Mathematical Classroom Quilts

Year: 2009 Authors: Elaine Krajenke Ellison

Core claim

Quilts can effectively teach mathematics by combining visual design with historical and cultural narratives.

Topics

mathematics education, visual learning, historical connections, quilting

Domains

geometry, number patterns, fractal geometry, trigonometry, textile art, composition, color design, visual arts

Methods

classroom quilts, lesson plans, PowerPoint presentation, historical organization

Media

cloth quilts, paper quilts, mathematical placemats, PowerPoint

Paper text

The text below is the locally extracted OCR/Markdown version of the paper. Raw PDF files remain local and are not published here.

Bridges 2009: Mathematics, Music, Art, Architecture, Culture

Mathematical Classroom Quilts

Elaine Krajenke Ellison Retired Mathematics Teacher 5739 Wilena Place Sarasota, Florida 34238 E-mail: eellisonelaine@yahoo.com

Abstract

In an effort to create a visual and historical basis to my classroom instruction, I began quilting high school mathematics topics in the early 1980’s. The visual approach to teaching a lesson was successful in that the quilts engaged the students immediately. Students’ motivation and enjoyment of mathematics were evident in their enthusiasm for the topic being studied. Cultural and historical connections evolved with the story of each quilt.

Introduction

During the early years of generating classroom quilts, two authors inspired me: Dan Pedoe [13] and Thomas Banchoff [1]. I began to think that a whole new way of teaching mathematics would be possible. Could I use color, form, composition, perspective and formulas to interest students in mathematics? Banchoff and Pedoe inspired me to show the beauty in mathematics.

As the number of quilts grew and lesson plans to go with the quilts were written, I found that other teachers were interested in learning about my unique classroom. Cloth quilts inspired paper quilts and mathematical placemats. My classroom was evolving creatively!

Most recently, I have taken the 39 mathematical quilts and organized them into a PowerPoint presentation that many groups have enjoyed over the last few years. The quilts are organized historically. Each quilt has been used in the high school classroom or could be used in the high school classroom. There is no need to limit the use of these quilts to the high school level.

Topics in the PowerPoint of the Mathematical Quilts

1. Golden Rectangle—around 500 B.C.E.

2. Golden Rectangle at Givemy

3. Fiddle Dee Dee Golden Rectangle #3

4. Labyrinth at Chartres Cathedral—Golden Rectangle

5. Blue-Breasted Hummingbird—Golden Rectangle

6. The Sacred Cut-around 500 B.C.E.

7. The Lutes of Pythagoras—582–502 B.C.E.

8. Spiraling Pythagorean Triples

9. My Spiraling Pythagorean Triples

10. Mathematical Harmony—500 B.C.E.

11. The Wheel of Theodorus—400 B.C.E.

12. The Six Trigonometric Functions—400 B.C.E.

13. The Parabola—375–325 B.C.E.

14. The Hyperbola and Ellipse—375–325 B.C.E.

15. Spiraling Squares—300 B.C.E.

16. Fibonacci x 3—1175–1250

17. Leonardo’s Dessert no Pi—1452–1519

18. Leonardo’s Claw

19. Lucy’s Quilt of Leonardo

20. San Gaku—1603–1867

21. Pascal’s Surprise—1623–1662

22. Pascal’s Pumpkin

23. Mascheroni Cardioid—1797

24. Poincaré Plane—1854–1912

25. Koch Curve—1870–1924

26. Sierpinski’s Gasket—1882–1969

27. Sierpinski’s Carpet

28. Indiana Puzzle—Snail’s Trail

29. Clifford Torus—1845–1879

30. Tessellation

31. Tessellation

32. Worlds of Geometry—1990—The Geometry Center

33. Orthic Triangles—talk by Douglas Hofstadter at Indiana University

34. Graeco-Latin Squares and Sudoku

35. Fabulous Fibonacci Flowers

36. The Music of the Genes—2007

37. Spiraling Spidrons—2007

38. Buckyballs and Bubbles—2008

References

• [1] Banchoff, Thomas F. Beyond the third Dimension-Geometry, Computer Graphics, and Higher Dimensions. New York: W. H. Freeman and Co., 1990.
• [2] Boles, Martha, and Rochelle Newman. Universal Patterns, Books 1 and 2. Bradford, MA: Pythagorean Press, 1990, 1992.
• [3] Boulger, William. “Pythagoras Meets Fibonacci.” Pp. 277–82 in The Mathematics Teacher. Reston, VA: NCTM Publications, 1989.
• [4] Cook, Theodore A. The Curves of Life. New York: Dover, 1979.
• [5] Emmer, Michele, ed. The Visual Mind: Art and Mathematics. Cambridge, Mass.: The MIT Press, 1993.
• [6] Eves, Howard. An Introduction to the History of Mathematics, 4^{th} ed. New York: Holt, Rinehart & Winston, 1976.
• [7] Frederickson, Greg N. Dissections Plane and Fancy. Cambridge, U.K.: Cambridge University Press, 1997.
• [8] Gleick, James. Chaos: Making a New Science. New York: Penguin, 1987.
• [9] Huntley, H. E. The Divine Proportion. New York: Dover, 1970.
• [10] Kappraff, Jay. Connections: The Geometric Bridges between Art and Science. McGraw-Hill, Inc., 1991.
• [11] Mathematical Association of America. Mathematics Magazine, Vol 62, No.3, June 1989.
• [12] Pappas, Theoni. Mathematics Appreciation. San Carlos, CA.: WideWorld Publishing/Tetra, 1986.
• [13] Pedoe, Dan. Geometry and the Visual Arts. New York: Dover, 1976.
• [14] Posamentier, Alfred. S., and William Wernick. Advanced Geometric Constructions. Palo Alto, Ca.: Dale Seymour Publications, 1973.
• [15] Seymour, Dale. Visual Patterns in Pascal’s Triangle. Palo alto, Ca. : Dale Seymour Publications, 1986.
• [16] Stevens, Peter S. Patterns in Nature. Boston: Little, Brown, 1974.
• [17] Wills, Herbert III. Leonardo’s Dessert—No Pi. Reston, Va.: NCTM Publications, 1985.