There are a lot of research on this topic. You can easily find a bunch by goolging. Here I list a few of them.
- simple number comparison - Queen is 9 points, and Knight is 3, so Queen is more valuable than Knight. (math)
- simple number addition and subtraction - If I lose a Knight (3), and a Pawn (1), I am losing 4 in total. If I gain a Rook (5) in the meaning time, I am actually up 1 point. (math)
- color and shape reorganization (science)
- make assumption - if I jump out my Knight, it will be attacked by his Pawn. (math, science)
- recognize straight lines and diagonals (geometry)
- logical thinking - the Bishop is in light square, his King is in dark square, so I can't check him with my Bishop. (math and all subjects)
- deep calculation - calculate those moves that are not played on board yet. (3-dimension geometry and advanced math)
- notate games - handwriting (english)
- read chess books and chess stories (english)
- explain reasons behind his moves (english)
- report game or tournament details to parents or coach (english)
- make friends (social science)
- remember countries, national flags, and etc. (geography, history)
- study chess history (history)
- read chess books in Russian, French, German, or Spanish (foreign languages)
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