"Bring" vs. "take" in American English

English (other than American English) has a clear differentiation between the two words. Both are about translocating something. In "bring" the something of somebody is moved to where the speaker is currently situated. "Take" is used to translocate something or somebody to a place that the speaker is not currently at.

You cannot “bring” your books to school if you are currently at home. You can only take them to school. Most of the time one can get the meaning from the context of the sentence but it can get very confusing when the other party is on the telephone and you do not know their location.

Why does American English not differentiate and when did it lose the differentiation?

Solution 1:

Take and bring in the sense of translocation do not have an exact, complementary usage bound by the location of the speaker as proposed by the question. Oxford Dictionaries defines this sense of bring simply as “Take or go with (someone or something) to a place”. Merriam-Webster defines the location binding of take as “to another place”, whereas bring is bound “toward the place from which the action is being regarded”.

The location binding of bring is not necessarily defined relative to where the speaker is currently situated. For example, in a telephone conversation, since the speaker and the hearer are not in the same location, to bring could be to the speaker's location, or it could be to another location contextually relevant to the conversation—“the place from which the action is being regarded”. You can say “bring your books to school” whether you are at school or at home, because you don’t have to actually be at school to regard an action from there. In context, you are simply imagining the action happening from the perspective of school.

Others agree. John Lawler parallels come and go with bring and take:

To summarize, both come and go mean to move, but their use is determined by their deixis, i.e, the identity and location of the speaker and addressee...

For instance, in a situation where someone has knocked on your door and you shout reassurance to them to let them know you're on your way to the door from somewhere else,... what you say is I'm coming, because you're moving toward the place your addressee is at; in English you can take either the speaker's or the addressee's position as the terminus ad quem for come, as well as the terminus a quo for go.

It's easy to see that bring and take have these stigmata, too.

I'll bring it right back.   (to you)  
I'll take it away.          (from you)  
Take this away.             (from me)  
Bring the car.              (to me)  

With this kind of fluidity..., there are lots of choices available for bring and take. If you are speaking to someone outside your office community, who will not be accompanying you tomorrow, you would be more likely to say I'll take the sausage to work tomorrow; but you could still say I'll bring it to work, because, after all, you'll be there, and it'll count as moving towards you, the speaker.

The Grammarist notes about hypothetical situations

When one is using the future tense, either of these verbs are correct because nothing has actually happened yet. Usage is based on which point of view the speaker wants to emphasize, the moving of the object or the removing of it.

Solution 2:

I speak Canadian English, so I don't know if this answer is relevant to you. But I would that your definition of "bring" allows a little lee-way, at least for colloquial use:

Take your books to school.

?Bring your books to school.

The second sentence is technically only correct if the speaker is at school, right? But given that this imperative statement is being told to someone, when they perform the action they are doing both, taking their books and bringing them to school. So I don't see it as strictly wrong for the parent to tell their child (while at home) to bring their books to school (when they next go to the school).

I would say that "He brought his books to school" is correct no matter where the speaker is.