Thursday, October 21, 2010

A child's mathematical mind - Part 2

The language area of the classroom also includes many activities that introduce important concepts in preparation for later mathematical experiences. "Just as the form of a language is given by its alphabetical sounds and by the rules for arranging its words, so the form of man's mind, the warp into which can be woven all the riches of perception and imagination, is fundamentally a matter of order." (The Absorbent Mind (1988) page 169).

One example of this is the Insets for Design. The child is reminded of the shapes in the geometric cabinet as she traces the shapes of the inset frames. Deep concentration is needed to fill in the designs with lines from left to right which also helps her to develop the precision needed for so many future tasks. As she develops her skill with the insets, her imagination is called into play and her designs become more and more intricate and abstract.

In the Cultural area, children are introduced to botany, zoology, scientific experiments, geography, history, music and art. This gives the child sensori-motor experiences based on the practical life activities, teaching the child to compare, grade and calculate.

Finally, we come to the mathematical area in a Montessori classroom. The mathematical exercises give children the satisfaction of learning by discovery. Basic arithmetic operations are learned as the child separates, combines, shares, counts and compares the mathematical materials. The specially designed math materials are presented in such a way that a natural progression takes place.

By working with quantity, then symbol, and eventually a combination of both, the child develops a true understanding of the numbers from 0 – 10 and a real reference for what a number means. This gives her a sound foundation for later work with the decimal system materials and in mathematical operations like addition, subtraction, multiplication and division. After working with the mathematics materials through touch and manipulative activity, the child discovers the physical nature of numbers and how, when combined, they make new numbers. Work in mathematics is profoundly satisfying to children because mathematical work corresponds with the way their minds naturally work.

This mathematical mind is that part of the mind which is orderly, observant, precise and imaginative.  Early preparation of the mathematical mind is achieved through use of manipulative materials from every area in the classroom.  These materials are carefully designed to present abstract concepts in concrete form and are presented in a specific way.  Through repeated work with the materials, the child is preparing herself for a smooth transition to more abstract thinking.  "There is a predisposition to exactness and detail, and it may be directed to detail of quantity. Arithmetic is a sort of abstraction and, therefore, brings this exactness to the abstract level.  The child, starting from the material, passes to the abstract number and thence to the more abstract stage of algebra, and he works with exactness in all three fields, material, abstract and algebraic, fascinated to be able to realise the play of the units (Education for a New World (1989) page 10).


Elle Belles Bows said...

Thanks for this post! We are going to look at a Montessori school next month for our little one. Kerri

Cynthia Dyer said...

How exciting! Let us know how the observation goes.