Should we? Basic arithmetic has long since been solved, but I've met plenty of people who struggle at higher level math because they haven't mastered enough ba

Should we? Basic arithmetic has long since been solved, but I've met plenty of people who struggle at higher level math because they haven't mastered enough basic arithmetic. Solving complex problems will often involve many much simpler problems that must be solved as well. The time to offload this to another system to solve it for you is immensely more expensive than being able to solve it mentally, meaning that to solve the complex problem ends up being far more expensive as well. Eventually students will reach problems whose price they can no longer afford. It is related to the reason we teach concepts starting with simple, small, easy to solve problems before building up. If I want to teach a student how to solve the limit of x*sin(1/x) as x approaches 0, I need them to understand quite a bit of math to even know what the problem is asking.