The most interesting part of observing a Montessori classroom is to see a child choosing his/her own learning materials. It gives them the opportunity to develop will and decission making skill, and also to take responsibility for their choice. And it is a Montessori teacher's task to observe every child as they work.
What I mean by obervation here is to identify the smallest development happening in a child. One morning a 5 year old girl shared to the class that she visited Pasar Burung in Jalan Pramuka the previous day. The term Pasar Burung refers to pet market in Indonesia. So she brought to school a pair of fluffy hamsters in cage as class pet. The children were so excited! They placed it on nature table. Using magnifying glass they took turns to observe the rodent's behavior. All of a sudden everyone talked about hamster: one child said what a cute animal; another asked would it grow wings one day; a 3-year old boy told me he had shrunk to hamster size last night, and many other. The teachers had prepared a theme but she quickly noticed the class' interest.
One teacher initiated to prepare Montessori extension materials related to hamster. She relized by catching this moment all children would learn passionately. With the help from her colleagues she prepared a set of terminology cards of rodent to learn body parts and internal organs of hamster, made poster of rats classifications, sang songs about mouse with a guitar. It was a hamster week.
What she did at that time was observing the children's interest in her classroom and identify development progress of each child. For reading child she would give a terminology card with name tags; non-reading child would match pictures; for those who are learning 1-10 she prepared an extension using recycled products. For children at beginning of 3, they learn the first sound of hamster, 'h'. Overall, the class was very much alive. And individually each child is progressing at their own pace and following their interest. This is what you will see in a Montessori classroom.
Every little thing a teacher prepares for her class, she must focus on development of individual child. Observation is a skill you can practice.