before conjunctions in compound constructions that are not compound sentences

No comma is needed before and because it is joining two phrases that modify the same verb, applies.

with restrictive elements

No comma is needed to set off the restrictive phrase of gifted children, which is necessary to indicate which parents the sentence is talking about.

Do not use commas to set off restrictive elements that are necessary to the meaning of the words they modify. Do not use a comma before a coordinating conjunction (and, but, for, nor, or, so, yet) when the conjunction does not join parts of a compound sentence. Do not use a comma before the first or after the last item in a series, between a subject and verb, between a verb and its object or complement, or between a preposition and its object. (See 35i.)