Arithmetic in the Montessori classroom provides not only a very thorough foundation in all the major operations, but it also permeates other subject areas and ensures that each student is able to comprehend necessary aspects of these areas. Starting from the very beginning, the Montessori math materials make it possible for even the most advanced operations to be performed by those with minimal exposure. Exchanging for tens up to a thousand becomes a game and makes it possible for dynamic addition to be successfully accomplished with only basic instruction. Then, dynamic multiplication is simply a process of understanding the vocabulary and once again exchanging for tens.
“As the materials progress in complication, the control of error is shifted to the child himself.”
The more difficult operations of subtraction and division are made less so by taking out the subtrahend (dividend) and taking away (dividing up) only what is there. If there is not enough, once again students go back to what they know and exchange for tens; only this time, they go backwards. By making it clear the role that the bank plays in every operation it is simply a matter of precision in counting and exchanging. Even precision errors, though, lessen automatically with time as the students’ own desire to learn more propel them to be more precise in order to move on to the next level in abstraction.
This foundation that Montessori students receive in the basic arithmetic operations enable them to take what they know and abstract it for use in the other areas of a Montessori classroom. In Language Arts, the students can abstract at their level in word problems using the language that is consistently used when that operation is taught. In Chemistry, the students use their math skills to compute the number of neutrons in a given element by subtracting the atomic number from the atomic weight. In History, the students can figure out an official’s term by subtracting the two dates that the person was in office. In Cosmology, the students explore even greater numbers than they already use when computing the size of planets and the distances of each planet from the sun.
These examples are just a few ways that math is used throughout the Montessori classroom. At no time do the students object to having to do math while they are doing a cultural work. Each work is understood to be part and parcel of the other. There is even a sense of accomplishment when the students are able to use a newly learned skill in a work that is seemingly unrelated to the skill learned. This comprehension, then, often encourages the students to review what they know because they are now able to see the practical applications of the work they have been doing.
“The exercise which develops life, consists in the repetition, not in the mere grasp of an idea.”
Additionally, the necessary memorization of arithmetic facts, while not forced upon the students, is made easy through games which focus only on the students gaining this type of knowledge. The students play such games as Bingo using math equations as questions and the answers in place of the letters. Another memorization game is the 24 Game, whereby the students are given four numbers and must use each number only once in an effort to get 24. They play this game only when they have a firm foundation in each operation. Once they have played these games a few times, the students notice that little by little their math facts have greatly improved, almost effortlessly. They also realize that their dynamic math work has gotten substantially easier and seek other ways to challenge themselves, such as timing themselves or increasing the difficulty of the problems.
“The essential thing is for the task to arouse such an interest that it engages the child’s whole personality.”
The Montessori math materials make it possible for students to, not only perform difficult math equations, but to also truly understand what they are doing. These students are not intimidated by very large numbers or complex problems, and generally seek ever greater challenges. Therefore, the next steps, including algebra and operations with fractions, are not beyond their level. In fact, these are simply other extensions that they embrace as a little something new from something they know very well. The greatest thing that Montessori students come away with is that math is not something to be feared or only understood by people with “mathematical minds.” Everyone is able to do a wide variety of mathematical equations, all they need is the material to show them how.
 Lillard, Paula Polk. Montessori: A Modern Approach. New York: Schocken Books; 1972: p. 64.
 Montessori, Maria. The Absorbent Mind. Wheaton, Ill.: Theosophical Press, 1964: pp. 357-358.
 Montessori, Maria. The Absorbent Mind. Wheaton, Ill.: Theosophical Press, 1964: p. 206.