I have a strong bias towards the first school, the point being that opaque calculation are simply harder to reason about. I also agree that handling complex co

I have a strong bias towards the first school, the point being that opaque calculation are simply harder to reason about. I also agree that handling complex computations is a relevant skill, but then what you need to learn is the mental book keeping of where you are and what you need to do that you need to learn. The only case where calculators are truly useful is in sciences, where numbers are just a tool to scientific insight. (moreover in math if you need trigonometric tables chances are that you are going to learn better math by keeping symbolic answers)