my son is not in MMI, but in a Montessori school. They have a very clear curriculum (checklist) where every child will have to go through all the items listed, which are part of the Montessori syllabus. The school also has full Montessori materials. I do not know what constitutes a full Montessori, but I feel that this is enough. There is time for social play with friends after completing their work. If they complete early, they are trained to do "shelf-work" (ie. take out a Montessori material to work on) either alone or with friends. All "toys" are educational and part of Montessori methods.
The key is there is no force, its all up to the child. Encouragement will be given should the child be too introvert, but teachers will not force. They believe when the child is ready, he/she will do it willingly and this facilitates learning. What I like is there is always individual time given to each child for teacher to work on problem areas. My K2 son has progressed pretty well there. He is now already on Primary 1 syllabus, learning multiplication and division problem sums. So, while I am not promoting the school, I just wish to share the advantages Montessori has brought to my son.