Jinx, take a few courses in linguistics (or read some books about it), enough that you understand some of the basics of generative grammar. The traditional division of the words of English (or of any other language) into the standard eight parts of speech is, at best, a rough first pass at dividing up the words into similar categories. Yes, in some ways, articles are a separate category with their own rules, but, yes, in some ways they work like adjectives in that they modify the nouns which they proceed. There’s no way for me to tell from your sketchy description whether the categories that this teacher is teaching his or her students are more useful than the standard division into eight parts of speech.
You sound like the parent of a child who comes home from school and says, “Hey, Mom, the teacher taught us how to do arithmetic in binary today. See, if you add 101101 and 110110, you get 1100011.” You say, “What, that’s not true. If you add 101101 and 110110, you get 211211. What kind of nonsense is that teacher telling you now?” When your kid says, “No, the addition is done in binary, not in decimal,” you say, “Nonsense, there’s only one kind of numbers. Your teacher is an evil person for not teaching you to calculate right, and I’m going to get her fired for it.”