What intelligence theory is being taught?
My impression is that the Cattell-Horn-Carroll model is the most established and well respected framework. I.e., the closest thing that we have to something like the &quot;Big Five&quot; in personality.
It incorporates the importance of g, which is arguably one of the most fundamental ideas in intelligence research.
But it also focuses quite a bit on the distinction between fluid and crystalised intelligence. It is a very developed taxonomy based on a lot of theoretical and empirical work.
Sternberg's model of practical intelligence and Gardner's model of multiple intelligences often seem to get mentioned in entry-level textbooks but I don't think they enjoy mainstream support in the intelligence community.