I've spent a whole lot of my life learning and/or teaching- both technical topics including some of the ones mentioned and non-technical topics like dance, presentation giving, and management topics.
I find that there's a big difference for most people between what I'll call "project time" and "study time", and I'd conjecture that there's probably other breakdowns for the benefits of other types of time as well.
Here's my basic division:
Project time
Time spent doing some sort of focused project. Examples include:
- a single, really hard math problem or writing a big math paper
- a lab in almost any science, or an engineering project like writing a web site or a feature in a program.
- an artistic work - like sewing clothing, sculpting, painting, being part of a show, etc.
- home repairs
There's a general theory in this kind of work that you have an overhead to the "context switch" - the time spent getting your brain ramped up into what you are trying to do. It can include true physical tasks - like finding your tools, or their mental equivalent - like mentally remembering all the things you learned the last time you were doing this particular project.
In general, if you give a person several projects of a similar ilk and tell them to perfectly balance their time, this won't go as well as if you let them start and finish each project with some sort of flow. Many people want to finish one before starting another - particularly if the projects are quite similar.
Study/learning time
Conversely, I've found that as a general metric, students can focus on learning a given topic for about an hour. Students can learn for many hours in a day, but the need a break and a shift in topics after approximately an hour. This refers to true learning - examples include:
- studying from a book
- doing a set of exercises that are taking you very carefully through some material (as opposed to an open-ended project)
- learning a given type of dance, or a particular dance choreography
- learning lines in a play
Push students too far past one hour and you will get diminishing returns. The brain will get overloaded and retention will drop off.
Note - this is for pure teaching - lecture/listen, or very directed studies. A class that mixes exercises, discussion, activities, and lecture will have a lot more play here and may manage to keep students meaningfully engaged for many hours.
A theory
When you do a project, you are actually flipping between ways of thinking - one minute you're learning with trial and error, the next your creating a solution, the next you are analysizing the results... but the whole time you build a body of knowledge. So your brain doesn't get worn down so easily, and being able to tie everything to a context is critical.
When you study, you are building up a set of knowledge about something - the repeated learning actions of your brain get worn out after a while, and the type of short term memorization with cramming in knowledge about a given topic takes a part of the brain that has limited capacity for each topic. The brain needs time to transition from short term to longer term memory and you can't do it while you're still struggling to learn.
