I wanted to make some thoughtspace to talk about these very important influences of my work and how they differ from each other. These are just my personal interpretations of them and shouldn't be used in isolation to draw conclusions about any of the models :)
Montessori education is all about setting up environments that facilitate a specific kind of learning, and then setting learners loose to discover the things that ought to be discovered. One of the most important pillars of Montessori for me is that it respects a child's natural curiosity and that children will learn the same concept in many a different way, and that it is important to embrace that. For this reason - Montessori schools have mixed-age classrooms. This is something that seems mind-numbingly obvious to me after entering the working world. Literally none of my colleagues are the same age as me. We are all learning different things at different speeds and times and trajectories. Montessori is also the only model of these three that extends past early-childhood education.
Reggio Emilia is most famous for it's concept of the child's "a hundred languages" that they have access to and use in different capacities to understand the world around them. The Reggio Emilia is characterized as constructivist and exploratory and founded deeply in a culture of respect for children. In the city of Reggio Emilia, children are given a lot more freedom and responsibility than they are here in the states.
This reminds me of something a colleague at littleBits Adriana Young told me (which I think about frequently) which was that kids a lot of the time just want to be involved. For example when you're cooking, you don't need to have the little kid chop onions with you, but if you give them a pot and a ladle, they can at least be practicing the fine motor skills and relational understanding of objects in the kitchen that are necessary to one day help out cooking.
Anji differs from Reggio Emilia and Montessori in that it is not a branch of constructivism. It is the most radically play-oriented model out of the three because the concept of the zone of proximal development is completely absent, whereas in the other two models, educators take it upon themselves to coach students along a path that they think is the most appropriate. The role of the educator in an Anji environment is to observe, document, and understand what children are naturally learning and discovering on their own. This can be seen as a the difference between an anthropological approach vs. a psychological approach to learning. I don't totally understand what this means yet, but it's related to where "knowledge" exists. Both Anji and constructivist approaches agree that knowledge is constructed in the child, but in Anji, the method of construction is inherently self-determined, wheres in constructivist approaches the method of construction can be designed by an outside agent.
The Anji model creates a virtuous cycle wherein the most interesting play leads to the most captivating research on the part of the educator, which means a more engaged and participatory environment for the children, which leads to more interesting play... etc. etc. Since educators at an Anji school are not concerned with the repetitive work of test scores and measuring students to arbitrarily defined scales, they can spend all of their energy on what motivates them the most - understanding children and their learning and all of the fascinating ways it can develop. Anji also relies on trusting that children are curious and motivated learners on their own, something it shares in common with Montessori and Reggio Emilia.
Of course in all three of these, there are extremely important cultural considerations to take into account. Outside of a culture that trusts children as much as Anji, Zhejiang, China, or Reggio Emilia, Italy, it might be hard for children to have an experience at home that mirrors what they have at school. The montessori method appears to have been more successful at internationalizing because the core concepts are a bit more adaptable to different cultural situations. It's yet to be seen how much of the Anji model needs to be replicated at each site, and how much can be bent to fit the cultural mold of a given site.