Formal calculation requires one to have a solid understanding of methods, and the ability to mechanically perform calculations based on this understanding without having to think about the meaning of each stage, one after the other. This allows one to conserve cognitive effort, and to easily execute operations. This also applies to measurements and drawing figures.
The mechanical execution of a predetermined set of procedures is referred to as using an "algorithm." Thinking that attempts to create algorithms based on an understanding of procedures is important.