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

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 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 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. 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. My weavings are a reflection of an ancient relationship rekindled. This is Waist Robe trimmed with deer toes for sound. 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. 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 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. Lori Hoover’s student creates a rotation symmetric design.

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

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

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

16. HOME http://www.math.utah.edu/~clemens/LOGO_Intro.html This is the home position. This is the home position. The turtle first appears in the center of the screen. 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. 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. With the Pen Down. In the work space at the bottom of the screen. In the work space at the bottom of the screen. The user types FD 90. The user types FD 90. The turtle moves forward 10 turtle steps. The turtle moves forward 10 turtle steps. Drawing a line. Drawing a line.

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

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

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

21. Dinosaur Turtle Students help each other. Students help each other. By reading the LOGO procedures they know how to move the dinosaur. 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. With the pen down. The user types: The user types: FD 50 FD 50 RT 90 RT 90 FD 50 FD 50 RT 90 RT 90 FD 50 FD 50 RT 90 RT 90 FR 50 FR 50 RT 90 RT 90 The Turtle draws a square.

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

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

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

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

28. Designs with SQUARE A. PROJECT A 1. RT 90 SQUARE 2. FD 50 SQUARE 3. FD 50 SQUARE B. Project B 1. SQUARE FD 50 2. SQUARE RT 90 3. FD 50 SQUARE C. Project C 1. RT 45 SQUARE

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

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

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

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

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

34. Mistake Try making the repeated TEE’s. Try making the repeated TEE’s. Type TEE TEE Type TEE TEE Oops! Oops! What Happened? What Happened? How can we edit TEE so the TEE’s are horizontal? 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. Add LT 90 at end of TEE procedure. Then type: Then type: REPEAT 6 [TEE] REPEAT 6 [TEE] Go to the Editor. Go to the Editor. Type a supper procedure: Type a supper procedure: TO PATTERN TO PATTERN REPEAT 6 [TEE] REPEAT 6 [TEE] END 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! After programming designs, it was time to weave! Students planned designs on graph paper Students planned designs on graph paper Calculated number of warps for the design Calculated number of warps for the design Estimated how many rows needed to make the pattern. Estimated how many rows needed to make the pattern.

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

42. Student’s made 100 Baskets Plastic cups of various sizes were used. Plastic cups of various sizes were used. Basket weaving was contagious. 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. Math Concepts in this Unit Geometry Geometry Polygons: Square, Rectangles, Triangles Polygons: Square, Rectangles, Triangles Angles: Right Turns, Left Turns, Degrees Angles: Right Turns, Left Turns, Degrees Symmetry: Reflection, Glide, Rotation, Flip Symmetry: Reflection, Glide, Rotation, Flip Fractions Fractions Half Half Fourth Fourth Eighth Eighth Sixteenth Sixteenth Measurement Measurement Vertical Vertical Horizontal Horizontal

46. Resources Bradley, Claudette. (1993). Making a Navajo Blanket Design with Logo. Teaching Mathematics With Technology Bradley, Claudette. (1993). Making a Navajo Blanket Design with Logo. Teaching Mathematics With Technology Chilkat Blanket http://www.mehs.educ.state.ak.us/resources/unit/chilkat/ blanket.html Chilkat Blanket http://www.mehs.educ.state.ak.us/resources/unit/chilkat/ blanket.html http://www.mehs.educ.state.ak.us/resources/unit/chilkat/ blanket.html http://www.mehs.educ.state.ak.us/resources/unit/chilkat/ blanket.html Raven’s Tail Weaving by Teri Rofkar http://www.terirofkar.com/ceremonial_weavings.htm Raven’s Tail Weaving by Teri Rofkar http://www.terirofkar.com/ceremonial_weavings.htm http://www.terirofkar.com/ceremonial_weavings.htm Fry, Eric. (2003) Bringing math and Tlingit art together, Juneau Empire, 08/10/2003 http://juneauempire.com/stories/081003/loc_mathart.sht ml Fry, Eric. (2003) Bringing math and Tlingit art together, Juneau Empire, 08/10/2003 http://juneauempire.com/stories/081003/loc_mathart.sht ml http://juneauempire.com/stories/081003/loc_mathart.sht ml http://juneauempire.com/stories/081003/loc_mathart.sht ml Hoover, Lori, (2003) Riverbend Elementary, Juneau, Alaska http://uashome.alaska.edu/~jflmh/TlingitBaskets 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 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 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. Roblyer, M. D. (2003) Integrating Educational Technology into Teaching. Upper Saddle River, New Jersey: Pearson Education, Inc. LOGO Foundation, LOGO Foundation,http://ed.media.edu/logo-foundation/logo/turtle.html

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