- Montessori Philosphy
Comprehension Strategies in Math
Dr. Maria Montessori emphasized the value of active learning for children—experiences involving the use of their hands for practical purposes and for the acquisition of knowledge. Today’s educators would call this experiential learning.
She wrote in her book The Secret of Childhood that the child’s capacity to distinguish similarities and differences impacts his or her capacity to “mold [their] own intellect.” As a result, in the Montessori classroom, we place much more importance on the process of understanding how a concept is formed and implemented, than upon the accuracy of the end product.
Accuracy is not necessarily the aim when teaching math to young children.
Perhaps no subject area in the classroom is more challenging than math to adhere to this idea of the supremacy of ideas and procedure over product. After all, what could be more straightforward than 1+2=3?
When the child writes a number backward.
When the concrete materials representing a quantity are short a few units, but the answer is correct.
When the written answer is correct according to the concrete materials but the equation is written inaccurately.
When the child clearly understands the procedure but executes it incorrectly.
Accuracy is Not Always the Aim
In the Montessori classroom, the young child learns mathematical concepts through experiencing progressive stages of work where the tangible, direct associations with real objects are slowly eliminated. He or she is building over time a knowledge base—a foundation of understanding—to reference when problem solving now and in the future. This is the most important task at hand.
Solid grounding in the theoretical always trumps accuracy for the immediate and the particular.
Dr. Montessori described this “construction of the mind’s content” in The Absorbent Mind as a process of abstracting; the process serves to simplify and unite with the end goal of expression. Many of the early childhood Math works are in actuality indirect preparation for much more conceptually complex operations, such as extracting square and cube roots. The young child is subconsciously absorbing many complicated mathematical concepts at an early stage of development. Whether or not he or she has a solid grounding in the theoretical may ultimately affect the acquisition of knowledge in later years.
Many of the Montessori materials serve as preparatory exercises for later, more complex math, including algebra, geometry, and eventually calculus.
In the Montessori classroom, one of our primary objectives is to nurture the capacity for active observation. A child receives images and data through the senses but eventually becomes more selective in his or her choices and conclusions. Experience is being integrated into a larger, more general understanding of the world. Trusting your child’s inner sensibility is trusting their capacity to function on a higher, rational level. Unnecessary correcting can plant seeds of self-doubt.
The ability to reason is gradually developed and significantly influenced by a child’s access to environmental stimuli. Increasing a child’s comfort level with math materials more often than not outweighs correcting isolated instances of inaccuracy.
Also, why diminish a child’s enthusiasm for math by needlessly correcting him? This is especially true with longer math works that methodically take a child through a series of steps, with the goal of reinforcing a particular concept.
The Bottom Line
Central to the Montessori Method is the idea that a child should feel fulfilled, content, successful, etc., as a result of manipulating materials. Outside intervention, positive or negative, has the potential to lessen feelings of confidence and self-sufficiency. Correcting (or praising) a child becomes superfluous.
In simple terms, the outcome of completing or failing to complete a work is just more information for the educator or parent. Observations of a child’s progress, ideally, lead to responses correctly reflecting where he or she is at developmentally.
For a child, the end product of his or her efforts is more data about the world—more information to absorb and more feedback that he or she will correctly apply later.
Final Note about Writing Numbers (or Letters) Backward
Current research indicates that recognizing mirror images comes naturally to children. According to an article in The Economist (10 July 2010, 77-78), the Federation of European Neuroscience Societies (FENS) concluded that learning to read requires the brain to “undergo profound changes, including unlearning the ancient ability to recognize an object and its mirror image as identical.” Montessori teachers have known for some time that it’s simply a matter of time; the child will eventually correct himself. So, don’t worry. It’s normal for a child to initially write his numbers backward.