Geometry for Elementary School/Introduction
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| Geometry for Elementary School | ||
| Introduction | Our tools: Ruler and compass | |
Contents |
[edit] Why geometry?
Geometry is one of the most elegant fields in mathematics. It deals with visual shapes that we know from everyday life.
Learning geometry does not require previous skills like basic arithmetic. Hence, geometry is suitable as an introduction to mathematics for elementary school.
[edit] Who should use this book?
This book is intended for use by a parent (or a teacher) and a child. It is recommended that the parent have some familiarity with geometry, but this is not necessary. The parent can simply read the chapter before teaching the child and then learn it together.
[edit] Book guidelines
The classic book about geometry is Euclid's Elements. This book helped teach geometry for hundreds of years, so we feel that writing this book based on the Elements is a correct step.
We will adapt parts of the book for children and modify the order of some topics in order to make the book clearer.
The learning will be based on constructions and proofs. A construction is a method of creating a geometric object (such as a triangle) using a set of tools. In the case of this book, the tools we will be using are a compass and a ruler. A proof is a logical trail where we can prove one fact by starting with some given information and make a series of conclusions based on that information. Often times it is more difficult to prove a result than to simply find the result.
The constructions are useful for letting the child experience geometric ideas and get visual results.
The proofs are a good way to understand geometry and are a good basis for future study of logic.
Since the book is for children, we omit some of the proof details and use intuition instead of precise definition. On the other hand, we insist on correct and elegant proofs. Precise definitions and exact proofs can be found in regular geometry books and can be used to extend to material to some of the children.
[edit] Notation
The notation that is used in the book is defined the first time it is used. However, in order to simplify its use, it is also summarized in the "Notation" chapter at the end of the book.
[edit] Euclid's Elements online
There is a wonderful online version of Euclid's Elements at this web site. The site was created by David E. Joyce, a Professor of Mathematics and Computer Science at Clark University. This site includes all the text of the Elements, applets that display the constructions, and many insightful comments. We give reference in this book to the original sources and encourage the reader to read those materials on his own.
