A Culture-Based Technology and Mathematics Project for K-12 Classrooms in Southeast Alaska

Presenter: Presenter: Dr. Claudette Engblom- Dr. Claudette Engblom-

BradleyBradleyAssociate ProfessorAssociate Professor

College of EducationCollege of Education

University of Alaska AnchorageUniversity of Alaska Anchorage

Math in Tlingit ArtMath in Tlingit Art

Tlingit BasketryTlingit Basketry Chikat BlanketsChikat Blankets Raven’s Tail WeavingRaven’s Tail Weaving Tlingit Language for Tlingit Language for

designs and artifactsdesigns and artifacts

LOGO ProgrammingLOGO Programming Turtle GeometryTurtle Geometry Tlingit Designs as Tlingit Designs as

LOGO projectsLOGO projects Using Math to programUsing Math to program

Geometric Patterns in Tlingit Geometric Patterns in Tlingit BasketsBaskets

Chilkat BlanketsChilkat Blankets

Raven’s Tail Weaving by Teri RofkarRaven’s Tail Weaving by Teri Rofkar

Geometric Weaving of Chilkat Geometric Weaving of Chilkat Robe/BlanketRobe/Blanket

The robe holds The robe holds symbols that tell a symbols that tell a storystory

Teri Rofkar from Raven Clan, Teri Rofkar from Raven Clan, from the Snail House.from the Snail House.

Tlingit name: Chas' Tlingit name: Chas' Koowu Tla'a from the Koowu Tla'a from the T'ak dein taan ClanT'ak dein taan Clan

I'm a full time artist in I'm a full time artist in Sitka, Alaska; I have Sitka, Alaska; I have been selling my work been selling my work since 1986. since 1986.

My weavings are a My weavings are a reflection of an ancient reflection of an ancient relationship rekindled. relationship rekindled.

This is Waist Robe This is Waist Robe trimmed with deer toes trimmed with deer toes for sound. for sound.

Teachers Learn to WeaveTeachers Learn to Weave

Juneau teacher Juneau teacher Topaz Topaz ShryockShryock, left, , left, watches as watches as Teri Teri RofkorRofkor, a weaver , a weaver from Sitka, from Sitka, demonstrates Tlingit demonstrates Tlingit basket weaving using basket weaving using materials suitable for materials suitable for children.children.

Juneau Empire, Juneau Empire, 08/10/2003 08/10/2003

Learning to Weave a BasketLearning to Weave a Basket

Weaving: Richard Weaving: Richard Dauenhauer, a Tlingit-Dauenhauer, a Tlingit-language expert, language expert, learns the intricacies learns the intricacies of weaving a spruce-of weaving a spruce-root basket during a root basket during a course at UAS. course at UAS.

BRIAN WALLACE, BRIAN WALLACE, photographer/ THE photographer/ THE JUNEAU EMPIREJUNEAU EMPIRE

The robe holds symbols that tell a story.The robe holds symbols that tell a story.

Rotational SymmetryRotational Symmetry

Lori Hoover’s student Lori Hoover’s student creates a rotation creates a rotation symmetric design.symmetric design.

Students learn about Tlingit Students learn about Tlingit DesignsDesigns

Symmetry in DesignsSymmetry in Designs Designs Represent:Designs Represent:

The EyeThe Eye CeleryCelery ButterflyButterfly The BackboneThe Backbone

4th Graders Study Symmetry4th Graders Study Symmetry

Lori Hoover’s 4th grade Lori Hoover’s 4th grade class class

Riverbend Elementary Riverbend Elementary in Juneau, Alaskain Juneau, Alaska

Refection Symmetry Refection Symmetry with Pattern Blockswith Pattern Blocks

Original Robotic TurtleOriginal Robotic Turtle Moved around the floor.Moved around the floor. User typed commands on User typed commands on

the computer.the computer. Typed FD 50Typed FD 50 Turtle moved forward 50 Turtle moved forward 50

Turtle Steps.Turtle Steps. Typed RT 45Typed RT 45 Turtles turns right 45 Turtles turns right 45

degrees.degrees.LOGO Foundation,LOGO Foundation,http://ed.media.edu/logo-http://ed.media.edu/logo-

foundation/logo/turtle.htmlfoundation/logo/turtle.html

HOMEHOMEhttp://www.math.utah.edu/~clemens/LOGO_Intro.htmlhttp://www.math.utah.edu/~clemens/LOGO_Intro.html

This is the home This is the home position.position.

The turtle first appears The turtle first appears in the center of the in the center of the screen.screen.

Whenever the user types Whenever the user types HOME the screen is HOME the screen is cleared and the turtle cleared and the turtle returns to the home returns to the home position.position.

Forward 10 Turtle StepsForward 10 Turtle Steps

With the Pen Down.With the Pen Down. In the work space at the In the work space at the

bottom of the screenbottom of the screen.. The user types FD 90.The user types FD 90. The turtle moves The turtle moves

forward 10 turtle steps.forward 10 turtle steps. Drawing a line.Drawing a line.

