Math in Tlingit Art

1. Math in Tlingit Art A Culture-Based Technology and Mathematics Project for K-12 Classrooms in Southeast Alaska

2. Presenter: Dr. Claudette Engblom- Bradley Associate Professor College of Education University of Alaska Anchorage

3. Tlingit Basketry Chikat Blankets Raven’s Tail Weaving Tlingit Language for designs and artifacts LOGO Programming Turtle Geometry Tlingit Designs as LOGO projects Using Math to program Math in Tlingit Art

4. Geometric Patterns in Tlingit Baskets

5. Chilkat Blankets

6. Raven’s Tail Weaving by Teri Rofkar

7. Geometric Weaving of Chilkat Robe/Blanket • The robe holds symbols that tell a story

8. Teri Rofkar from Raven Clan, from the Snail House. • Tlingit name: Chas' Koowu Tla'a from the T'ak dein taan Clan • I'm a full time artist in Sitka, Alaska; I have been selling my work since 1986. • My weavings are a reflection of an ancient relationship rekindled. • This is Waist Robe trimmed with deer toes for sound.

9. Teachers Learn to Weave Juneau teacher Topaz Shryock, left, watches as Teri Rofkor, a weaver from Sitka, demonstrates Tlingit basket weaving using materials suitable for children. Juneau Empire, 08/10/2003

10. Learning to Weave a Basket • Weaving: Richard Dauenhauer, a Tlingit-language expert, learns the intricacies of weaving a spruce-root basket during a course at UAS. • BRIAN WALLACE, photographer/ THE JUNEAU EMPIRE

11. The robe holds symbols that tell a story.

12. Rotational Symmetry • Lori Hoover’s student creates a rotation symmetric design.

13. Students learn about Tlingit Designs • Symmetry in Designs • Designs Represent: • The Eye • Celery • Butterfly • The Backbone

14. 4th Graders Study Symmetry • Lori Hoover’s 4th grade class • Riverbend Elementary in Juneau, Alaska • Refection Symmetry with Pattern Blocks

15. Original Robotic Turtle • Moved around the floor. • User typed commands on the computer. • Typed FD 50 • Turtle moved forward 50 Turtle Steps. • Typed RT 45 • Turtles turns right 45 degrees. LOGO Foundation, http://ed.media.edu/logo-foundation/logo/turtle.html

16. HOMEhttp://www.math.utah.edu/~clemens/LOGO_Intro.html • This is the home position. • The turtle first appears in the center of the screen. • Whenever the user types HOME the screen is cleared and the turtle returns to the home position.

17. Forward 10 Turtle Steps • With the Pen Down. • In the work space at the bottom of the screen. • The user types FD 90. • The turtle moves forward 10 turtle steps. • Drawing a line.

18. The Turtle Returns Home • The user types HOME. • The screen is cleared. • The turtle returns to home position.

19. Right Turn 90 Degrees. • In the work space • The user types RT 90. • The turtle turns 90 degrees.

20. Playing Blindfold Turtle • A student is blindfolded. • Safe obstacles are placed in the floor. • Other students tell the turtle how to move around the floor.

21. Dinosaur Turtle • Students help each other. • By reading the LOGO procedures they know how to move the dinosaur.

22. Students are ready for LOGO.

23. Turtle Learns to Make a Square. • With the pen down. • The user types: • FD 50 • RT 90 • FD 50 • RT 90 • FD 50 • RT 90 • FR 50 • RT 90 The Turtle draws a square.

24. Create Procedure SQUARE • The user goes to the Editor. • A procedure is defined by typing TO plus the procedure name. • The user types: • TO SQUARE • REPEAT 4 [FD 50 RT 90] • END

25. OR • The user types: • TO SQUARE • FD 50 • RT 90 • FD 50 • RT 90 • FD 50 • RT 90 • FD 50 • RT 90 • END

26. Flag = Line Plus Square • The user types: • HOME • FD 50 • SQUARE The turtle draws a line plus a square. Let’s call this a FLAG.

