This impulse to produce order out of disorder is called the "mathematical mind". Dr. Montessori borrowed this phrase from the works of Blaise Pascal, a French philosopher and mathematician, who said "man's mind was mathematical by nature and that knowledge and progress came from accurate observation." (The Absorbent Mind (1988) page 169). For the purpose of this post, however, it is important to distinguish between the words arithmetic and mathematics.
Observation, representation and investigation of patterns and relationships are also involved in mathematics. "Mathematics is often defined as the science of space and number…but a more apt definition is that mathematics is the science of patterns. The mathematician seeks patterns in number, in space, in science, in computers, and in imagination. Mathematical theories explain the relations among patterns." (The science of patterns (1988) pages 611-616). To summarize, the spontaneous ability to organize, classify and quantify patterns and relationships within the context of daily experiences is what Dr. Montessori calls the mathematical mind.
The sensorial dimensional materials make a huge contribution to the ordering of the child's sense perceptions. These materials encourage observation and enhance awareness of differences in dimension. The pink tower, for example, consists of 10 cubes that increase in size by increments of one centimeter squared. This provides a visual and muscular perception of dimension and prepared the child for mathematices. The fact that there are ten cubes is a preparation for the decimal system. The child forms a sensory impression of the precise size of one cubic centimeter as well as the size of a litre. It is also a preparation for later work with cube roots in the bead cabinet.
Part 2 to follow.