Sure, typing is a useful skill, it's part of programming, but is it programming? - no of course not. In fact it's insulting to programmers to make the confusion.
It's the same with those of us who have taken the time to get good at mathematics - it's not arithmetic. Being good at arithmetic does not mean you are good at math, being good at math does not make you good at arithmetic.
This confusion is especially detrimental to children, many of whom will be put of mathematics because they equate it with the wrote learning and peculiar mental gymnastics of arithmetic, rather than what it is: An exploration of the beautiful and fundamental symmetries that emerge from structure and process.
Not really. Mental arithmetic is the ability to move numbers around in your head, it really is equivalent to being able to type as a programmer. Mental arithmetic is to number theory as being able to type is to programming. That you do not understand this, shows that you too have been damaged by the standard teaching of maths within education - pre university level.
I think this is one of the many cases where you emerge out the top of an ideath to come right back to where you started at the bottom, but for different reasons.
I grade school many are taught that math === arithmetic. Then they get to interesting stuff in high school and college and realize arithmetic was just a tiny part of the story. So many at that phase are emphatic about refuting what they were told early on about arithmetic being math. Then when you calm down from that notion, you can get back to realizing that while arithmetic is only a small part of math, it is still very much a part.
just as
Typing != Programming
Sure, typing is a useful skill, it's part of programming, but is it programming? - no of course not. In fact it's insulting to programmers to make the confusion.
It's the same with those of us who have taken the time to get good at mathematics - it's not arithmetic. Being good at arithmetic does not mean you are good at math, being good at math does not make you good at arithmetic.
This confusion is especially detrimental to children, many of whom will be put of mathematics because they equate it with the wrote learning and peculiar mental gymnastics of arithmetic, rather than what it is: An exploration of the beautiful and fundamental symmetries that emerge from structure and process.