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

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Mathematics is all around the young child from day one. For example certain matters like “How old are you?” “You were born on the 2nd” “I have 2 brothers”. Number itself cannot be defined and understand of number grows from experience with real objects but eventually they become abstract ideas. It is one of the most abstract concepts that the human mind has encountered. No physical aspects of objects can ever suggest the idea of number. The ability to count, to compute, and to use numerical relationships are among the most significant among human achievements. The concept of number is not the contribution of a single individual but is the product of a gradual, social evolution. The number system which has been created over thousands of years is an abstract invention. It began with the realization of one and then more than one. It is marvelous to see the readiness of the child’s understanding of this same concept. Arithmetic deals with shape, space, numbers, and their relationships and attributes by the use of numbers and symbols. It is a study of the science of pattern and includes patterns of all kinds, such as numerical patterns, abstract patterns, patterns of shape and motion. In the Montessori classroom, five families with math are presented to the child: arithmetic, geometry, statistics and calculus. More precisely, the concepts covered in the Primary class are numeration, the decimal system, computation, the arithmetic tables, whole numbers, fractions, and positive numbers. We offer arithmetic to the child in the final two years of the first place of developments from age four to age five and six. "If education is always to be conceived along the same antiquated lines of a mere transmission of knowledge, there is little to be hoped from it in the bettering of man's future" -Maria Montessori-

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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