“The real abstraction is a creative process undertaken by the child to construct her own
knowledge. The indirect preparation and the presentations lead the child to discover
important facts, derive formulae, and so on.”
—John McChattin-Nichols, The Montessori Controversy
Montessori math materials were designed to allow the child to explore a concept in a hands-on form. Here, the child manipulates objects by sight and touch to learn mathematical concepts. The lesson presentation begins simply and slowly gains complexity, moving from concrete to abstract. Children move through the concepts at their own developmental pace. The materials are introduced left to right and top to bottom (except when working with place value, which is right to left). Through repetition the child develops order and concentration by the use of actual objects to move toward the end result of a more mathematical abstract level.
This use of hands-on or actual objects will decrease as the child understands the process of a particular mathematical concept. If needed, a three-period lesson may be given by the directress to focus on what is not known. For example, Sequin designed the teen board, which helps children learn numerals eleven through nineteen. The board contains movable wooden numbers (symbols) and golden beads to show quantity. In playing with the board, “A child must therefore remember his number not only while he moves among his companions as he approaches the large table, but also while he is picking up his pieces and counting them one by one.” The child directly develops the concept of abstract theories order, as well as stimulates his mathematical mind, defined as containing “mathematical structures necessary for the order, sequences, and precision of mathematics.” Indirectly the child gains recognition of numbers eleven through nineteen in symbol, as well as the association of the quantity to the numeral.
Historically, the sensorial area is a preparation for math, because the lessons for dimension (pink tower, brown stair, and red rods) all have ten pieces (unit of the decimal system). The pink tower, brown stair, and red rods are all built in metric dimensions, preparing the child indirectly for an understanding of the metric system. The red rods used in sensorial materials are the same size as the red and blue rods that the child will encounter in the math area, and aid in the sequence and progression skills cognitive skills that will be used in understanding math; as you can see, all the categories build upon one another.
In the Montessori classroom ages three through six, the absorbent mind is fast at work learning mathematical concepts. During this sensitive period “a child must experience stimulation or grow up forever lacking the adult skills and intellectual concepts that he missed at the stage when they can be readily learned!” Montessori designed her classroom so that every area could be related in some fashion to mathematics. For example, in the Practical Life area, numeration is found in the number of tables, chairs, rugs, insets, and pencils set out to perform the insets. In Music it is found with time counting and rhythm. Science and Geography offer mathematics through the study of distance, time, and weight. The Language area prepares the child for left to right progression of reading or tracking through incidental reading, pictures, and objects. And as mentioned above the biggest contribution to mathematics is the sensorial area, where the lessons are attractive while offering abstraction. There, mathematical concepts are built through the repetition which satisfies the child’s curiosity.
The mathematical materials aid in developing a child’s sense of order, concentration, and ability to grasp abstract concepts. The following is a small selection of mathematical activities to introduce to your child. Because mathematics spans such a wide array of concepts and has a varied range of complexity, there is no way I could include an activity for every concept! You can find comprehensive lists of activities, including the decimal system, the concept of zero, and linear counting, on the web. For now, I hope you enjoy the lessons I have created for “At Home Montessori”.