Can you tell me if sentence 2 is a mistake? Thank you.

I remember going to primary school..
I remember I went to primary school..

It's not a mistake, but the first sentence is a smoother and clearer sentence. The second sentence is missing a word -- the connecting word between the main clause "I remember" and the subordinate clause "I went to primary school." What would you put there? "that"? "when"? "where"? or what?