Everything we learn comes first through our senses. Babies are able to discriminate the sound of their parent’s voice, the shape of their family’s faces, the smell of milk, and the touch of skin. This is the beginning of learning about the world. So much of what is taught in school, especially in math is rote learning and many students have little idea of how to put their skills to use in everyday life. Montessori education works with concrete educational materials first and later introduces abstract concepts once the understanding of the process has been internalized. For instance, in the Sensorial Area, we have materials called the Red Rods. The Red Rods are 10 graduated rods, each 10 centimeters longer than the one before. Three-year-old children learn to carry these rods with two hands, one rod at a time to a work rug. As their small arms stretch to carry the last rod that is 100 centimeters long (one meter), they learn the terms short and long, longer, longest as they compare and contrast the 10 rods. This is the very beginning of measurement and base 10 system.
The corresponding materials in the Math Area are the Red and Blue Rods. These rods are identical in size to the Red Rods; however, every 10 centimeters they are painted red or blue, alternating to distinguish their segments. The children are familiar with arranging longest to shortest in a stair. They count each segment. This material helps them visualize the concept of quantity first and the numeral second – concrete to abstract.
Later, in a follow-up lesson, they can put the corresponding numeral card next to the correct rod. In addition to nomenclature, the students learn about hierarchical inclusion. One is part of two; two is part of three, etc. They can also learn about addition. If I put the one-rod and the two-rod next to each other, they are the same length as the three-rod. They are able to explore similar relationships with all of the rods. Similarly, the Spindle Boxes provide a way for children to count the correct number of spindles to go into a box with the number indicated. The boxes are labeled 0 to 9. As the child picks up each spindle with one hand and transfers it to the other hand, and then into the box, the number grows. One spindle is easy for a small hand to manage. Nine spindles are not. Again, this material teaches a very concrete lesson of quantity getting larger. No spindles are put into the box labeled “0”. At a very young age, children are taught that “0” is the empty set.
If the child has counted correctly, there will not be any spindles left over. If there are leftovers or not enough, somewhere a mistake has been made. The additional benefit of Montessori materials is the control of error. No person has to tell the child a mistake has been made, the child discovers the mistake and can recount. Part of Montessori’s genius was in the well thought out design of materials and the built-in control of error that allows children to learn from their mistakes. All of the carefully designed activities that Montessori teachers put on the shelves for children to discover, enjoy, and learn have elements of sensory inspiration. The pouring work with jingle bells in the Practical Life area teaches fine motor skills, preparation for pouring dry and wet materials, and makes an enjoyable tingling sound when the small bells fall into the dish.