I couldn't tell you in any detail how my computer works. I use it with a layer of automation.
Every math curriculum in the world is based on the idea of hand-calculating, and most of what you're teaching is how to calculate. And I think the resistance to this is very variable.
Calculating does not equal mathematics. It's a subsection of it. In years gone by it was the limiting factor, but computers now allow you to make the whole of mathematics more intellectual.
Maths should be more practical and more conceptual, but less mechanical.
Computers do the calculating to allow people to transform the world.