Montessori students often refer to their “work,” meaning the particular material they are using or the name of an activity. The materials are designed to be “self-teaching,” meaning a child taught to use them can learn to verify the lesson’s correctness without a teacher’s presence. The material itself has “control of error,” which may mean, for example, that it only fits together in a particular way.
Montessori designed the materials 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 can recognize letters well before having the fine motor ability to hold a pencil. In the math curriculum, students use beads to count and do math problems. For example, they can easily grasp the concept of subtraction because they are 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. The materials also provide depth as they teach various concepts. An excellent example is the binomial cube, composed of 8 wooden blocks that 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 represent the algebraic equation (a+b)3 physically. As the children mature, they can be introduced to new ideas through familiar works, making the learning process feel like a natural unfolding rather than a series of unconnected concepts.