How children learn Math in the Montessori classroom?
Learning mathematical concepts in a Montessori classroom begins concretely and progresses towards the abstract. They are developed from simple to complex. Process is taught first and facts come later. Order, coordination, concentration, and independence are experienced by the child using these materials.
The math activities are organized into five groups.
Group one introduces sets of one through ten which prepares the child for counting and teaches the value of quantity. Children begin to associate numeral and quantity with number rods and number cards. A child will gain a growing understanding of sequence. Spindle boxes, cards and counters, the short bead stair, and other 1- 10 additional counting activities a teacher may add, reinforce the one through ten numeral concepts.
Group two involves the decimal system using the golden bead material. The child will become familiar with the names of the decimal categories; units, tens, hundreds, and thousands. A concrete experience with each category is represented by beads. Quantity will be followed by symbol and association.
Group three deals with the operations using the golden bead material. The concept and process of addition, subtraction, multiplication, and division are presented. Children work with each other and benefit from these exercises using the bank game. Progression then continues using operations with the stamp game.
Group four consists of linear counting. Quantity is presented using the teen and ten boards followed by symbol and association. The one-hundred board and bead chains develop number concepts and recognition of numbers one through one-hundred. The bead chains also introduce the child to skip counting; five, ten, fifteen, twenty, and so on.
Group five contains activities such as strip boards, snake game, and memorization of facts. Fractions are also a part of this group. Fraction skittles and insets serve this purpose.
The activities in the Math area are not to be implemented at a set pace. Providing the child with the materials at precisely the right challenge level will enable the child to demonstrate his development to the teacher through his progress. A child that is able to grasp such math concepts as addition and subtraction demonstrates the successful use of the math materials. The materials are so beautifully designed and appropriate for each child during his sensitive periods of learning math. Mathematical apparatus provides the necessary stimulation for the child to learn math concepts more readily.
By age four, the child is ready for the language of mathematics. A series of preparations have been made. First the child has established internal order. Second, the child has developed precise movement. Third, the child has established the work habit. Fourth, the child is able to follow and complete a work cycle. Fifth, the child has the ability to concentrate. Sixth, the child has learned to follow a process. Seventh, the child has used symbols. All of this previous development has brought the child to a maturity of mind and a readiness of work. The concrete materials for arithmetic are materialized abstractions.
They are developmentally appropriate ways for the child to explore arithmetic. The child gets sensorial impressions of the mathematical concepts and movement supports the learning experience. The material begins with concrete experiences but moves the child towards the abstract. There is also a progression of difficulty. In the presentation of the material, a pattern is followed. It is used throughout the arithmetic Exercises. For the presentation of the mathematical concepts, the child is first introduced to quantity in isolation, and is given the name for it. Next, symbol is introduced in isolation and it is also named. The child is then given the opportunity to associate the quantity and symbol. Sequence is given incidentally in all of the work. Various exercises call for the child to establish sequence.
The mathematical material gives the child his own mathematical experience and to arrive at individual work. There are some teacher directed activities but these are followed with activities for the individual. Some work begins with small group lessons, these too will be toward independent, individual work.
The adult is responsible for the environment and the child’s experiences in it. It is important to provide the indirect preparation of experience with numbers before it is studied. The arithmetic materials must be carefully presented as the child is ready. Montessori has emphasized that young children take great pleasure in the number work. It is therefore important that the adult not pass on any negative overtone onto the child’s experiences with arithmetic. These Exercises are presented with great enthusiasm. They must be carefully and clearly given to the child. In this work, it is also important for the directress to observe the child’s work. From observation, the directress will know if the child is understanding the concepts or if further help is needed. As always, the adult encourages repetition and provides for independent work, which will lead to mastery.
When the child is ready, the absorption is as easy and natural as for other areas of knowledge. It is empowering and brings the child to a level of confidence and joy in another path of culture. The abstract nature of man is not an abstraction if the child’s development is understood by the adult.