Well, if we all learned the old way, and are capable of counting change in our heads and such, then why can't today's students do it? Are they too stupid? Because if that's the case, then no teaching method will be sufficient, and the future is doomed. OR...maybe the difference is that we learned the old way, and they learned the new way?
It's hard to say how any of us learned math. I remember my parents being frustrated in working with me in math, as the techniques had changed somewhat (long division was rough to learn because of that, and the fact that we moved between states, and the two states had different times to teach long division--the first state taught long division in 5th grade, the second state taught it in 4th grade. We moved between my 4th and 5th grade years, so it was assumed that I learned long division in 4th grade at my new school. I hadn't). So many different methods of teaching math have been used over the years. My wife is 9 yrs younger than me and grew up in a different state. Our methods of doing common math differ. We get the same answer, we just use different arithmetic. When she taught math (7 yrs ago, pre-common core), the book she used often taught math a third way from what we learned. When students didn't get how to do a problem in the book's prescribed method, she would teach them her own method, and if that didn't work either, she would ask me how to do a problem, and I'd show her a third way. There are a lot of correct ways to do arithmetic. Some work for some people, others work for other people.
I have some other thoughts about maths in my mind. I think it is not for me. I feel very tough for me to understand all these things.
