Montessori students often refer to the “work” they are doing, by which they mean a particular Montessori material. These materials are designed to be “self-teaching,” in that a child who is taught to use them can learn from them without having a teacher present to verify whether the lesson has been completed correctly. The material itself has “control of error,” which may mean, for example, that it only fits together in a particular way.
Montessori materials are designed to teach abstract concepts through hands-on activities. Sandpaper letters are an example from the Early Childhood language curriculum: students trace their fingers along a letter made of sandpaper and the physical movement and texture create a muscle memory of the letter’s shape. A child is able to recognize letters well before he or she has the fine motor ability to hold a pencil. In the math curriculum, students use beads to count and do math problems. They can easily grasp the concept of subtraction, for example, because they are literally taking away a certain number of beads.
Montessori materials are sequential. Each work prepares the child for the one after it, which adds to their learning. Materials also have depth, in that they can be used to teach a variety of concepts. A good example of this is the binomial cube, a cube composed of 8 wooden blocks which fit together in a binomial pattern, representing the cube of two numbers, (a + b). This work is first used as a three-dimensional puzzle to help the child learn to recognize patterns. Later, students use it to physically represent the algebraic equation (a+b)3. New ideas can be introduced through the use of familiar works as children mature, which makes learning feel like a natural unfolding rather than a series of unconnected concepts.