I took this video of Tyler working with his cylinders several weeks ago to show those who are new to Montessori, or who are unfamilair with the philosophy, what is meant by the use of self-correcting materials. He hadn't used these cylinders more than ten times at this point so it took much longer for him to complete the work than it does now, though my point isn't to show how smart Ty is, but to demonstrate the focus and thought processes that a child must go through to complete a work. There's only one way to complete a Montessori work, which is easily apparent to the child after demonstrations of it. No adult intervention or correcting is needed which provides a sense of independence, and as a result, self-esteem. Especially in the "me do" toddler years, this holds great importance!
This is a work I developed and made myself inspired by the Montessori cylinders, so it is not official, though it follows all of the criteria as far as I'm aware. Tyler typically takes the cylinder work off of the shelf then returns it, but here he works mostly on the shelf. I love observing him at work and hope this is helpful to someone!