Barkley has had a breakout season for Everton with four goals in 21 appearances in all competitions, while he also made his senior international debut for England in September.
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The 20-year-old attacking midfielder is expected to be part of England's World Cup squad to go to Brazil and Martinez believes Barkley has a level of technique and control on the ball that is decidedly un-English.
"He [Barkley] has the physical elements of the British game; the intensity and the power," Martinez told reporters on Friday.
"But Ross also has the touch of someone brought up in a different culture."
"Nothing fazes Ross. That temperament, I'm not sure we've seen that too often over the years.
"For some reason, the English talent is often the naughty boy.
"It's a short fuse or he gets into some kind of trouble. Drinking, smoking.
"Ross is the opposite. I think partly because he had a big injury at 17 [when he broke his leg in three places].
"All of a sudden something took it all away from him. He realised what he could lose. But home is good too.
"He's well-grounded. His mum is a great influence. He's one in a million."