Tadzio wrote:
"Understanding" is the fraud. "Memorizing" is less of a fraud. Radical Behaviourism revealed the frauds decades ago.
One of my earliest many interests of the fraud came about when I tried to determine why 19th century "synthetic division" in algebra was called "synthetic" when the technique was no more contrived than doing long division in arithmertic. The "understanding" used in doing arithmetic is no more than "rote memory" used so long and so often that it is no longer labeled as "memory tricks", but is then regarded as an "understanding". The "memory tricks" are readily apparent when a person use to using base-10 Arabic Numerals tries doing "simple" and "easily understood" calculations using Roman Numerals without taking the detour of firstly converting them to Arabic Numerals (what is MDCCCLIX times CDLXXIV???). (All the "rules of logic" are "memory tricks" too, just think of reading right-to-left versus reading left-to-right).
The movie "Rain Man" pulled the "arithmetic versus understanding" trick with making change for a $Dollar$, but using an older "Pound and Pence" system would make the "normals" no longer normals with understanding.
Trying to exploit "Prime Numbers" as displaying an "understanding" ends up revealing no more than an "understanding" of the Zodiac of rules of "rote memory" as "belief".
These issues lead to the "love/hate" relationships between philosophy and the insult of reductionism, like everything Humanity knows being reduced to long binary numbers on the internet. Sure, "Casper the Friendly Ghost" has "wisdom and deep meanings".
Tadzio
See, I understand things in math, I never said I was good at arithmetic. Manipulating numbers like that is for a computer. That doesn't mean that I can't understand things as arithmetic isn't even at all the same as mathematics. That just means that they don't teaching understanding in school - which is something you'll definitely get my agreement on for math. Doing arithmetic isn't understanding, its taught as memorization.
All I see that you really are arguing is that math education is terrible. You completely have my agreement in that. And in my view a good math education would include understanding and
thinking, rather than just memorizing patterns of arabic numerals.