A lot of times in high schools there is such a shortage of science teachers that they have teachers who do not have a degree in science teaching science (they have to take science courses as part of their credential package which supposedly "qualifies" them to teach it, but sadly this doesn't mean they did well in those courses). This seems like one such case.
To the TC, now you know how he is handling it, so do what you can to follow your textbook and online sources so that you can build an undamaged knowledge for yourself. The teacher might innocently think to himself, "well what is the difference?", and so he thinks he is making the idea simpler, but the way the teacher is teaching it ignores the concept of valence (which is why you need multiple chlorines for instance; it is to balance the +3 valence on aluminum). This is obviously something you don't want to do if you plan to go further in chemistry in the future (something the teacher might be assuming you don't want to do because perhaps he doesn't like it?).
However, a word of advice TC, on the test give the teacher the answer that he taught you in class and don't point out his mistakes to him any longer. It is a general rule that the less someone knows about something the more apt they are to viciously defend their ignorance when challenged. If you pointed it out to him once already and he ignored you, don't point it out again. Instead just make do and pass the class. Hopefully you will get a teacher that conforms closer to the accepted standards the next time around.
EDIT: Well, in thinking about it maybe I was a bit too harsh here. We do not know the context of the class, and maybe the teacher wants to introduce some sample reactions first and then balance them at a later point? It is not the way I would do things (he could use reactions like NaOH + HCl
O + NaCl that are simple enough and are viable chemical equations at the same time), but so long as he intends to make things right eventually (one would hope) I guess it isn't overtly wrong to do it this way. The equation Al + HCl
AlCl + H does describe an experimental fact, it just is not considered a valid chemical equation until it is balanced. That is the only difference between the two statements. At least he isn't doing Al + HCl
NaOH. I mean, it could be worse...