This PREP workshop was made possible by the NSF grant DUE: 0341481

Workshop Program

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Contents

Lead-in Activities

Wimba Connectivity Tests

  • 10am-12 (CDT) Thursday, June 12
  • 1-3pm (CDT) Monday, June 16

We will run live tests of the Wimba site for this conference: Math Conference. We've scheduled two time blocks for this short test. You should "attend" for about 10-20 minutes during one of these two times. Check the main page for a phone number to call for help during these times. (Phone: 314-681-8752)

Reading

Go to our online escherwiki:Main_Page Escher Wiki and look through our online materials. We suggest reading the section about Tessellations and look through some of the suggested explorations. Similarly read through the section about Spherical Geometry and look at some of the explorations. There's no need to do the explorations, although you are of course welcome to do so if you want.

On-line connectivity tests with each participant site were conducted in consultation with each participant before the start of the workshop.

Suggested Books

This is a short list of the best and most important reference works we have found for the material in this workshop. None are required, but you may wish to gather some of these from your local library. The escherwiki:References is (the beginnings of) a more comprehensive reference list.

  • M.C. Escher: Visions of Symmetry by Doris Schattschneider . WH Freeman, 1990. ISBN 0-810-94308-5. Required in SLU's Math & the Art of Escher class. Deep insight into Escher's methods.
  • The Magic Mirror of M.C. Escher by Bruno Ernst and M. C. Escher. Originally published 1978, reprinted in a number of editions. ISBN 1-886-15500-3. A wonderful resource, with explanations of Escher's work and the math surrounding it. Both Anneke and Bryan authors have used this book "behind the scenes" when teaching Math & the Art of Escher.
  • Symmetries of Culture by Dorothy K. Washburn and Donald W. Crowe. University of Washington Press, 1987. ISBN 0-295-97084-7. Classifications of symmetry groups of patterns and applications to anthropology.
  • Tilings and Patterns by Branko Grunbaum and Geoffrey C. Shephard Freeman, 1986. ISBN 0-716-71194-X. The definitive mathematical reference on tessellations.
  • Introduction to Tessellations by Dale Seymour and Jill Britton. Dale Seymour Publications, 1986. ISBN 0-866-51461-9. A book for teaching tessellations to K12 students.
  • The Fourth Dimension and Non-Euclidean Geometry in Modern Art by Linda Dalrymple Henderson , Princeton University Press, 1983. ISBN 0-691-04008-7. Analysis of the artwork and the historical setting.

On-line Program (June 23 - June 27, 2008)

The on-line portion runs for two one and a half hour time blocks, 10:00 am - 11:30 am and 2:30 pm - 4:00 pm Central Daylight Time, each day. Participants are expected to spend time on workshop activities between the on-line sessions.


Schedule

This schedule is not representative of exactly what was covered during the workshop, as it was created before the workshop as a working plan. For a better idea of what was covered, see the day-by-day table on the Main Page, or see the Wimba Archives.

As a general overview, the workshop will cover:

  • Symmetry and Tessellations. This includes a discussion of how and why we use Escher as our main artist of reference, Using projects and fieldtrips, and writing worksheets.
  • Non-Euclidean Geometry. We cover an introduction to Sperical and Hyperbolic geometry in our class.
  • The Fourth Dimension and Perspective in Art. These are more art related topics and we will show what materials we have developed.

Monday June 23: Introduction to Geometry & Art and Euclidean Geometry: Symmetry and Tessellations

  • Developing the Math and Escher course A short introduction to our Math and Escher course. A quick overview of the history of the course, the reasons it was developed and the intended audience and level of sophistication.
  • Math and Art Assignment
  • Writing worksheets There are slightly different ways to write worksheets (or explorations as we call them). We will discuss some techniques we have used.
  • Teaching Symmetry The symmetry and tessellation sections are important topics in the way that we teach the course. We will discuss what topics we teach and how this ties in with the rest of the course.


Tuesday June 24: Continuation from Monday and introduction to non-Euclidean geometry

Teaching non-Euclidean geometry: How to motivate the material, useful computer software, how to write worksheets, etc. Compare and contrast teaching methods for Euclidean and non-Euclidean geometry.


Wednesday June 25: Non-Euclidean geometry, fractals etc.


Thursday June 26: The 4th dimenstion, perspective, history and other topics


Friday June 27: Wrapping up the workshop

  • Using Projects We have found it useful to include projects in our course. We will talk about how we developed our projects.

Possible Assignments

Follow-Up Activities

After the On-Line workshop:

  • Participants are expected to implement workshop-created activities in their own classrooms
  • Participants are expected to participate in an on-line discussion list, sharing their experiences in the classroom
  • Participants are encouraged to disseminate materials they develop both within the participant group, and also to the wider mathematics community
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