Remember Geometry? What was the point of that class? Well, if you are planning on being an architect, it is to some degree your core set of skills. But for the vast majority it was a PITA class that everyone dreaded. After all, you had to learn those theorems and then do the proofs, which was the part everyone HATED. Most people have a very difficult time doing proofs and typically the failure to grasp the method of proofing can cause one to fail the class.
Now let me take a side trip very quickly. Ever take an IQ test? Being in all the gifted this and that and being promoted ahead early in grades, I was subjected to several different forms of experimental versions of the IQ test. But one thing that was common to them all was the "If all A's are B's and all B's are D's, are A's D's?" style questions that were asked from several different angles. I was always quite good at these, even as a young tyke. This was partially due to the way my brain is wired, but also because I was a guinea pig in may of the early alternative learning methods that were tested on many of the gifted students in the 70's and 80's. Many of these techniques have since been adopted due to their effectiveness.
Now fast forward to later in my life and I am taking Geometry. Not to brag, but I was the Michael Jordan of proofs. I was and am very good at it and cannot remember ever missing a single one. As I said, I attribute some of this to my wiring, but also to the alternative ways I was taught at a very young age. Proofs are the A=B and B
therefore A
questions. They are the exact same thing as the most common IQ test question style that is used to gain someone's pure intelligence (ability to reason, solve problems, think 3 dimensionally, creativity, etc.).
Once I asked my Geometry teach why everyone had to go through this hellscape class. Did she really think everyone was going to be an architect, or worse, a MATH TEACHER? She laughed and said "No of course not. You take Geometry because it
teaches you logic and logical thinking." That is why you learn proofs! I have always remembered that moment. It was a light bulb moment for me about the things you learn in school and ultimately why. But the main thing to take away is that these proofs, seemingly unrelated to logic, are nothing but PURE logic and by lighting up the part of your brain where logic is governed it ultimately exercises that mental muscle.
And THAT is why educators want to move to it. And I still go back to, I hear your concerns and the logic of them and will say again they were mine as well at first, but if the old way was the best, then we'd be the top in these areas. We just aren't. That isn't 100% attributable to old ways of learning math of course, there are many other factors (Funding, every kid gets a trophy false praise, undeserved criticism and rebuke of the teaching profession, insistence of dogmatic values, etc.), but when our kids are tested on math problems, which just say "solve this" and they are 52nd in the world at it, something is wrong in the way they are learning to solve these problems. Maybe common core isn't the panacea and to think so would be naive, but the more inexcusable approach is to keep banging our heads against the wall and/or do or try nothing new.
And for me this isn't about one is right and one is wrong... it's just different.