Have said it before, but it's a mentality issue IMO, the lad looks like he's carrying the world on his shoulders, he thinks he needs to be our main man week in, week out, it's almost as if he's scared to try certain things that a couple of seasons ago he would just do instinctively, maybe he's aware of the groans from the crowd when something doesn't come off and that's affecting his game.
The first thing he needs to do is start enjoying his football again, he just looks like he doesn't want to be out there at times, also, he looks like one of those players who needs an arm around him now and again, under Koeman though, that seems unlikely.
Good... a large part of his learning imo is thinking about what he is about to do and then judging whether it is a good idea or not.
He did not do that enough previously for me, but if he keeps doing it he should instinctively develop an understand of what is a good move and what isn't, instead of just assuming everything is good but maybe he didn't get it technically right, when the opposition are running at our defence with the ball he just gave away, and he's blaming himself for a lack of ability he clearly has.
If he questions his moves now, soon he will question them in advance as the ball is arriving, then question them in advance and come up with the right answer, then his sheer ability can kick in, and he will grow in both confidence and quality and become the player we want him to be...
If he doesn't question what he's doing as he does it, then he will just remain as he is, mostly decent, with a few great touches and few terrible ones...
For me, great midfielders know where players are around them, can decide where the ball is going to go before they get it, can trap the ball from most angles, and can send it where it needs to go...
Barkley currently can trap the ball regularly from that list, the other things are not so far away but separate him from greatness imo.