I'm a lefty, and I hold my pen "correctly". I say that in quote because I don't think there should be a right and wrong way as long as the person writing is comfortable, and the writing is correct.

DS7 is a righty, and I WISH I could get him to hold his differently because he presses so hard on the paper (making a huge mess if he erases). It's impossible for him to just "relax" when he writes causing friction if he has to write for very long.

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DD8 is a righty for eating, writing, drawing and things like that, but we found out last year that she is athletically a lefty.
It is more complex than saying that a person is right handed or left handed, it has to do with how they visually perceive things.

This may change for him as he gets older. I started athletically as a righty, and by the time I was 12, I was a lefty. DS7, when he was 4, would interchange between being a lefty or righty on the baseball field. It was dependent on his mood.