Maria Montessori, the Italian physician and educationalist, believed in self-directed learning for the child in what we now know more commonly as 'child-centred education.' She held that if properly provided for and adequately equipped, children would enjoy experimenting and finding out new principles themselves. This method became known as the 'Montessori Method.' In this method of 'teaching' the adult serves as a guide or as a director of learning - supporter rather than teacher. This trained person needs to provide the equipment and resources as well as filter out any obstacles to picking up new information - including disruptive behaviors. Records are kept of the child's acquisition of learning milestones but generally children are free to explore them in their own time and order.
The term Montessori is most frequently used in connection with the Montessori method of education, first introduced by Maria Montessori (1870-1952), an educator and doctor, to aid young children up to 12 years old in development of intelligence and independence. While the Montessori method is definitely based on understanding of some aspects of psychology, I am note sure if there is a formal branch of psychology called Montessori psychology.
Also I am not sure about the what is implied by difficulty in studying Montessori psychology. The methods of Montessori methods and the psychological principles that support it are no more difficult to study than other comparable areas in educational methods or psychology.
Montessori method requires creation of right environment suitable for three distinct age groups, from infancy to 2.5 years, 2.5 years to 6.5 years, and 6.5 years to 12 years. The learning is accomplished by the activities undertaken by the students that involves skills of exploration, manipulation, order, repetition, abstraction and order. The students in the first two age groups are encouraged to use their sense of touch, hearing, smell and taste. They are encouraged to explore the objects in their immediate environment. Children in higher age group are encouraged to deal with abstract concepts using on their capability for imagination, reasoning, and creativity developed earlier.
International standards for guidance of Montessori teachers and schools are now set and issued by Association Montessori Internationale (AMI). Link to the official website of this organization is given below.
Maria Montessori believed that children learn when they are ready and learn best when they are not placed in competition with other children. She was a trained psychiatrist who worked with children with disabilities. She developed her own theories of cognitive development. One of the defining things that she brought into the classroom setting was the idea of tactile stimulation. She made sandpaper alphabets and thought that children learned best through exploration versus lecture.
It is difficult to study Montessori psychology because she presented much of her information through practical use. She did not really leave behind enough formal data to support her schools, but other psychologists picked up where she left off and have expanded upon her theories. Her theories are often blended with other theories.
When you say "How can we overcome them?," I am not sure as a teacher that I feel that we need to. I am much more in favor of embracing her ideas. I teach students with disabilities and many of the methods that she used are the tools that I use to make teaching more relevant for my students. In addition, my children attended Montessori schools and I loved the level of creativity they experienced.