So I want some practice talking about Montessori while I'm in my training course, so ask me a question or two about Montessori education and I will try to give you a brief but informative answer.
First, some background. Maria Montessori was a doctor in Rome, the first to graduate from medical school if I recall correctly, her became very interested in the education of children. She started with a group of children in an asylum where she utilized the observation skills she developed in medical school and materials developed by Jean Marc Gaspard Itard. After some time, she signed these children up to take a major academic test where they scored on par with average Roman student, something thought impossible at the time. Faced with this result, she "became convinced that similar methods applied to normal children would develop or set free their personality in a marvellous and surprising way.” By applying these methods, and altering them through trial and error based on observation of the child, the children in her first "Casa de Bambini" in the slums of Rome were labeled "miracle children." At the risk of oversimplification, the main thrust of Montessori education is to give the child a prepared environment that will lead him to and maintain his concentration, which itself will lead to normalization of "deviated" behavior.
Over the next 100 years, Montessori education has spread throughout the world. It even almost became the standard of kindergarten education in American ~1911 but quickly lost steam after a noted educator, William Kilpatrick, wrote a mostly negative review of it that is actually an interesting read that echoes many of the objections to Montessori still heard today. Unfortunately, this spread included many many many schools that simply called themselves Montessori despite applying little to no part of Montessori's work; courts ruled that she was not able to copyright and thus control the usage of her name in the education setting.
So please throw some questions at me, and I will do my best to answer them