In a recent article in the New York Times titled “Learning to Think Like a Computer,” author Laura Pappano mentions the need for students in all disciplines to understand and practice “computational thinking.” She defines these skills as “recognizing patterns and sequences, creating algorithms, devising tests for finding and fixing errors, reducing the general to the precise and expanding the precise to the general.” As I read through the article, I thought of the scientific Montessori materials used daily in our classrooms that give our students experiences with these skills. From the time they are toddlers, Montessori students are challenged to identify patterns, follow sequences, and recognize errors in their own work.
At its most basic level, the layout of a Montessori classroom is designed to aid the recognition of patterns and sequences. The shelves are organized neatly from top to bottom and from left to right, reinforcing the same orientation with which we read. On a deeper level, the materials themselves are designed to appeal to the senses and entice curiosity and repetition, thereby enhancing the young child’s ability to directly compare, contrast and discover the patterns and sequences inherent in the environment. Dr. Maria Montessori once said, “The education of the senses has, as its aim, the refinement of the differential perception of stimuli by means of repeated exercises.” It is through these independent, repeated exercises that children gain this deep perception of patterns that exist in the world around them.
In traditional educational settings, children go to school and do work that is prescribed by the teacher. Lessons that employ Montessori materials are teaching students to think through a complex algorithm of steps each time they independently take an activity off the shelf: selecting the activity, identifying and following each step of the activity, completing the task at hand, and then returning the work to its space on the shelf. The child then has the freedom to create his or her own algorithm in how the material can be used effectively. Each material has variations and extensions (new steps in the algorithm) that can be shown by the teacher guide, or more often, discovered by the student. This logical process is applied across all areas of the curriculum.
In addition to thinking through algorithms, learning to devise tests for finding and fixing errors is another aspect of computational thinking. Dr. Montessori was intentional about creating learning materials to “provoke auto-education,” in other words, materials that were self-correcting. In this way, the child could experiment with a material and deduce the correct answer through trial and error, rather than having the teacher validate the correct answer. “Indeed, it is precisely in these errors that the educational importance of the didactic material lies.” (The Montessori Method, p. 171) Devising tests for finding and fixing errors is an essential element the Montessori method of education.
Another skill listed as essential to computational thinking is reducing the general to the precise and expanding the precise to the general. The Montessori math materials are the best example of the student’s ability to breakdown abstract concepts into concrete examples and vice versa. From the start, the red and blue rods in the Primary classroom allow a child to explore the concept of one to 10 with his or her hands. Also, an exploration of the introductory golden bead tray involves realizing that the 10-bar is made up of 10 single unit beads, the 100-square is comprised of 10 10-bars, and the thousand cube is comprised of 10 100-squares. This understanding of place value and quantity is further reinforced by its relationship to the geometric forms of a line, square and cube.
My favorite example of how the materials demonstrate the connection between precise and general, or concrete and abstract, is in the math bead cabinet. In the Primary classes, the student uses the square chains to physically count one-by-one up to the square of each number, then uses the cube chains to count to the cube of each number (i.e., the cube chain of threes counts to nine, and the cube chain of threes counts to 27). In Elementary classes, the chains are then used for skip counting (e.g., three, six, nine, 12, 15, etc.), which becomes a lesson in multiples. Studying multiples provides a peek into the abstraction of pre-algebraic formulas.
So far we’ve explored some of the ways the Montessori materials are leading children to develop computational thinking. In Part Two of this three-part series, we will interview Jonathan McLean about how our sixth, seventh and eighth level students are applying computational thinking in his Creative Labs course in the Middle School.