# Montessori Materials: Mathematics

Montessori education is a system where a child constantly moves objects with his hands and is very active in exercising all his senses also focuses attention on the child’s aptitude for mathematics. The system believes that mathematical concepts can be absorbed by children naturally. There is the recognition that there are periods in a child’s development that the acquisition of ideas about mathematics is acquired indirectly through preparation and repetition of exercises that are scientifically developed didactic materials.

The Montessori materials on Mathematics provide the child the needed experience to form concepts of sequence and order, measurement, calculations, and exactness, thus laying the groundwork for the formation of the mathematical mind. The concept of order is introduced to the child in the way Montessori education set up the classroom shelves and trays and how materials for exercises are laid out in the work mat in the Montessori environment. Montessori materials are displayed in the class environment in a fashion that shows progress and sequence while every exercise is done into component steps that are logical and sequential.

Early exposures to calculations are introduced in the Montessori environment when a child estimates the number of drops of water needed to fill up a container. Precision is learned by the child when he starts measuring out drops of plant food. The early activities in the Montessori environment are not only meant to teach a child gain independence; they are indirect preparations for higher skills in mathematics. The child’s awareness of mathematical relationships is bolstered by the Montessori Sensorial Activities where he learns to distinguish the similarities or differences of objects. As the child constructs and compares different sensorial activities, he discovers the relationship between objects and activities learn how to make scientific hypothesis, and finally drawing conclusion. These experiences in the Montessori environment prepares the child to encounter more mathematical materials which will induce him to form more abstract thoughts, beginning with the concept of quantity.

*Learning Math the Montessori Way*

Montessori education readies the child for learning mathematics through a serious of preparations. The child is first prepared to establish internal order followed by the development of precise movement. The child is then prepared to establish the necessary work habit until he can ably follow and finish an assigned work cycle. By this time, the child would have developed his ability to focus his concentration and must have learned the skills of following a process. Finally, the child must learn how to use symbols. These preparations are aimed to bring about in the child the required maturity of his mind and the readiness to work. Materialized abstractions are concrete materials needed for the learning of mathematics.

Montessori mathematics education follows developmentally designed ways a child can explore the subject. The child first acquires sensorial grasps of the concept while different movements support the learning process. Montessori materials on Mathematics begin with clear experiences for the child but move later towards abstract concepts. The child also gets the impression of difficulty of the subject. The presentation of the different Montessori materials follows a definite pattern that is found throughout the mathematics exercise.

The presentation of the mathematical concept, the child is initially introduced to quantity in isolation and is provided the corresponding name for it. Next, the child is introduced to symbol, also in isolation and is also given a name for it. The next step is to give the child the chance to make an association of the quantity and symbol. All the exercises are to follow a sequence which the child must follow. The Montessori mathematical materials enable the child to acquire his very own experience in mathematics as he finishes the individual work.

Mathematical exercises are grouped. Some exercises are sequential while some are parallel.

- The first group of exercises is about Numbers through ten. This is an example of sequential group experiences. The child is prepared to have a full understanding of numbers through ten.
- The second group is the Decimal System which is introduced to the child after he acquired the full understanding of the first. The focus of the exercise is on the hierarchy of the decimal system and how it functions. This is also the stage when the child is readied to have exercises on simple computations.
- The third group is started when the exercises on the decimal system is ongoing. The third group, Counting beyond Ten, also includes the teens, the tens, and linear and skip counting.
- The fourth group involves the memorization of the arithmetical tables. Work on this group can be started while the child is involved in the later exercises of the decimal system and the counting beyond ten.
- The fifth group involves the passage to abstraction which requires the child to form an understanding of the process of every form of arithmetic and to memorize and internalize the tables of every operation. The works on the different groups sometime overlap with each other. After learning the tables and process for addition, the child can begin to the addition for another group.
- The sixth group is Fractions. The work on this group can be done parallel to the group that is making abstractions. The work on Fraction may also be started earlier than that because Sensorial exercises on fraction material can be started parallel with other groups of arithmetic.

**Sample Montessori Mathematical Exercises:**

**A. Numbers through Ten**

- Number Rods
- Sandpaper Numbers
- Number Rods and Cards
- Spindle Boxes
- Concept of Zero
- Cards and Counters
- Memory Game

**B. Decimal System**

- Introduction to quantity
- Symbols
- Formation of Numbers
- Changing
- Addition
- Multiplication
- Subtraction
- Division
- Stamp Game
- Dot Game
- Word Problems

**C. Linear & Skip Counting**

- Teens: Quantity
- Teens: Symbol
- Tens: Association
- Linear Counting
- Skip Counting
- Number Roll

**D. Arithmetic Tables**

- Addition Snake Game
- Strip Board – exercises
- Addition Strip Board
- Addition Charts
- Subtraction Snake Game
- Subtraction Strip Board
- Subtraction Charts
- Multiplication Bead
- Multiplication Board
- Multiplication Charts
- Unit Division Board
- Division Charts

**E. Passage to Abstraction**

- Small Bead Frame
- Wooden Hierarchical Material
- Large Bead Frame
- Racks and Tubes

**F. Learning About Fractions**

- Fractions

Montessori teachers must carefully present arithmetic materials only when the child is ready. While children enjoy working with numbers, the teachers, and any adult for that matter, must not impose any negative overtone into the child’s experiences with mathematics. The exercises must be introduced to the children with enthusiasm and must be given in careful and clear manner. When the child is ready for mathematical exercises, his absorption will come easily and naturally.