Far from being dumbed down, we were taught principles which have stayed with us.
(You can't prove a negative was my expression, not the teachers--didn't realizew how I contradicted myself on that one DUH!)
To simplify: (not geometry, but same principle)
Prove you are not 75 years old.
The easy way, of course is pull out the license and say "I was born in 1954 which makes me 50" I just proved I was not 75 years old.
In geometry class I did not prove I was not 75 years old.
I proved I was greater than or less than 75 years old.
I was not dumbed down by any stretch of the imagination. Looking back, I realize it was the logical process we were being taught.
Your example:
If A, then B.
Not B.
Therefore, not A.
What is not in your problem is how you arrived at "not B"
You proved C.
I am a nurse and have done many, many dosage calculations in my career. Instead of being dumbed down, I always say a prayer of "Thanks" to the excellent teachers I had in algebra and geometry when faced with a complicated dosage calculation.
I learned how to set the problem up, how to solve it, & how to check my answer. Taking shortcuts instead of using a logical process would have made for alot of medication errors. (Okay, maybe I could call the pharmacy, but they do not allow you to call the pharmacy when taking an exam.)
BTW--forgot add this.
I am not an abtract thinker in any walk of life. For me to master anything, I must see it. I cannot do simple math calculations in my head...it has to be on paper. So it isn't that I cannot do it. It is how I do it.
For example, I am making window cornices in my home and putting up trim using many miter joints. Even after all I have done, I cannot go to the miter saw and automatically position it for an inside or outside angle. I must to place the blade on the wood each so that I can confirm the direction of the cut. So for people like me, logical shortcuts are dangerous and costly. LOL! Had I learned those principles in high school I would have been dumbed down.
Glad you like my freep name....