Regarding using the MT method for topics outside of language, I have successfully converted his method into how I teach maths. I would say that really, I was inspired by MT to develop my method rather than use HIS method in my maths teaching, but there is considerable overlap. One thing I would say is that if you asked MT how is method worked, he'd actually struggle to tell you. As you've listed below it's a combination of many thought out factors that make it work, as well as some Je ne sais quoi, and all you can do is borrow as much as possible.
The initial thing that MT starts with would be a structure, or script that he follows, pretty much no matter what. I suppose these might be called 'learning objectives'. However it is much more concrete that that, as it spans the whole subject. For Michel, he decided what order he would teach things and make sure they all interconnect, so that he could use a concept he has taught to teach the next concept. That is something that underlies my maths teaching. In other words, I may be teaching multiplication, but at the same time I'm really subliminally teaching algebra, so that when it comes to algebra all I have to say is…'Remember what we did for multiplication? It's the same.' Students then see the pattern and learn more easily.
So with my math teaching there is a whole structure and script behind it that I don't have to alter much, through evolution and time with students, but if I need to alter it, there is some flexibility to do so. It seems to me that school teaches topics at random depending on age and skill rather than in a logical structured order.
My learning environment is always one of a relaxed atmosphere which, essentially, isn't school. Michel believed school to be akin to prisons, and in reality, they are factories that produce people that can pass exams. They still have Victorian layouts of desks for example. I tutor one-to-one, talking to an individual student. With this I can achieve more in a few days than a school achieves in years, if ever. It is a mistake to think it is more efficient to teach classes in maths because there are large numbers taught at a time. The problem with that is that if one student falls behind, they stay behind for ever, and begin to hate maths, also forever.
As you mention, 'layering' is critical to learning. That is why my method is so effective. It is pre-layered. The structure lends itself to repetition of the important methods because they are also used for more advanced topics. For instance, the same method is used to multiply two numbers as to multiply (x+3)(x+2). These are also easy to do.
Avoidance of jargon is absolutely critical. I never use any technical words in my teaching. If any are introduced, it is in relation to the fact that these are needed to be known because school uses them. If I could use none, I would.
Responsibility is vital. I always ask 'Whose fault is it if you don't understand?' and they always say it's their fault. I tell them, no, it's mine, as I'm the teacher, and this gives them a huge amount of relief. HOWEVER, I also say, but whose fault is it if you don't practice the methods and concepts? And they realise they must take some responsibility themselves, in order to become fluent at the methods.
Regarding 'no guessing'. Wow, when students guess, I immediately say 'Never Guess!' Do you guess your way to a different town? If so, good luck with that. Use common sense, and stop trying to give the right answer for the teacher, but instead THINK!
I used to do no negative feedback. Even Michel didn't. In MT Spanish, he has a very poor student who he gets frustrated with because he can't pronounced 'puede' by disc 7. It is hilarious to listen to by the way. To save time and be honest, I just say no. Not correct. But why is it not correct? Rather than tell them why, I get them to tell me. One way I vary that is by asking 'Are you sure?' when they give me an answer and it makes them have to re-think and be sure. Then I ask if they'd bet on it and so on. It just trains them to not just give out answers at will but actually think first.
Regarding what the learner knows, this is easy for me to do as I follow a script that has a hierarchy. At the start of a new session I will revise what we've done by eliciting it from the student. If the answers are satisfactory, we can move on with new material. Otherwise that foundation needs shoring up some more. That is fine. Different students move at different speeds, and it's important to tell what they are as soon as possible.
