In your description, mathematics is the pure study of theoretical computing machines. However, I think that the act behind mathematics is what people are interested in -- general or capricious analogy-making ability. That's what we want to develop in young people.
We want the thing or process that operates the math, including novel operations for novel situations, and I believe that analogy-making is that thing.
And this is may be why people have an emotional resistance to arithmetics in school. Because arithmetics is an instance of math, but what people are practicing is a particular instance of operation, rather than the skill of operation.
We want the thing or process that operates the math, including novel operations for novel situations, and I believe that analogy-making is that thing.
And this is may be why people have an emotional resistance to arithmetics in school. Because arithmetics is an instance of math, but what people are practicing is a particular instance of operation, rather than the skill of operation.