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Teaching and Learning Geometry.

Teaching and Learning Geometry Douglas French Douglas Charles French (born 20 March, 1944) is a retired Conservative Party politician in the United Kingdom.

He was elected to the House of Commons at the 1987 general election as Member of Parliament for Gloucester, succeeding former minister Sally Oppenheim.
 Published by Continuum International Publishing Group, 2004 ISBN ISBN
International Standard Book Number

ISBN International Standard Book Number

ISBN n abbr (= International Standard Book Number) → ISBN m 
 0826473628 169 pp., soft cover; 25.00 [pounds sterling]

This book is designed to offer practical advice and ideas for the classroom in the teaching and learning of school geometry and has presented a variety of ways of achieving this. However, to change what happens in practice in the classroom may be difficult!

In the book are twelve chapters:

* The Role of Geometry

* Learning Geometry

* Beginnings: Experimental Geometry

* Polygons: Symmetry and Angle Properties

* Construction and Congruence con·gru·ence  
a. Agreement, harmony, conformity, or correspondence.

b. An instance of this: "What an extraordinary congruence of genius and era" 

* Perimeter, Area and Volumes

* Enlargement and Similarity

* The Theorem of Pythagoras

* The Circle

* Linking Geometry and Algebra

* Polyhedra

* Vectors.

Working through Chapters 3, 4 and 5 highlight important initial ideas and skills to do with recognising shapes and their properties, the importance of symmetry, tessellations and the transformations of reflection and rotation, angle properties and triangles, the properties of quadrilaterals and polygons. Also to be found is an introductory lesson plan on regular polygons using LOGO. The plan indicates lessons are timed for fifty five minutes. Constructions and congruence and Van Shooten's Theorem conclude this section.

In Chapter 6 the author suggests finding the area of a sector of a circle is a good example of a task that should be presented as a problem to be solved from first principles, rather than as a task to be worked out using yet another remembered standard procedure. At this stage in the book only the area of a circle has been met. Thus only first principles are possible.

The direct link of similarity to the transformation of enlargement and for the introduction of scale factors provides a more simple approach than using equal ratios. Such is the content of Chapter 7. This also includes both Varignon's theorem and the intercept theorem being proved using the midpoint mid·point  
1. Mathematics The point of a line segment or curvilinear arc that divides it into two parts of the same length.

2. A position midway between two extremes.

Pythagoras' Theorem (spelling) Pythagoras' Theorem - It's Pythagoras's Theorem.  has a multitude of different proofs but those considered in this book involve areas, congruence, transformations, similarity, trigonometry trigonometry [Gr.,=measurement of triangles], a specialized area of geometry concerned with the properties of and relations among the parts of a triangle. Spherical trigonometry is concerned with the study of triangles on the surface of a sphere rather than in the  and algebra. The trigonometric identities In mathematics, trigonometric identities are equalities that involve trigonometric functions that are true for all values of the occurring variables. These identities are useful whenever expressions involving trigonometric functions need to be simplified.  and Apollonius' Theorem are also introduced.

The linked circle theorems of Chapter 9 are familiar to many students and Miquel's six-circle theorem also appears.

In the following chapter the use of a coordinate system coordinate system

Arrangement of reference lines or curves used to identify the location of points in space. In two dimensions, the most common system is the Cartesian (after René Descartes) system.
 allows both an algebraic 1. (language) ALGEBRAIC - An early system on MIT's Whirlwind.

[CACM 2(5):16 (May 1959)].
2. (theory) algebraic - In domain theory, a complete partial order is algebraic if every element is the least upper bound of some chain of compact elements.
 and a geometric perspective.

It was a surprise to find a chapter on polyhedra included in a course on geometry, so often has it been considered a recreational topic in Australian courses.

The book closes with an interesting chapter on the use of vectors in solving geometry problems. For many this could be unfamiliar territory. A slight typing error typing error nfaute f de frappe

typing error typing nTippfehler m

typing error n
 appears on page 159:


Throughout the book use has been made of dynamic computer programs and software as well as graphical calculators. Diagrams are many and include graphs and tables of values. The presentation of the book is pleasing to the eye. This book has presented a way of looking at geometry from various perspectives. Consequently each teacher of geometry should have access to a copy.

Margaret McDonald
COPYRIGHT 2005 The Australian Association of Mathematics Teachers, Inc.
No portion of this article can be reproduced without the express written permission from the copyright holder.
Copyright 2005 Gale, Cengage Learning. All rights reserved.

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Author:McDonald, Margaret
Publication:Australian Mathematics Teacher
Article Type:Book review
Date:Sep 22, 2005
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