A standard way to lecture to students on theoretical physics or mathematics is to write down basic theory. Next a number of worked examples are shown to the students. Outside the lecture, the students have to work homework problems, which are similar to the examples shown in the lectures.

When I used to teach calculus to first year student's at the University of Liverpool, I used to write up some basic examples of differentiation. Some of the students at the back of the classroom used to gasp in amazement. It wasn't clear how to help them use the worked examples. Also a common concern is that they just memorize the solutions methods, so only gain "surface" knowledge.

While preparing something else I found out about worked example effect. A collection of studies seem to find that it is very efficient for the students to study worked examples rather than just do problem solving.

For many complicated topics, it would surely be too time consuming to do problem solving from first principles.

The theory behind this is cognitive load theory.

I liked the idea of tbe faded example, where not all the steps in a calculation is included. This should be used for "experts", so perhaps start the course with fully worked examples, before moving to examples with "missing steps."