality of instruction wasn't any better at the college level than it was in high school. (I did eventually graduate with honors with a math degree.)
Mathematics_education#Methods https://en.wikipedia.org/wiki/Mathematics_education#Methods :
> [...] Rote learning: the teaching of mathematical results, definitions and concepts by repetition and memorisation typically without meaning or supported by mathematical reasoning. A derisory term is drill and kill. In traditional education, rote learning is used to teach multiplication tables, definitions, formulas, and other aspects of mathematics.
If you do not memorize small things that you frequently need, it will slow you down.
But if keep memorizing things without understanding, at some moment your memory will return an incorrect result, and you will be unable to notice it.
They tend to have a surprisingly good handle on the specific topic being studied that they're failing. I can have them tell me what to do on a problem on the whiteboard, and do all the arithmetic and simpler things for them, and they're flawless.
They also tend to have problems in arithmetic and in getting confused on simpler concepts. Context switching is expensive and they lose working memory of the higher order task, and then make silly mistakes.
Most outside tutors work to try and solidify the higher level topic even further, by drilling the heck out of it... this conceals the problem for it to reappear on next unit. (And, it ossifies the new knowledge in a way that compounds the problem for next year).
I don't like the whole "layer cake" model of teaching math that "builds" upon other math in the way we do in the US. But to some extent, it is justified in places. If you struggle with basic arithmetic and integers, algebra is much, much harder.
‘Literally memorize’ as opposed to what? Counting your fingers?
Our entire society is organised so that even university graduates are very rarely called upon to sum two single-digit numbers.
Adding up purchases in a shop? The till does it automatically. Admittedly, the cashier will need to be able to make up change promptly - but a customer needn't check their change.
Paying for parking? There will be a sign listing how much money you need to put in for 1 hour, 2 hours, 3 hours and so on.
Picking 14 items in a warehouse? You only need to count one at a time. There's a chance to speed things up by picking 2 packs of 6 plus 2 singles? Then the computer will print that on the pick list. No computer? Then the boss will print a sign with a lookup table like "14 items -> 2 six packs + 2 singles" and tape it to the shelf.
Trying to figure out whether you can get 9 people to lunch in two cars, one of which is kinda small? Add it up on your fingers, or keep your mouth shut and one of the other 8 people will figure it out.
Just don't get into board gaming :)
Then if the maximum parking time is 3 hours, it's 10:15 and you want to know at what time you need to leave you take out a cardboard clock, set the current time, and advanced the small hand one, two, three steps. And to know whether you can afford both the parking and a coffee with the money you have on you you make two piles and keep the parking money in one pocket and the coffee money in another pocket. I got it. [I'm joking, our society is organised in such a way that you don't need to be able to read a clock or handle money.]
A jaw-dropping moment. Maybe school education is more important than we though.
If you are renting a hotel room by the hour, it is highly likely that the staff are poorly educated
The arguments against schools are generally made[1] by people who do not remember how it was before compulsory education.
[1]At least in Europe.
Not at all - you simply count hours using your fingers.