No, they didn’t absorb these things.
They were forced to MEMORIZE them. The educrats claimed that this “stifled childrens’ creativity” and “killed their souls” and other such twaddle.
I cannot fathom how children today need to resort to a calculator to multiply two numbers together, much less do addition and subtraction. I’m taking classes at a junior college right now, and it startles many younger people when I can multiply two two-digit numbers in my head in less than a second without a calculator. Someone once asked for 13 times 13... and I just said “169” without even thinking about it... and heads turned around.
Didn’t everyone use to memorize the multiplication tables up to 15? That’s how I was taught as a kid...
There’s a huge number of things about mathematics where I cannot tell you the why, who, when, where and so on. I might have been taught all of these things at one time, but the why, who, when and where was useless. The only thing that mattered was the “what?”
But I know them to be true and I used them all the time in engineering.
We should dispense with trying to make all kids into self-actualized polymaths, accept that some of them are going to be drones and just tell some of them “Look, don’t give me a bunch of static about this. Just memorize this stuff. There will be a test.”
Shocking.
I didn’t like Math all that much, but I persevered, and got an A in the class by the end of it.
When I jumped up to IB, there was so much ground I had to cover in a short amount of time. I wonder now, if my math understanding suffered as a result. It brought home to me just how deficient the regular program is with math.
And yes, very true about the teacher’s college. If your GPA is too low, they won’t let you teach, regardless of the courses you took. This directly rewards the students who take ‘basket weaving’ and punishes the students who take calculus and linear algebra. And I have an arts degree!
They were forced to MEMORIZE them.
I have noticed that there are quite a few people who can temporarily memorize facts about math but it's basically like pouring water in a sieve because they don't ever really have a full understanding of the concepts.
For instance someone studying for a test might be able to memorize the formula for adding fractions. But the majority will forget this after the test, whereas someone who understands what fractions mean might not even need the formula to do simple problems, and yet will also be more likely to remember it.
Didn’t everyone use to memorize the multiplication tables up to 15?
No. Perhaps you were lucky to get a school that did, but my recollection is that most schools did not require full memorization of the times tables beyond 10 x 10. What would have been really useful is if schools taught the various tricks that can be used to mentally multiply all two-digit numbers, but I doubt many of them did that either.
When I was a kid, numbers didn't go that high ;^)