One thing that every engineering class has taught me so far is how I should approach my problems. Not in the sense that the classes tell you exactly what to do, but each class emphasizes that each problem must be approached methodically.
For example, in Thermodynamics, for every problem, you start by extracting all the information you can out of the question. You start with the knowns and the unknowns. Then you draw the picture or Free Body Diagram, then you write out all the equations that relate the variables to each other. Then, you manipulate the equations and then plug in the numbers needed.
Everything has a certain rigidity to it, but that doesn’t make it boring, it makes it efficient. And not everybody has the same method to approaching a problem, everyone has an approach that works the best for them.
Even though it’s kind of stereotypical for engineers to try to make everything as efficient as possible, it’s not exactly only engineers that do this. Mathematicians, physicists, and many other scholars all have a method in which they approach to solving a problem, and more often than not, the methods overlap.
So instead of just dumping numbers down on your paper, writing everything out in an organized fashion not only speeds up the process once you get used to it, but it also makes it harder to make careless mistakes.