wow. very linguistic question. according the sentence you gave, ba here indicates a situation rather than an action. gei/给 per se is an action word, = give, at its basic meaning; however, you can only use 给without 把 in very short imperative sentence, e.g 给你这本书！给我一个苹果！给他一杯水！ you can see the subject is either the speaker or the listener. but with 把, the sentence is more of a description of a specific situation with the subject of the sentence (老师) is neither the speaker nor the listener. yes, ba-sentence and bei-sentence are very complicated linguistic issues which can be confusing to the newcomers of the language (i'm a little confused too : P).

Actually "把sth."can be a prepositional phrase as an adverbial and the predicate is "给", though some grammar persons might not agree with me. And some disagreement does leave room to be quibbled about. It's far beyond me to judge them right or wrong. But there is a problem I'm sure in them that some Chinese teachers borrow English grammar once in a while in teaching non-native Chinese speakers, though subconsciously. The reason is our Chinese as a language still has room to be analyzed and generalized. But there's also an embarrassment that Chinese language borrows a large amount of expressions from English. Sorry, it seems a little astray from the topic.

在汉语中，“把”和“被”是相对的。 “把”表示主动，有点像英文中的“do”汉语中“某人+把+名词+动词+怎么样”和英文中“某人+do+动词+名词+怎么样”意思是一样的，只是中文的动词的位置不一样。例如“老师+把+词典+给+学生了”=英文“老师+do+给+学生+词典了”把的作用就是“do”作用，意思是老师处于主动地位。 “被”表示被动，有点像英文中的“be done”。就是这么简单。 如果你没看懂可以明天再问我。

“把”sentence is a very common structure in chinese. This kind of sentence means 处置（handle;deal with），the object has some changes or has some results through the action. in this sentence the position of 词典is from 老师 to 学生。we use “subject+把+object+verb+在/到/给/成+object+（了）”to express that.