Yeah, no, the way we were taught was often lacking too. Definitely not advocating for the old school methods as a whole. It was still very prescriptive and the whole "show you work" mentality with a rigid methodology expectation meant that even though I could rapidly do stuff in my head by using these shorthand techniques, I still had to write out the slower longer methods to demonstrate that I was able to. For my ADHD ass, that shit was torture.

I think common core went in the right direction. Teaching shorthand techniques that may not have been naturally apparent to some students probably made doing arithmetic more accessible to some. But I think it was an over correction. They should have been teaching them the basics without the rigidity and prescriptivity, but following that up with giving them useful techniques/tools to make arithmetic smoother and easier for different types of thinkers. Instead, they skipped or breezed over the basics, went straight to the techniques and then maintained that prescriptive expectation of the "show your work" mentality to ensure and enforce the techniques are being followed properly.

I understand why they maintained that show your work mentality to an extent. The teachers need to be able to understand how you arrived at an answer, correct or incorrect, and identify mistakes in logic so that it can be fixed. But the entire point of those techniques is that you understand the underlying logic but find a method of thinking that makes it easier for you and makes sense. As demonstrated in this thread, there's a number of different shorthand methods, and different preferences for them for every person. Teaching and practicing all these different patterns of meta techniques to add numbers and forcing them to write them out and explain them in weird esoteric ways is the literal opposite of the point of the techniques. I have to imagine it mostly confused their understanding of the basic logic as well.