The center of Montessori pedagogy and the foundation upon which all is based, is the revelation of a nature of a child. She observed differently; the one the child had previously been known by a nature so different that journalists of long ago claimed the term "the new child".
Dr. Montessori stressed that our first and foremost goal is to assist the development of the child, which entails supporting each child's progress along the path of self-construction. She believed that one section of that path was mathematical, and she worked to bring mathematics to children in such a way that they could understand it, and so that they could appreciate and enjoy it.
Going out allows children to discover and satisfy their curiosity. Although we do plan lessons to spark interest and excitement, going out and classroom work must come from the questioning of the reasoning mind of the child. The children must be participating and experiencing society to some extent and this starts indoors: navigating and contributing to the classroom community.
A glance at typical geometry text might lead to the conclusion that geometry is far removed from daily life. Nothing could be further from the truth. The world that surrounds us is composed of shapes, lines, curves, and angles. There is geometry in nature - In the angles and planes of a mineral crystal, and in the symmetry of a butterfly's wings.
When it comes to language, we focus on helping the children understand their place, the place of our species in this world. Language is, of course, connected to our species deeply. If we think about the human tendencies, there is a tendency to communicate, and that takes language.
When we talk about a study of many aspects of the physical world we combine it under the general heading of Geography, which is the area of work that has a central place in the Montessori elementary class though for the children it is life and physical reality, in which every fascinating thing under the sun and beyond it appears.