Department of Mathematics Education

Dr. J. Wilson, EMAT 6690

**Introduction**

I have used the *Discovering Geometry* textbook by Michael
Serra in my past teaching experiences and have become a proponent
of the text and the discovery approach. Most of the lessons of
the textbook are designed to investigate one or more properties
of a geometric figure, and at the end of most lessons, a section
titled "Take Another Look" suggests confirming new conjectures
using Geometer's Sketchpad (GSP). Key Curriculum Press, who publishes
*Discovering Geometry*, also publishes many supplementary
materials that provide excellent GSP investigations. The two that
I have used and highly recommend are *Exploring Geometry with
the Geometer's Sketchpad* and *Discovering Geometry with
the Geometer's Sketchpad*, which both provide blackline activity
lessons that complement the textbook. Another resource that I
am not familiar with, but suspect is outstanding, is *Rethinking
Proof with the Geometer's Sketchpad* by Michael de Villars.

My purpose is to develop investigations that can be pursued
in a virtual classroom using GSP as the tool for discovering and
proving a conjecture. I am using* Discovering Geometry*
as the foundation for the GSP investigations, but these investigations
could be used with any textbook with minor modifications. In a
virtual setting, I believe these investigations will provide students
with a solid understanding of the basic properties of parallelograms,
help develop and strengthen the concept of proof, and help students
to analyze the similarities and differences between special parallelograms.
In a more traditional classroom environment, these investigations
can be used as a lesson, part of a lesson, or supplemental materials
to be used with students who are having difficulty understanding
a particular conjecture.

The most common criticism of *Discovering Geometry*
that I have heard from other teachers is the de-emphasis of proofs.
Many students develop the false belief that a conjecture is a
proof. Similarly, students often misinterpret a GSP sketch as
a proof. The word conjecture tends to lose its true meaning. Therefore,
a major aspect of these investigations is to use GSP to outline
the approach to a proof of each conjecture.

For more information on *Discovering Geometry*, supplemental
resources, and/or GSP, contact the publisher, **Key
Curriculum Press.** To find instructions on setting up GSP
as a **helper application** **click
here.**

__ Table of Contents__: I recommend that each
page be printed out, so that the instructions are easier to follow.

**The Virtual Classroom**

A Discussion**Parallelograms**

a. Discovering some special properties (C-52 through 55)

b. Construction

c. Outline of Proof 1 (C-52)

d. Outline of Proof 2 (C-53)

e. Outline of Proof 3 (C-54)

f. Outline of Proof 4 (C-55)**Rhombuses**

a. Discovering some special properties (C-57 and 58)

b. Construction

c. Outline of Proof 1 (C-57)

d. Outline of Proof 2 (C-58)**Rectangles**

a. Discovering some special properties (C-59 and 60)

b. Construction

c. Outline of Proof 1 (C-59)

d. Outline of Proof 2 (C-60)**Squares**

Discussion of special properties and Construction**Parallelogram Relationships**

Venn Diagram and Family Tree**Bibliography**

If you have any questions while trying to complete this investigation,
or suggestions that would be useful, especially for use at the
high school level, please send e-mail to **esiwdivad@yahoo.com**.

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