Thanks for all the suggestions. Sounds like there are no shortcuts to just working hard. Isn't that always the problem with chess :-)
Honestly, I don't think it's worth much time and effort to actually FOCUS on learning algebraic notation. I agree with sparowe's remark that when working on your chess in general you will slowly develop a habit of naming the squares correctly (although I admit it took me some time to stop confusing squares in White's "territory" with their respective counterparts on the black side). If you still want to train that habit systematically, though, I suggest you incorporate into your study of openings, since this the phase of the game where you routinely put your pieces on the same squares over and over again. For instance, if you like to play the Sicilian Najdorf as Black, you love to see your opponent advance their king pawn two squares to E4, which you eagerly answer by advancing your queen's bishop's pawn to C5. Every Sicilian starts like that, "e four c five". I guess mumbling the names of the squares while going further down the line could help both your ability to name the squares and the process of memorising. By the time you can verbally lash out "E four C five knight F three D six D four C takes D four knight takes d four knight f6 knight c3 pawn to A six" in four seconds, you probably will know where to find the respective squares on the board ;)
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