Montessori primarily developed her academic approach by watching children. She observed sensitive periods for various areas of development and then focused on presenting those concepts at certain ages. She also focused on helping children develop a clear understanding of concepts as opposed to just an understanding of how to get the answer (in math, for example). All of her original materials were designed to solve a specific problem for the children she worked with. She started with the Children's House level (3-6) and expanded from there to cover a full range of curriculum.
The curriculum itself is self directed to the extent that lessons are based on individual assessments of where a child is at. Not all 3 year olds, for example, get the same lesson on the same day as in a traditional preschool. Some 3 year olds may be primarily in the sensitive period for practical life, some may be deep into sensorial activities, and others may be moving into the works to prepare for writing. This is where knowing your child and the phrase, "follow the child" comes into play. A teacher or guide has to know each child as an individual and know when to move on and when to back off. If it sounds like a lot of work, it is! I can't imagine doing what I do for 3 kids with 24 or 30!
Additionally, lessons are not typically provided in every subject every day. In our homeschool (which I model off the way Tim runs his classroom), each day of the week is designated for a specific content area. Mondays are for Language, Tuesdays are Mathematics and Geometry, and so forth. Each boy gets one lesson per day in the appropriate area. The rest of our work period is spent in child directed explorations of the materials. Aidan, being older, has some minimal expectations of follow up work, but he has control of the majority of what he does each day. We have a set daily work time and they are expected to work only on school.
That being said, however, they are not allowed to work ahead of the materials they have been presented. There are many things that Caleb is not allowed to work with. He is allowed to request a presentation if he would like to complete a new work, but most of the time I tell him not yet (because its usually something way beyond where he is now-like when he asked for a presentation on the stamp game this week). Even if I don't present the lesson, I do use their interest to perhaps address moving ahead in something I didn't think they were ready for.
The idea is that by controlling their own learning experience children will choose activities that are challenging and relevant to their education. I find this to be true the vast majority of the time.
I have often heard unschooling referred to as "Montessori without the materials". In some ways that is very true and in others less so. Children learn through doing and there is little to no pencil paper work and no textbook work. As I wrote about in this post, there are definitely two sides to the Montessori Method, the materials and the philosophy. To take the philosophy and apply it without the materials would probably look much like unschooling. In all honesty, we probably lean slightly towards this end of the spectrum in terms of where we place our emphasis (materials or philosophy).
Montessori is very unlike unschooling, however, in that the curriculum is quite academically rigorous from the start. Children learn levels of grammer, math, and science that most American adults today have never experienced. What Aidan does as a "1st grader" would be foreign to most traditionally schooled first graders and most 1st grade teachers would probably tell you that a 1st grader couldn't possibly understand the math concepts that he is able to complete confidently. Yet, he is probably a very average Montessori 1st grader at the same time! The familiar unschooling style approach to interest and delight driven learning as the primary means of education comes at a later age, after the child has had a broad exposure to the curriculum and has had adequate time to move from concrete to abstract levels of thinking.
Do you have more specific questions about Montessori? I am happy to answer them and to send them to Tim if I can't answer them. Would you be interested in having Tim do a Q & A on Montessori curriculum, materials, and philosophy?