The materials for mathematics introduce the concept of quantity and the symbols for the numbers 1 through 10. The quantity is introduced by a series of rods, which the child can count and compare. He matches sets of symbols cards with the rods. Using a variety of beads and symbol cards, the child becomes familiar with the numbers as a decimal system including concrete experiences with the operation of addition, subtraction, multiplication and division. These exercises not only teach the child to calculate, but they provide a deep understanding of how numbers function. He learns concrete mathematical concepts and the materials lead him to the abstract, so that his understanding has substance. Because of the concrete nature of the materials, the child is able to work with basic concepts of fractions, geometry and algebra.Language
According to Dr. Montessori, the evolution of language begins with the infant's unique capacity to absorb fragments of language, which serve as a basis for his development. The child first discovers that sounds have meaning, and then he isolates the parts of speech. Finally, he grasps the use of sentences. The constant assimilation of language results in a sudden expansion of the vocabulary. The child learns language naturally- he automatically takes it from his environment. The work of the parent and the teacher are to expose him to the equivalent forms of written language, which he learns through the same general pattern of development. The Montessori child begins reading when he is ready and proceeds at his own pace. His experiences in practical life and sensorial education serve as a preparation for this. The sandpaper letters provide a phonetic basis for reading. The child's desire and sensitivity to touch are utilized by these letters that are cut out of sandpaper and mounted for tracing. He not only hears the sound and sees the shape, but trains the muscles for when he begins writing. With cut-out letters, the child builds his own words on a mat. The material frees him from the fatigue of his still developing writing skills, and yet gives him the opportunity to pursue his interest in words. The child builds up his store of words through storytelling, conversation, and many other exercises. These activities serve as preparation for the time when the child assimilates what he knows and explodes into writing.Other Academic Areas
Montessori introduces grammar, geography, geology, biology, history, etc. to children between the ages of three and six. The reason is that at this age children can joyfully absorb many difficult concepts if they meet them in concrete form. The common stumbling blocks in the middle elementary grades can be exciting if they are presented to youngsters at an earlier age when they enjoy manipulating with their hands. In a Montessori classroom a unit or fraction is not simply a number on a paper; it is something, which a child can hold in his hand. A verb is not just a word on a paper; it is something, which he can cut out. In similar fashion he can pour water around an island or form a square with five rows of five beads each. The materials that make these concepts tangible for him will serve as touchstones in his memory for many years, to clarify the abstract terms when he meets them again and again in future learning situations.