I don't know much about the Montessori program, and maybe this is entirely out of the philosophy. But when my 3 y/o doesn't want to clean up, I hold her upside down by her feet and have her start picking up toys that way. It gets her laughing and in a different frame of mind, and she will usually start picking them up.
I always imagine that inside their little brains the neural pathways and chemicals are all set up to say "no" and be defiant. If you want a different response, you are going to have to shake things up and reset their brains on a different path. Do a magic trick, do something physical, play a little game, etc.