Even an accredited Montessori can require that a child complete each task in lockstep with the program before allowing them to move on to the next task. Ours was accredited and did require it, at least until we really pushed hard midway through the school year to skip the stuff that our DS had already mastered. It was not a pleasant situation.

It doesn't matter if the advanced materials are in the room if the child doesn't get to use them!

I'm with kcab and Incogneato that the teachers are what really matter. If they get it, it's smooth sailing, regardless of the program. If not, it will be an uphill slog.

Kriston