To truly be an invitation to learn, and not a mandate, the student has to be free to choose.
In a Montessori classroom, children are free to choose their own work as long as they are respectful of the materials, the other children, and the classroom environment. Just as infants go through periods of activity focused on learning how to walk, for example, Dr. Montessori observed that older children also have a need to focus on areas of their own development, such as developing their senses or writing or mathematics. Independent choice allows children to direct their work according to their own developmental needs and interests. They can spend as much or as little time as they need to master a material before they move on to something else. This freedom to choose also allows children to develop their powers of concentration and self-discipline, as their work activities are not interrupted or controlled by the teacher. They work out of internal motivation and self-satisfaction rather than learning to depend upon external motivations.
Independent choice is the key feature of Montessori education, in my opinion. I think of the other features of Montessori education discussed in earlier posts (no grades, the big picture overview of the curriculum, multi-age classrooms, the prepared environment, control of error, and the work period) as essential supports to making independent choice–learning by invitation and not mandate–in the Montessori classroom possible.
A final thought on invitations and mandates: making an effective invitation to learn requires an acceptance that children will progress through the curriculum at not only different rates but at different depths. This is at odds with the push for standardization and high-stakes testing.