# “the Montessori Math Materials Progresses from Concrete to Symbolic Representation. Illustrate This Progression with Appropriate Exercises”

The objective of Montessori is to develop the concept first. By using concrete materials during the early, sensitive years, the Montessori child can learn the basic concepts of mathematics and language. Montessori students use concrete hands-on learning materials that make abstract concepts more clear. Lessons and activities are introduced simply and concretely in the early years and are reintroduced several times during the following years at increasing degrees of abstraction and complexity.

All of the materials in the Montessori classroom have been specifically designed to attract the interest of the student, while at the same time teaching an important concept. The purpose of each material is to isolate a certain concept the child is bound to discover. Montessori believed that “what the hand does, the mind remembers”. Concrete materials make concepts real, and therefore easily internalized. The student works abstractly (paper and pencil) when he or she has internalized the pattern and no longer needs the Montessori material. Maria Montessori believed that all humans are born with a “mathematical mind”. The use of concrete materials to learn abstract concepts and operations is fundamental to the development of the mathematical mind in the Montessori classroom as the materials represent abstract ideas. The materials can be felt and manipulated so that the hand is always involved in the learning process. This approach to math is logical, clear and extremely effective. It allows the students to internalize math skills by using concrete materials and progressing at their own pace toward abstract concepts. Students understand and develop a solid foundation in mathematics. Later, as they master the concrete they begin to move to the abstract, where the child begins to solve problems with paper and pencil while still working with the materials.

Geometry too, relies on the concreteness of the materials. Traditionally, geometry is taught as an abstract series of rules, theorems, and propositions meant to be memorized by the student. Maria Montessori saw geometry as firmly rooted in reality. Her geometry curriculum uses concrete,...

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