The Turtle Returns HomeThe Turtle Returns Home

The user types HOME.The user types HOME. The screen is cleared.The screen is cleared. The turtle returns to The turtle returns to

home position.home position.

Right Turn 90 Degrees.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 The turtle turns 90

degrees.degrees.

Playing Blindfold TurtlePlaying Blindfold Turtle

A student is A student is blindfolded.blindfolded.

Safe obstacles are Safe obstacles are placed in the floor.placed in the floor.

Other students tell the Other students tell the turtle how to move turtle how to move around the floor.around the floor.

Dinosaur TurtleDinosaur Turtle

Students help each Students help each other.other.

By reading the LOGO By reading the LOGO procedures they know procedures they know how to move the how to move the dinosaur.dinosaur.

Students are ready for LOGO.Students are ready for LOGO.

Turtle Learns to Make a Square.Turtle Learns to Make a Square. With the pen down.With the pen down. The user types:The user types:

FD 50FD 50 RT 90RT 90 FD 50FD 50 RT 90RT 90 FD 50FD 50 RT 90RT 90 FR 50FR 50 RT 90RT 90The Turtle draws a square.The Turtle draws a square.

Create Procedure SQUARECreate Procedure SQUARE

The user goes to the The user goes to the Editor.Editor.

A procedure is defined A procedure is defined by typing TO plus the by typing TO plus the procedure nameprocedure name..

The user types:The user types: TO SQUARETO SQUARE REPEAT 4 [FD 50 RT REPEAT 4 [FD 50 RT

90]90] ENDEND

OROR The user types:The user types:

TO SQUARETO SQUARE FD 50FD 50 RT 90RT 90 FD 50FD 50 RT 90RT 90 FD 50 FD 50 RT 90RT 90 FD 50FD 50 RT 90RT 90 ENDEND

Flag = Line Plus SquareFlag = Line Plus Square

The user types:The user types: HOMEHOME FD 50 FD 50 SQUARESQUARE

The turtle draws a line plus The turtle draws a line plus a square.a square.

Let’s call this a FLAG.Let’s call this a FLAG.

RIGHT TURN SQUARERIGHT TURN SQUARE

HOMEHOME RT 90RT 90 SQUARESQUARE

Designs with SQUAREDesigns with SQUARE

A.A. PROJECT APROJECT A

1.1. RT 90 SQUARERT 90 SQUARE

2.2. FD 50 SQUAREFD 50 SQUARE

3.3. FD 50 SQUAREFD 50 SQUARE

B.B. Project BProject B

1.1. SQUARE FD 50SQUARE FD 50

2.2. SQUARE RT 90SQUARE RT 90

3.3. FD 50 SQUAREFD 50 SQUARE

C.C. Project CProject C1.1. RT 45 SQUARERT 45 SQUARE

LOGO ProjectsLOGO Projects

Project AProject A RT 45 SQUARERT 45 SQUARE REPEAT 3 [RT 90 REPEAT 3 [RT 90

SQUARE]SQUARE] Project BProject B

FD 50 SQUAREFD 50 SQUARE REPEAT 3 [LT 90 FD REPEAT 3 [LT 90 FD

50 SQUARE] 50 SQUARE]

Tlingit Spruce Root BasketTlingit Spruce Root Basket Made with geometric motif, Made with geometric motif, Made in the traditional way, Made in the traditional way,

with bear grass, dyed bear with bear grass, dyed bear grass, andgrass, and

Done traditionally with what is Done traditionally with what is known as false embroidery.known as false embroidery.

““Baskets of the Northwest Baskets of the Northwest People”People”

http://www.mimbresfever.com/http://www.mimbresfever.com/north.html north.html

Tlingit Design LOGO ProjectTlingit Design LOGO Project

Challenge – to make the Challenge – to make the repeated pattern.repeated pattern.

Find the repeating unit.Find the repeating unit.

Do you see the same Shape?Do you see the same Shape?

The repeating unit looks The repeating unit looks like a “T”like a “T”

Plan to make the “T” Plan to make the “T” shape with LOGO.shape with LOGO.

Type the “TEE” Procedure.Type the “TEE” Procedure. TO TEETO TEE RT 90 FD 15RT 90 FD 15 LT 90 FD 10LT 90 FD 10 LT 90 FD 10LT 90 FD 10 RT 90 FD 10RT 90 FD 10 RT 90 FD 30RT 90 FD 30 RT 90 FD 10RT 90 FD 10 RT 90 FD 10RT 90 FD 10 LT 90 FD 10 LT 90 FD 10 LT 90 FD 15LT 90 FD 15 ENDEND

MistakeMistake

Try making the repeated Try making the repeated TEE’s.TEE’s.

