Dr. Maria Montessori from The Absorbent Mind

Mathematics is relevant to most aspects of our daily lives. It gives us the means to communicate in concise way, allows us to run our finances, commerce and industry and allows the development of logical thinking. In teaching mathematics we are teaching for life. Our aim should be to provide an environment rich in pre-number and early maths experience so that the child can build a firm foundation upon which to base later mathematics concepts.  The child will encounter indirect preparation for later mathematics in many curriculum areas so that a considerable amount of mathematical experience can be accumulated at an unconscious level through the senses.  Mathematics is part of the child’s world. It is not just about interpreting numbers or in mastering the tricks of addition or multiplication. Mathematics is about ideas. These ideas have been developed over time to help explain particular qualities such as size, weight, height, as well as relationships and comparison. Most adults can solve simple mathematical tasks by doing them in the head. Young children find such abstractions impossible to master. They need to see, talk, touch and experiment.

The first introduction of number for the young is through songs. These songs give names and sequence of numbers:  “one, two, three four five, once I caught a fish alive” etc. Some stories too contain mathematical ideas.  For example, in Goldilocks and the Three Bears everything comes in sets of three.  As children are becoming aware of numbers they should be encouraged to spot them in the environment, perhaps on outings, bus routes, number plates and prices in the shops. Each child can look for their own special number – his or her own age. Many maths skills are built on the ideas of matching, pairing, sorting and ordering. We can, by using numbers in a natural way as part of the everyday routine, prepare for the difference between Cardinal numbers (how many) and also understand the concept of zero.

Being able to recite numbers in sequence is not the same as counting (knowing how many four is) so children have to learn to match the word “one” and the number “1” to 1 object, and so on. The Montessori environment provides lots of practice in counting things while touching them, for example counting pegs for the clothes line, the number of children in the circle, plates at meal time, and parents can assist their children to build their numeracy skills by encouraging similar activities at home, and about town.  Incorporating numbers in this way prevents children from racing through number words in a meaningless way. Many maths skills are build on the idea of matching, pairing, sorting and ordering. Children do many of these activities naturally and can be encouraged to work at them from a very early age.  They involve concentration and making comparisons and as such are very important for cognitive development. Matching is the process of looking for one set of things from a larger mixed group, e.g. counting all the forks from the pile of cutlery or all the apples from the fruit bowl.

Conservation, the idea that the number of items in a group doesn’t vary if the items are rearranged from a circular, say to a linear arrangement, or that a quantity remains constant if poured from a jug into several smaller containers, can be provided with varied experiences like counting out and rearranging bobbins, sorting beads with tongs, pouring water, rolling and flattening balls of dough. We can by using numbers in a natural way as part of every day routine, prepare for the differences between cardinal numbers (how many) and ordinal numbers (first, second, third) and also assist understanding of zero by ensuring children encounter ‘nothing’ and ‘none left’ in every day experience.

Once a child understand the concept of numbers in a very fundamental way, manipulation comes easily.  Addition, then subtraction are introduced in meaningful, logically progressive steps.  Once these concepts are well understood, multiplication and then division are introduced.  Meal times are excellent for discussing the concept of addition, subtraction, multiplication and division.  We can talk about:  “You’ve got two raisins. If I give you two more how many will you have? Shall we count?”, or “You have five if you eat three, how many have you left?” If there are three children at the table and each gets three slices of apple, how many apples pieces do we need to put out?  We can talk about division as equal sharing, or fractions when we cut fruit.  There are many, many opportunities to include real examples of mathematics for the child.  The Montessori mathematics curriculum allows the child to work with concrete materials, then work with paper and materials, and finally the student begins to work simply with pencil and paper, while being introduced to new, more challenging materials.  

Number in the Practical Life Exercises

Less directly, but very important are the exercises of Practical Life. The ordered and logical approach to cleaning a shoe encourages mathematical thinking’ the materials are set up but they must be selected in the correct sequence and the tray must be checked at the end to ensure it is complete for the next user. Patterns are important in mathematics, both visual and number patterns. This is because mathematics is all about thing being in order, regular and systematic. Paper cutting introduces the ideas of pattern and symmetry and the folding of table napkins gives experience of geometry and of halves and quarters. The child adapts to the world and constructs reality from what he sees adults doing.

Number in the Sensorial Exercises

Mathematical order is present in many of the sensorial materials, allowing the child to work with units of 1-10 in several dimensions, all of which give concrete experience of discriminating between sizes, sequencing, grading or comparison. The child’s language is enriched by descriptive terms of measurement like narrow, long, short and wide. Much later the longest rod can be used as a unit of measurement. Children receive a visual and muscular impression of plane and three-dimensional shapes with the geometric cabinet and solids. As Montessori herself says” if we look now at the sensorial apparatus which is able to evoke such deep concentration (remarkable in very small children between the ages of three and four) there is no doubt that this apparatus may be regarded not only as a help to exploring the environment but also to the development of the mathematical mind.”

The Montessori Classroom is rich in opportunities for the child to acquire pre-maths skills and we need to leave the child free to explore and develop more advanced mathematics skills as he or she matures.  By the time the child is six, and ready to move into the Montessori Elementary classroom, the student should be proficient with addition, subtraction, and have a working knowledge (and may be quite advanced in) of multiplication, division and fractions facts and manipulation.

Montessori Maths Materials (in order of work progression)

To establish the numbers to ten:

• Sandpapers Numbers
• Number Rods
• Number Cards
• Spindle Boxes
• Card and Counters
• Memory Game of Numbers

To give a picture of the Decimal System as a whole and an impression of how the systems functions and of the four basic mathematical functions:

• Decimal Tray One
• Decimal Tray Two
• Decimal Numeral Layout
• Bank Game Addition, Subtraction, Multiplication, Division.
• Stamp Game

 To introduce Teens and Tens, and develop the ability to recognize, count and manipulate any number:

• Introduction with beads 11 to19 (Beads Stair and Tens Bars)
• Introduction with Cards
• Association of Quantities with symbols 11 to 19 (Teen Boards and Beads)
• Tens Board with Beads 11 to 99
• Linear Counting - Hundred Chain, Thousand Chain
• Skip Counting – all chains
• Memory Work to establish abstract terms;
• Addition
• Snake Game
• Addition Strip Board
• Subtraction
• Subtraction Strip Board
• Multiplications Board
• Division Board
• Fractions Boards

Each year at IMS we hold Montessori Curriculum evenings to review the materials in each of the five major areas of the classroom with parents.  We encourage you to come to these meetings to learn more.

Back to Newsletter