Learning process

The learning process has 2 distinct start points:

1. Learner looks at world, sees someone do something, wants to do it themself, starts learning.
2. Teacher looks at syllabus, sees a requirement for learner to "learn X", starts teaching.

Actually, #2 has a Student syllabus option as well. But the principle is the same.

In case 1, what is learned, and what should be learned is student driven...not syllabus driven. Almost all syllabi fail on this count. As an example I've probably told before. One day a kid came up to me (after class) and said: hey, I want to write programs to create fractals. Can you teach me how? I'm not real good at algebra.

Of course, I did...but the path to getting there was much shrunken from a normal course on complex arithmatic. I seem to remember teaching him what the mandlebrot set was doing, and how to do arithmatic on complex numbers. I did NOT push him to become fast at complex numbers. I don't think we discussed e^iπ notation. Why? He had a learning goal, and didn't need the other stuff. Why someone is learning makes a big (all the?) difference. After he was able to do 2-3 problems in complex arithmetic multiplication...he went home, looked up some C++ graphics libraries, and came back the next weekend with a working fractal generator. Cool kid. Of course, unschooled before visiting me.

However...that's not the main point. The main goal here is to understand the standard learning- with-teacher process. Aretae's line from the student PoV:

1. See Process A
2. Perform Process A
3. Receive Feedback on Attempt at Process A
4. Perform Process A again.
5. Feedback again.
6. Goto 4

Once process has been automatized...

7. Demonstrate to evaluator the capability to perform process A

The business of becoming an expert is:

8. Perform Process again.
9. Feedback again.
10. Goto 8

And then, finally, one reaches enlightenment, one will know:

11. When to use process B instead.