Making the Math Visible:

Explorations in College Geometry Using The Geometer's Sketchpad

June 4 - 11, 2006

an MAA-PREP workshop

Thanks for your interest in our workshop. We have a busy week planned, a week that we hope you will find valuable for

teaching geometry and for teaching with technology. We also hope you will have some fun!

Bill Fenton, Bellarmine University, 502-452-8430 (office)

Sr. Barbara Reynolds, Cardinal Stritch University


Goals of the Workshop

Calendar questions

Living arrangements — and what to bring

Checking In



Workshop Materials

Goals of the Workshop

The objectives for participants in this workshop are fourfold:

The workshop will model the pedagogies of exploratory activities and cooperative learning. Participants will experience firsthand a course taught using cooperative learning in a computer lab setting. Class discussions will focus on the underlying pedagogy and the issues of a course that utilizes these teaching strategies. The workshop will provide direct experience using technology and also will provide information on effective ways to integrate technology in a course.

While we are not assuming that participants will be familiar with Sketchpad, experienced Sketchpad users will still find much of interest in the workshop. In addition to the planned presentations on geometry, cooperative learning, and technology, we anticipate that a variety of alternative approaches and insights will surface during lab work and during class discussions. Thus, the collective wisdom of the participants will add to the presentations, not only for the geometry activities but also for the pedagogic discussions.


Calendar Questions

The workshop will begin with dinner on Sunday evening June 4th and close with dinner on Saturday evening June 10th. The 11th is purely a travel day.

A typical day at the workshop will begin with the morning spent in a computer lab, working on the exploratory activities. After lunch, there will be class discussions on pedagogic issues related to cooperative learning or technology. Later in the afternoon, there wll be discussions of the geometric content of the lab activities. In the evenings, there will opportunities for further lab time, further discussion, or reading on the workshop topics.

Here is our tentative plan for the week.

Tentative Daily Schedule

  Sunday Monday Tuesday Wednesday Thursday Friday Saturday Sunday
Morning 8:00-8:30   Breakfast Breakfast Breakfast Breakfast Breakfast Breakfast Breakfast


8:30 – 11:30


Lab time

Chapter 2

Lab time

Chapter 3

Lab time

Chapter 4,

Appendix A

Lab time

Chapter 5

Lab time

Chapters 6,

part of Ch. 8

Lab time

Chapter 9

11:30-12:30 Lunch Lunch Lunch Lunch Lunch Lunch

Early afternoon

12:30- 2:00

Integrating technology The Role of Proof Cooperative Learning Discussion of Chapter 5: content, Sketchpad, pedagogy Assessment

Implementing this course;

a discussion

Late afternoon


Discussion of Chapter 2: content, Sketchpad, pedagogy Discussion of Chapter 3: content, Sketchpad, pedagogy

Discussion of Chapters 4, A: content, Sketchpad, pedagogy

Possible group excursion /

free time

Discussion of Chapters 6, 8: content, Sketchpad, pedagogy

Discussion of Chapter 9: content, Sketchpad, pedagogy

4:30-6:00 Free Free Free Free Free
6:00 Opening banquet Dinner offsite Dinner offsite Dinner offsite Dinner offsite Closing banquet
Evening Campus Tour and Reading assignment Reading assignment Reading assignment Reading assignment Reading assignment Free


Living Arrangements

Workshop participants will be staying in Anniversary Hall, a residence hall on the Bellarmine campus. It is a five minute walk from the center of campus. Anniversary Hall is air-conditioned, as are all buildings on campus. Further, all buildings on campus are non-smoking.

Anniversary Hall is laid out in small suites. Each suite consists of two bedrooms separated by a bathroom. In each bedroom, there is furniture for two people---bed, desk, wardrobe. However, each workshop participant will be assigned an individual bedroom. Each room has a microwave and refrigerator, and internet access is available. Coin-operated laundry facilities are provided. Note that telephones are not provided in the rooms, though local phone access is available in each room. There are telephones in the lobbies. Anniversary Hall also has vending machines and a computer lab.

More information on Anniversary Hall can be found at

Breakfast and lunch each day will be in one of the cafeterias on campus. For dinner, participants are asked to eat at local restaurants. (There is a large selection of restaurants on nearby Bardstown Road and a map will be provided.) Participants will be reimbursed for dinner expenses.

It will be necessary for each participant to bring

Dress for the workshop will be casual. June temperatures in Louisville typically range from 65° to 83°.

Because this workshop is being supported by the Mathematical Association of America, there will be no cost to the participants for room and board.

If you have questions about local arrangements, please contact Bill at

Checking In

When you arrive, go to Anniversary Hall. (See

for a campus map.) The student workers there will have your materials. If you are arriving close to 6:00 p.m. on Sunday, please go directly to the dinner in Frazier Hall.


While we have a busy week planned, there will be some flexible time each afternoon, and we have built in a break on Thursday. Here is some local information.

On Campus

Workshop participants may use the SuRF (the Sport, Recreation, and Fitness center) which has exercise equipment, basketball courts, and tennis courts. The SuRF hours are 8 a.m. - 9 p.m. Monday - Friday, 8 a.m. - 2 p.m. Saturday.

Bellarmine also has a nine hole, par 3 golf course on campus. The cost is $7, and clubs are available at no cost. The golf course is open 8 a.m. - 8 p.m.

Off Campus

A large variety of activities are available. Here are some options to consider for Thursday afternoon/evening.


Bellarmine University is about a ten minute drive from the Louisville International Airport. We will make arrangements to meet participants at the airport, so no ground transportation will be necessary. If you prefer to drive, see

for directions and maps. During the summer months, no permit is required for parking on campus. There is ample parking near Anniversary Hall.

Note: transportation costs will not be covered by the M.A.A. funding. You are responsible for your own transportation to and from Louisville.


Workshop Materials

The main text for our workshop is the book College Geometry Using the Geometer's Sketchpad, by Reynolds & Fenton (Key College Publishing 2006). Here are the chapter titles.

    1. Using the Geometer's Sketchpad: Exploration and Conjecture
    2. Mathematical Arguments and Triangle Geometry
    3. Circle Geometry, Robust Constructions and Proofs
    4. Analytic Geometry
    5. Taxicab Geometry
    6. Transformational Geometry
    7. Isometries and Matrices
    8. Symmetry in the Plane
    9. The Hyperbolic Plane
    10. Projective Geometry

    Appendix A. Trigonometry

    Appendix B.Calculating with Matrices

Participants will be asked to complete the exploratory activities from Chapter 1 prior to coming to the workshop. During the workshop, we will work on Chapters 2, 3, 4, 5, 6, 8, and 9.

Our basic scheme for this text is that each chapter opens with a set of exploratory activities. These activities use Sketchpad extensively. They are designed to introduce concepts and issues for that chapter. There is some written discussion of the concepts and of the activities, giving definitions, theorems, and proofs. Then the chapter closes with a set of exercises, mostly paper-&-pencil work.

You can see the syllabi for our respective geometry courses at the following websites:

Barbara Reynolds  

Bill Fenton             

In addition to College Geometry Using GSP, we will furnish other materials related to cooperative learning and to teaching with technology.