Kroll’s Revised Hierarchical Model and the Inhibitory Control model are other models I was introduced to in grad school, and they are an incredible help in explaining how students develop proficiency in their second language, why we shouldn’t use English translation in a world language class, and why back-translation (L2 to L1) is easier than forward translation (L1 to L2).
Read up on it! The Oxford Handbook of Applied Linguistics has a whole chapter on this topic (by Kroll herself, with Dijkstra).
Why don’t they teach this to undergraduate language education majors?!?