The education plan envisioned and implemented by Maria Montessori was based on her observation of children in diverse cultures and the required response to their needs. This led her to the conclusion that children have basic behavioral tendencies of exploration, imagination, order, repetition, manipulation, precision and communication.
Students who learn math by rote method often do not have a real understanding or ability to put their skills to use in everyday life. Montessori students use hands-on learning materials that make abstract concepts clear and concrete. Using math materials in the early years lays the foundation for later cognitive development and prepares students for the gradual transition to abstract thinking - transforming ideas into actions using concrete materials.
Mathematics are introduced by concept, not solely by pattern and are carefully engineered to introduce both the concept of quantity and the related symbols, beginning with numbers 0 through 9. The child is introduced to concepts with visual and tactile material that corresponds to each new idea. The simplicity and the tactile nature of the materials allows the child to not only calculate, but to achieve a deep understanding of number concepts and function. A strong understanding of mathematics provides children with a concrete foundation to find alternative solutions to problems. They are not dependent on following patterns, but rather learn the reasons for a function and learn to use logic to apply it in various situations. Due to the concrete nature of the materials, the child is able to work with the basic concepts of fractions, geometry and algebra.