I think the teacher is mistaken, based on the account in the question. I see "thorugh" here as much the same as "by means of". If I were writing this I might well use dashes to set off "through getting exposure to media and listening to daily news", as it is a prepositional phrase. it explains how children are able to "determine what the wrong and right things are". I can't see what verb could possibly follow "children" to make this a better sentence with an essentially similar meaning.
The sentence could be recast as:
Through getting exposure to media and listening to daily news, children can determine what the wrong and right things are.
also, the phrase "the right and wrong things" seems a bit awkward, but context might help that. Right and wrong in what way? Things to do? things to say? The sentence does not specify. But perhaps other sentences in the paragraph do.