Both of my children go to a Montessori school - they are 3 and 8. I love it, but it is a private school and it is a benefit of my job. If I did not have this opportunity, I would not be sending my kids to a private school at all. But, since the option is there, we do...and we love it. Our kids' school goes from toddlers (18 months) through 5th grade.
I have learned a good amount about the Montessori system over the last 6 years and am a very enthusiastic supporter. You are welcome to PM with specific questions.
Bear in mind that being "affiliated" and "certified" Montessori are two different things. "Certified" schools are the real deal. "Affiliated" are often hybrids or modifications. In some public settings, for example, schools are not allowed to have more than two grades together in the same classroom. Montessori operates on a system of "cycles" that are usually 3 years in length. Thus, a child at the Primary level (pre-school ages 3 to 6) is in the same classroom working with the same materials in increasing complexity during those three years. Over this time, they take on maturing roles - from the youngest novice, to the oldest mentor. Its a rather beautiful system, but since this doesn't dovetail with some public system requirements, it doesn't always happen this way.
These would be good questions to ask about a public Montessori school - do they have three year cycles? Are the teachers Montessori certified? Is the school Montessori certified?
One thing I like especially is that the research, materials used and the schooling all certified teachers must pass are rooted in ongoing scientific research about child development. Montessori often has a reputation for being unstructured, loose and undisciplined because if you drop into a classroom, its hard to figure out what is going on. Kids appear to be choosing their own work at random and its not even clear what that work entails.
But now that I know what is going on, I realize that the education is, in fact, very structured and the learning very "deep." The materials children work with are not toys - they have specific rules and ways of being used and children are not allowed to just play blocks with them or whatever. They get a presentation on the correct way to use the materials and need to abide by that. When they are done, they pack up their materials and put them back on the shelf where they found it.
Which isn't to say that there is not lots of room for creative thought, artistic expression, etc. Jut ask my son. He can't think conventionally to save his life. Or maybe its just an 8 year old thing...
Recently, I went to presentation on how math concepts are dealt with across different Montessori grade levels. Holy crap is this stuff genius. The way concepts are taught means that children often inherently understand the concepts before they can put a name to it, which is part of the "deep" learning concept. The learning is very graphic, too, giving a sense of tactile-ness. A chain with 5 beads, for example, can be strung together 5 times to form a long chain. The child counts the beads on the chain, gets used to counting by 5s and then later, the beads are folded to form a 5X5 square. Guess how many beads it has? 25 - its 5 squared! This is the first time that I actually understood that "squaring" a number is actually physically making a square out of the units. They can also cube it in the same way - stack 5 squares and voila! This is all first and second grade work, BTW. I won't even tell you about the Pythagorean Theorum and how they teach that one using visuals. Just brilliant.
Similar approaches apply also to language acquisition, including writing and reading. At the primary level (again, this is pre-school in Montessori nomenclature), children trace letters with their fingers on a sandpaper card, feeling the roughness. Then they write that letter, while saying its sound, in a small container of sand. Then they write it out using a pencil on paper. So, children integrate the aural, oral and tactile all at once with the result being that when it all comes together - it REALLY comes together in a big big way.
My son began reading completely on his own around the time he turned 7 and it all seemed rather magical because of this "deep learning." No Dick and Jane books for him. He began around November and from December to March, he read all seven Harry Potter books entirely on his own. Now he is a reading fiend with a bigger vocabulary than me!
I would add at the end of all of this that there really are many great ways to educate a child and every child is different. I don't think the Montessori method is necessarily the "best" but it has been great for our son. Our daughter is only 3 so its hard to tell if she clicks with it all in the same way, but I expect she will. As a foundation, especially through the primary years (3 to 6), I think it really is wonderful, but not the only wonderful thing you can do for your kids' education. Keep your options open. You've got some time.