In this world, students often learn math by rote, without any real understanding or ability to put their skills to use in everyday life. Learning comes much more easily when they work with concrete educational materials that graphically show what is taking place in a given mathematical process.

WillisMathIn Montessori, we use hands-on learning materials that make abstract concepts clear and concrete. Students can literally see and explore what is going on. Our approach to teaching mathematics is based on the research of Drs. Maria Montessori and Jean Piaget. It offers a clear and logical strategy for helping students both understand and develop a sound foundation in mathematics and geometry.

As an example, consider the very basis of mathematics, the decimal system: units, tens, hundreds, and thousands. Since quantities larger than twenty rarely have any meaning to a young child, Dr. Montessori reasoned that we should present this abstract concept graphically. Children cannot normally conceive of the size of a hundred, thousand, or million, much less the idea that a thousand is equal to ten hundreds or one hundred tens.

Montessori overcame this obstacle by developing a concrete representation of the decimal system. Units are represented by single one-centimeter beads, a unit of ten is made up of a bar of ten beads strung together, hundreds are squares made up of ten ten-bars, and thousands are cubes made up of ten hundred-squares. Together, they form a visually and intellectually impressive tool for learning. Very young children can form great numbers. “Please bring me three thousands, five hundreds, six tens, and one unit.”

From this foundation, all of the operations in mathematics, such as the addition of quantities into the thousands, become clear and concrete, allowing the child to internalize a clear image of how the process works.

We follow the same principle in introducing plane and solid geometry to very young students, using geometric insets and three-dimensional models that they learn to identify and define. Five-year-olds at The Renaissance International Schoolh can commonly name geometric forms that most adults wouldn’t recognize. The study of volume, area, and precise measurement in everyday applications around the school is introduced in the early years and continually reinforced and expanded.

Montessori mathematics climbs in sophistication through the higher levels. It includes a careful study of the practical application of mathematics in everyday life, such as measurement, handling finances, making economic comparisons, or in gathering data and statistical analysis.

Elementary level students continue to gain hands-on experience by applying math in a wide range of projects, activities and challenges. They prepare scale drawings, calculate area and volume, construct three-dimensional geometric models, and build scale models of historical devices and structures.

Precise measurement and comparison is a crucial application of mathematics, and our math students engage in all sorts of calculations: determining the amount of gas used by the family car, the electricity burned when our lights are left on overnight and the perimeter of buildings.