Question

what is the economic term for the practice of assigning small parts of a complicated job to individual workers who sepcialize in doing just their small part?

Answer 1

That term is the division of labor.
Division of labor refers to the fact that each person will be assigned a certain task they specialize in, based on their education and skills. Every person can present the employer with a particular set of skills, and then he can decide who will do what within that complicated job.