Maria Montessori believed that a child learns the basic concepts of mathematics in two ways: by using concrete materials during the early years and by abstract methods in the elementary years. If a child has access to the wonderful, concrete materials within a classroom during the early years, building a wonderful foundation for future learning, then he/she is much more likely to learn the facts and skills that come in the elementary years. Consider how many of us learned our math facts too early through abstract drill and drudgery only to walk into a Montessori classroom and exclaim, “If only I had been taught this way, it would have made more sense!”
Through careful observation of the individual child, a trained teacher knows when a child is ready to progress. Therefore, the child sets the pace of the lessons, not the teacher. It is important to note that before a child gets to the math materials themselves, a lot of mathematical concepts are being discovered within the other areas of the room, specifically, within the Sensorial and Practical Life areas.
Within the Practical Life area, a child is building up the following: Order, Concentration, Coordination, and Independence, or OCCI. Without these skills, a child will have more difficulty manipulating smaller mathematical manipulative items or lack the concentration level required to stick with the lesson. Also, consider how the Mathematical mind requires a sense of order at this young age and how these materials foster growth because of the order of steps involved. Also, with the food preparation curriculum the child is beginning to recognize concepts such as one-to-one correspondence, measuring, equal parts, and counting snack items.
Within the Sensorial area the child is exposed to the concept of base ten because many works have ten items (ten pink cubes, ten brown rectangular prisms, ten knobbed cylinders, ten knobless cylinders). The child is absorbing this through the senses and self-discovery, not by direct instruction. Also, the geometry of this area is amazing. All of the correct terminology is being introduced enriching the child’s vocabulary along with introducing basic geometric principles. The Geometric Cabinet and the Triangle Boxes all help the child discover not just geometry but also how parts can make a whole, a beginning to fractions. The other wonderful works allow the child to refine the senses giving the child the ability to discriminate size, shapes, and differences more effectively, a skill needed in all mathematics. Lastly, this area gives the child the necessary pre-numeration concepts such as above, below, beside, etc. so that the child can begin to build the skills needed later in mathematics.
After the foundation for math is laid in the Practical Life and Sensorial areas, what is the first math lesson and how does the sequence of lessons proceed? We start at the beginning by progressing through several works that help a child with the numerals and quantities: zero through ten. After the child has a strong concept of zero through ten, the next step takes the child in two parallel paths. One path takes the child into the decimal system (thousands, hundreds, tens, and units) and the other path takes the child into linear counting (1-1000). Both paths intertwine and support one another to give the child a strong understanding about numerals and quantities as well as experiences with operations (addition, subtraction, multiplication, and division).
This system in which a child is constantly moving objects with his hands and actively exercising his senses, also takes into account a child’s special aptitude for mathematics. When they leave the material, the children very easily reach the point where they wish to write out the operation. They thus carry out an abstract mental operation and acquire a kind of natural and spontaneous inclination for mental calculations. ~The Discovery of the Child, Maria Montessori.
One way to learn more about the Montessori math materials is by utilizing YouTube videos to see demonstrations of Montessori math materials. Or, join us in January for the Journey of Discovery to get a chance to see and work with the materials first hand in the classroom. We hope to see you all there! Click here for pics!