The following is the text from this section of the 2009-2010 edition of Child of the World, Montessori from Three to Twelve Years
To see other sections of this publication return to: http://www.michaelolaf.com/CWcontents.html

INTRODUCTION
Geometry, math, and invention are languages used to explore and manipulate, to theorize and create, real objects in a real world. At this age children continue to enjoy exploring math and geometry concepts if they are related to real life, and if they are presented with materials which can be handled, manipulated, used to create. We must keep sight of this fact when teaching children. We give manipulative materials in all areas of math and leave it to each child to decide when she is ready to work without materials—in the abstract—on paper with pencil.

We encourage children to make up their own problems—especially story problems related to their lives and the subjects they are studying—for themselves and for their friends, in order to come to a very practical and clear understanding of geometry and math. Children enjoy making up problems for each other, and examples that stump their teachers. This process of math concepts makes them stick in the child's mind.

With higher math, geometry and algebra, we give many practical examples and help the children come up with their own formulae after much experience. For example, if a child measures all of the rectangles in the room—tables, windows, books, etc. for figuring surface area, he will easily create, and even better understand, the formula "A=lw."

For each grade level, from 1st through high school, the children are shown the state requirements of math, just as any other subject. Then they learn to plan and schedule their work. It is left to each child to decide the best system and schedule, through trial and error, and with adult help, depending on learning styles, and interests.

This teaches the math of planning, scheduling, allotting sufficient time, and it teaches responsibility.

When children are given this solid, material foundation, and see the relationship of geometry and math to the real world, it makes it easier for them, in later years, to spend long periods of time working on paper.

This is because they know that these steps are just that—steps which will take them to a new level of understanding in the exciting world of math and science.

MATH
Abstract work is a higher mental level of work, which comes naturally after the child has learned to picture the object being measured or related to other objects in her mind.

In the elementary class stories are told and experiments carried out to show children how humans used their imaginations in the past, and how they are using them today, to solve problems and come up with great inventions—the use of fire, measuring the earth, compasses, boats, and many others. They see how inventions, geometry and math came about as the result of human progress, to meet specific needs.

Geometry, for example, arose from the practical need to reestablish planting boundaries after the annual flooding of the Nile in Egypt. In "geometry," geo  stands for earth, and metry for measure.

Children of this age love to reach back into history with their imaginations and reconstruct these needs and solutions and the creation of systems of learning. The Hindus introduced the use of "0." Let the child try to do math without it! Where did algebra, calculus, trigonometry come from? They want to know!

Children are inspired by these stories, and by examples and pictures, to find out more. Children come to realize that mathematics has evolved and is still evolving from a practical need. Math, graphing, fractions, all become logical tools for recording and measuring, and algebra a short cut for recording.

© Susan Mayclin Stephenson, 2010 (www.susanart.net)
Permission to reprint or link to a website is granted if these words are include:
"Shared with permission of The Joyful Child Montessori Company: www.thejoyfulchild.us"

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