Making the Math Visible:

Explorations in College Geometry Using the Geometer's Sketchpad

June 5 - 12, 2005

an MAA-PREP workshop, with support from NSF Grant DUE-0338301

Our sincere thanks to the participants who worked so hard and contributed so much to the success of our workshop. It has been a real pleasure sharing the week with you.

Some photos!

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:

  • to introduce an exploratory learning approach to college geometry;
  • to develop understanding of and skills with cooperative learning;
  • to develop proficiency with The Geometer's Sketchpad; and
  • to prepare the participants to teach effectively a geometry course based on the materials presented.

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—and those faculty who have seen earlier versions of our materials—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 5th and close with dinner on Saturday evening June 11th. The 12th 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 wll be discussions of the geometric content of the lab activities. Later in the afternoon, there will be class discussions on pedagogic issues related to cooperative learning or technology. 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

Discussion of Chapter 2: content, Sketchpad, pedagogy Discussion of Chapter 3: content, Sketchpad, pedagogy Discussion of Chapters 4, A: content, Sketchpad, pedagogy Discussion of Chapter 5: content, Sketchpad, pedagogy Discussion of Chapters 6, 8: content, Sketchpad, pedagogy Discussion of Chapter 9: content, Sketchpad, pedagogy

Late afternoon


Integrating technology The Role of Proof

Possible group excursion /

free time

Cooperative Learning Assessment

Implementing this course;

a discussion

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


Living Arrangements

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

Petrik Hall is laid out in suites. Each suite consists of a common living room, four bedrooms, and two bathrooms. A typical bedroom in these suites is 11' by 15'. In each bedroom, there is furniture for two people--bed, dresser, desk, armoire. However, each workshop participant will be assigned an individual bedroom. Internet access is available in the dormitory, as is local phone access. Each floor of Petrik Hall has coin-operated laundry facilities. The first-floor lobby has a microwave and a television. There are soda and candy machines on the first floor, plus a small room with a half dozen computers.

It will be necessary for each participant to bring

  • sheets (single bed, extra long), blankets, and a pillow
  • towels and toiletries
  • alarm clock
  • reading lamp, if desired
  • phone card for long distance calls (Each room will have a phone.)

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 National Science Foundation, 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, which is quite close to our dorm. (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 Wednesday. 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 Wednesday afternoon/evening.

  • The Kentucky Derby Museum: Open 7 a.m. - 5 p.m., admittance $9. About a fifteen minute drive from campus.
  • Churchill Downs: Open 11:30 a.m.; first race at 1:15. Admittance $2. About a fifteen minute drive from campus.
  • Louisville Zoo: Open 10 a.m. - 6:00 p.m.(last admittance 5:00) Admittance $9.95. About a five minute drive from campus.
  • Louisville Riverbats: AAA professional baseball. 7:15 p.m. game against Charlotte Knights. Admittance $5 - $9. about a twenty minute drive from campus. (Note: seats along the first base side will be in the sun.)
  • Louisville Slugger Museum: Open 9 a.m. - 5 p.m. Admittance $8. About a twenty minute drive from campus. The last tour begins at 4:00; to see baseball bats in production, you need to begin a tour before 3:00.


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 Petrik Hall.

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


Workshop Materials

The main text for our workshop is the forthcoming book College Geometry Using the Geometer's Sketchpad, by Reynolds & Fenton. It is due to be published by Key College Publishing in August 2005. 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, and 4, plus other chapters to be determined.

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.


Information - 502.452.8000
© Bellarmine University, Louisville, KY 2002-2004