The Montessori Method and Memorization
This second article in a two-part discussion describes additional areas of the Montessori math curriculum as practiced by our teachers at The Montessori Schools. However, the following explanation delves deeper into how Dr. Montessori’s teaching methods help bridge concrete applications for computation to a more nuanced understanding of mathematics. Skills developed here will serve the child well in elementary grades.
Progression Away from Concrete Aids
In a Montessori classroom, young children often begin by counting beads to solve simple addition, subtraction, and multiplication problems. More advanced mathematical concepts are also comprehensible through direct manipulation of classroom materials.
In the final years of Primary, the goal is to successfully solve a problem on paper with pencil, independent of the Montessori materials. However, it typically takes several years (usually into the elementary years) for a child to completely wean himself or herself from such concrete aids.
In response, our early childhood math materials include numerous works designed to help a child gradually memorize the basic math data contained in more traditional memorization tables. These works include the Snake Games, the Strip Boards, the Finger Boards, and the Tile Boards. For multiplication memorization, we also have the Bead Box and Board.
Memorization in Practice
Addition with the Bead Stairs is an early memorization work, as it still relies heavily upon concrete representations of numeration, or individual beads as units. The work performs an important role at a critical juncture in a child’s cognitive development: practice adding while building equations using the symbols + and =.
Practice and more practice with equations is necessary, for young children don’t readily comprehend higher numbers without one-to-one correspondence.
The Short Bead Stairs reinforce the abstract idea of quantities from two through nine. Addition with the Bead Stairs uses a second Bead Stair to initiate the child into the process of memorizing simple addition facts.
fig. 1. The Montessori Bead Stair. Each quantity (1-9) is represented by the corresponding number of beads, wired together as a bar.
Each bar in the Bead Stair is a specific color, which enables a child to visualize combining one quantity of beads with another quantity of beads. The answer is secured from the second bead stair, which provides a kind of control of error, as the child can match the combined beads with the final sum.
Dr. Montessori designed a series of memorization charts to assist the child in more advanced (and more abstract) stages of working with the operations. The Subtraction Strip Board prepares the child to work on memorizing subtraction facts through exploring all the combinations when the numbers are subtracted from one another.
fig. 2. The Montessori Subtraction Strip Board. Red and blue sets of wooden strips increase in size: the shortest corresponds to one square on the board; the longest is nine times the length of the first.
Three sets of wooden strips (red, blue, plain) enable a child to “build” a problem on the board. He or she uses a plain strip to cover numbers greater than the largest number, which has a quantity being subtracted from it (represented by a blue strip). The remaining red strip represents the solution to the problem. The child can continue to exchange components, therefore, exploring all the ways that numbers 1 to 18 can be subtracted from one another.
The Multiplication Finger Boards are simple visual aids to assist a child in memorizing multiplication tables. Consistent with an important tenet of Dr. Montessori’s philosophy, movement is employed for cognition—or, more simply put, a young child’s comprehension is increased with (literally) hands-on learning.
After placing the right index finger on the smaller number and the left index finger on the larger number, a child moves one finger at a time, slowly inching his or her way toward the solution. The two fingers meet where the select column and row naturally convene.
All of the memorization boards have a control chart, which permits the child to check his or her own answers. The control charts are also indicative of the Montessori Method’s emphasis on nurturing within children, even within very young children, a sense of autonomy and personal responsibility for their own education.
Our teachers also encourage children using the boards to write the answers to problems on paper, further reinforcing the concepts embodied in the work. The boards are tools to aid children in their abstract memorization of math equations. Although the materials are somewhat abstract, the process is still concrete.