Is it correct to classify Obama as the first black president"

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My grandparents came from Italy in 1912. Am I in touch with my Italian roots?

Well, I like lasagna and red wine. Does that count?

Obama may be in touch with his African-American heritage/culture. I doubt he knows all that much more about "Africa" than any of the rest of us.

Well, he certainly is an african-american of the newer generations.
Meaning, he knows exactly of which tribe or ethnicity in Africa he is, and from which country his paternal line comes from, Kenya.
Under that context, he is nothing like the common african american whose parents came to Africa as slaves from unknown parts of the african continent, from tribes they themselves have little knowledge on.
That's why the prominent African-American nationalist organisation known as the "nation of Islam" claimed heritage from a fictional "Shabazz" tribe to account for their lineage. At least you can account for your heritage, by stating that your grandparents were Italian.

Those people can't. And once again, Obama's mother was of european-american heritage, so that makes him as much as a white-american person, as a black-american person.
However, the fact he's hailed as the first black president shows the extent to which the false notion that one's skin colour determines one's heritage is prevailant in America.

He don't look white to me.
But that shouldnt matter as long as he does his job well.

But he is partly white. 50-50, you see.
And he did not even grow up within the rest of the afro-american community, like you know, a stereotypical ghetto.