Read the sentence and determine which revision, if any, is necessary. "Valentina’s mother an art history professor often gives lectures at the local museum.” The phrase “an art history professor” should be set off with commas. The phrase “Valentina’s mother” should be set off with a comma. The phrase “at the local museum” should be set off with a comma. The sentence is correct as written.

The phrase “an art history professor” should be set off with commas because it is a nonrestrictive appositive phrase. To better understand why so, an appositive phrase is a noun or a noun phrase that renames, identifies or gives further information of another noun right beside it. Now, this type of phrase can be either nonrestrictive (when it's not essential to the sentence, and therefore should be set off with commas) or restrictive (when its essential to the sentence and no comma is required).

In the sentence, the phrase "an art history professor" gives further information to the noun beside it: "Valentina’s mother", and it is nonrestrictive because without this information the sentence would still make complete sense, it would still have full meaning, that is to say, is not essential to the sentence, and since it is not essential it has to be set off by commas.