Type TEE TEEType TEE TEE Oops!Oops! What Happened?What Happened? How can we edit TEE How can we edit TEE

so the TEE’s are so the TEE’s are horizontal?horizontal?

Correct and Repeat the TEE.Correct and Repeat the TEE. Add LT 90 at end of TEE Add LT 90 at end of TEE

procedure.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 PATTERNTO PATTERN

REPEAT 6 [TEE]REPEAT 6 [TEE] ENDEND

Student’s T PatternStudent’s T Pattern

Student’s U & Cross PatternStudent’s U & Cross Pattern

Grid and Cockleshell PatternGrid and Cockleshell Pattern

Stair and Hokha PatternsStair and Hokha Patterns

Time to WeaveTime to Weave

After programming designs, it was time After programming designs, it was time to weave! to weave!

Students planned designs on graph paper Students planned designs on graph paper Calculated number of warps for the Calculated number of warps for the

designdesign Estimated how many rows needed to Estimated how many rows needed to

make the patternmake the pattern..

Student’s Weave BasketsStudent’s Weave Baskets To insure success of the first To insure success of the first

basket, basket, all students wove the Cockle all students wove the Cockle

Shell pattern. Shell pattern. The Cockle Shell pattern The Cockle Shell pattern

uses dark and light colored uses dark and light colored yarn on alternate warps. yarn on alternate warps.

Students could easily and Students could easily and quickly see the pattern.quickly see the pattern.

Student’s made 100 BasketsStudent’s made 100 Baskets

Plastic cups of various Plastic cups of various sizes were used.sizes were used.

Basket weaving was Basket weaving was contagious.contagious.

Teacher ResponsesTeacher 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)

Math Concepts in this UnitMath Concepts in this Unit

GeometryGeometry Polygons: Square, Polygons: Square,

Rectangles, TrianglesRectangles, Triangles Angles: Right Turns, Angles: Right Turns,

Left Turns, DegreesLeft Turns, Degrees Symmetry: Reflection, Symmetry: Reflection,

Glide, Rotation, FlipGlide, Rotation, Flip

FractionsFractions HalfHalf FourthFourth EighthEighth SixteenthSixteenth

MeasurementMeasurement VerticalVertical HorizontalHorizontal

ResourcesResources Bradley, Claudette. (1993). Making a Navajo Blanket Design Bradley, Claudette. (1993). Making a Navajo Blanket Design

with Logo. with Logo. Teaching Mathematics With TechnologyTeaching Mathematics With Technology Chilkat BlanketChilkat Blanket

http://www.mehs.educ.state.ak.us/resources/unit/chilkat/http://www.mehs.educ.state.ak.us/resources/unit/chilkat/blanket.htmlblanket.html

Raven’s Tail Weaving by Teri RofkarRaven’s Tail Weaving by Teri Rofkarhttp://www.terirofkar.com/ceremonial_weavings.htmhttp://www.terirofkar.com/ceremonial_weavings.htm

Fry, Eric. (2003) Bringing math and Tlingit art together, Fry, Eric. (2003) Bringing math and Tlingit art together, Juneau Empire, 08/10/2003Juneau Empire, 08/10/2003 http://juneauempire.com/stories/081003/loc_mathart.shthttp://juneauempire.com/stories/081003/loc_mathart.shtmlml

Hoover, Lori, (2003) Riverbend Elementary, Juneau, Alaska Hoover, Lori, (2003) Riverbend Elementary, Juneau, Alaska http://uashome.alaska.edu/~jflmh/TlingitBasketshttp://uashome.alaska.edu/~jflmh/TlingitBaskets

More ResourcesMore Resources

Corey, Peter L. (1995). A Proposed Glossary of Spruce Corey, Peter L. (1995). A Proposed Glossary of Spruce Root Basketry. Root Basketry. Alaska State Museums Concepts,Alaska State Museums Concepts, 3 3

Miller, Dirk & Haygood Monika (2001). Miller, Dirk & Haygood Monika (2001). Math Through Math Through Basketry. Basketry. Juneau School District, Juneau, AlaskaJuneau School District, Juneau, Alaska

Roblyer, M. D. (2003) Roblyer, M. D. (2003) Integrating Educational Integrating Educational Technology into Teaching. Technology into Teaching. Upper Saddle River, New Upper Saddle River, New Jersey: Pearson Education, Inc.Jersey: Pearson Education, Inc.

LOGO Foundation,LOGO Foundation,http://ed.media.edu/logo-foundation/logo/turtle.htmlhttp://ed.media.edu/logo-foundation/logo/turtle.html

The EndThe EndThank You for Thank You for

Coming!Coming!Math in Tlingit Art Math in Tlingit Art

ByBy

Dr. Claudette Engblom-BradleyDr. Claudette Engblom-Bradley

University of Alaska AnchorageUniversity of Alaska Anchorage