27. RIGHT TURN SQUARE • HOME • RT 90 • SQUARE

28. Designs with SQUARE • PROJECT A • RT 90 SQUARE • FD 50 SQUARE • FD 50 SQUARE • Project B • SQUARE FD 50 • SQUARE RT 90 • FD 50 SQUARE • Project C • RT 45 SQUARE

29. LOGO Projects • Project A • RT 45 SQUARE • REPEAT 3 [RT 90 SQUARE] • Project B • FD 50 SQUARE • REPEAT 3 [LT 90 FD 50 SQUARE]

30. Tlingit Spruce Root Basket • Made with geometric motif, • Made in the traditional way, with bear grass, dyed bear grass, and • Done traditionally with what is known as false embroidery. “Baskets of the Northwest People” http://www.mimbresfever.com/north.html

31. Tlingit Design LOGO Project • Challenge – to make the repeated pattern. • Find the repeating unit.

32. Do you see the same Shape? • The repeating unit looks like a “T” • Plan to make the “T” shape with LOGO.

33. Type the “TEE” Procedure. • TO TEE • RT 90 FD 15 • LT 90 FD 10 • LT 90 FD 10 • RT 90 FD 10 • RT 90 FD 30 • RT 90 FD 10 • RT 90 FD 10 • LT 90 FD 10 • LT 90 FD 15 • END

34. Mistake • Try making the repeated TEE’s. • Type TEE TEE • Oops! • What Happened? • How can we edit TEE so the TEE’s are horizontal?

35. Correct and Repeat the TEE. • Add LT 90 at end of TEE procedure. • Then type: • REPEAT 6 [TEE] • Go to the Editor. • Type a supper procedure: • TO PATTERN • REPEAT 6 [TEE] • END

36. Student’s T Pattern

37. Student’s U & Cross Pattern

38. Grid and Cockleshell Pattern

39. Stair and Hokha Patterns

40. Time to Weave • After programming designs, it was time to weave! • Students planned designs on graph paper • Calculated number of warps for the design • Estimated how many rows needed to make the pattern.

41. Student’s Weave Baskets • To insure success of the first basket, • all students wove the Cockle Shell pattern. • The Cockle Shell pattern uses dark and light colored yarn on alternate warps. • Students could easily and quickly see the pattern.

42. Student’s made 100 Baskets • Plastic cups of various sizes were used. • Basket weaving was contagious.

43. Teacher Responses • I have been using LOGO for two weeks now with my students.  Some are doing very well. (Ryan Dorsey, 9th grade teacher in Chatnam) • We have been doing some pre- learning of skills before going to the software.  We have spent time on symmetry and reinforcing vocabulary needed. (Lori Hoover, 4th grade in Juneau) • My 8th graders are doing a great job, but my 7th graders are struggling a little bit because some of the math introduced is so new to them. (Topaz Shryock of Juneau)

45. Geometry Polygons: Square, Rectangles, Triangles Angles: Right Turns, Left Turns, Degrees Symmetry: Reflection, Glide, Rotation, Flip Fractions Half Fourth Eighth Sixteenth Measurement Vertical Horizontal Math Concepts in this Unit

46. Resources • Bradley, Claudette. (1993). Making a Navajo Blanket Design with Logo. Teaching Mathematics With Technology • Chilkat Blankethttp://www.mehs.educ.state.ak.us/resources/unit/chilkat/blanket.html • Raven’s Tail Weaving by Teri Rofkarhttp://www.terirofkar.com/ceremonial_weavings.htm • Fry, Eric. (2003) Bringing math and Tlingit art together, Juneau Empire, 08/10/2003http://juneauempire.com/stories/081003/loc_mathart.shtml • Hoover, Lori, (2003) Riverbend Elementary, Juneau, Alaska http://uashome.alaska.edu/~jflmh/TlingitBaskets

47. More Resources • Corey, Peter L. (1995). A Proposed Glossary of Spruce Root Basketry. Alaska State Museums Concepts, 3 • Miller, Dirk & Haygood Monika (2001). Math Through Basketry. Juneau School District, Juneau, Alaska • Roblyer, M. D. (2003) Integrating Educational Technology into Teaching. Upper Saddle River, New Jersey: Pearson Education, Inc. • LOGO Foundation, http://ed.media.edu/logo-foundation/logo/turtle.html

48. The EndThank You for Coming! Math in Tlingit Art By Dr. Claudette Engblom-Bradley University of Alaska Anchorage