Thank you very much Toritoribe-sensei!
So let me see if I understand:
I want to say (well, the sample sentence wants to say) "I remembered [the fact] that he is a teacher."
So just declaring that "he is a teacher" would simply be 彼が先生だ。
思い出す is a transitive verb, and I need the object of that verb to be "[the fact] that he is a teacher" to be a noun, so I have to nominalize 彼が先生だ.
My dictionary (
Amazon.com: A Dictionary of Basic Japanese Grammar (9784789004541): Seiichi Makino, Michio Tsutsui: Books) says that nominalization can occur with verbs, adjectives and nouns* themselves -
but 彼が先生だ is neither, it is a clause, so I have to convert the clause to a verb, adjective, or a noun - which I do with the adjectival form of だ, which is な. So the な effectively turns 彼が先生だ into an adjective, then the adjective 彼が先生な is nominalized with の.
*One would have to use this logic with nouns themselves as not to be confused with the possessive function of の.
How does that sound?
Thank you greatly, again!