There is a 2006 paper "Training in chess: A scientific approach" by Dr. Gobet from the University of Nottingham, and Dr. Jansen from Carnegie Mellon University, which goal was "...to show how recent findings in cognitive psychology can be applied to improve techniques of chess training, teaching, and learning"
It concludes that learning occurs best:
- from the simple to the complex
- when the elements to be learnt are clearly identified
- when following an "improving spiral" (this is similar to what DeGroot found in how a chess player thinks with progressive deepening).
Then using the above knowledge the authors used their "template theory" and used it to review various chess training techniques.
Some conclusions they get doing that are:
(in the area of Explicit Knowledge)
- focus on a limited number of positions and openings and learn the various methods in these positions thoroughly.
- repetition will be necessary.
- avoid too much historical and anecdotal details.
(in the area of Implicit Knowledge)
- Using a computer to view variations can greatly cut down on the time to do so, but may offer less efficient encoding of the information [in your brain].
- Find a balance between rote learning and understanding (specifically in studying the opening).
- study openings from different points of view -- for example, by linking it to the middlegame or endgame.
- use a chess database for your repertoire as "memory is fallible!) and you will need to review it frequently.
They also mention the "decomposition method" which consists of studying and playing basic endgame positions -- basically removing most the pieces from the board in common middlegame structures.
In studying endgames the claim the "improving spiral" can be best applied. I would compare this to how endgame table-bases are being created; basically solving the game backwards.
In studying tactics they suggest starting by themes and only later random.
They also defy some previous claims like "go through each variation once" and "blindfold chess is good for your chess"; going as far to say blindfold chess may actually be harmful to one's development.
They also think that studying composed puzzles is useless.
They then reiterate DeGroot's earlier findings on the importance of "pattern recognition".
As the paper was built on past studies I think it pretty much shows what scholars think of how chess learning should be approached scientifically.
Personally, I agree with their suggestion of studying in chunks and repetition. It is easy to get overloaded when studying chess.