WORKSHOP ON SCIENCE AND MATHEMATICS FOR INDIGENOUS EDUCATION

ALASKA NATIVE KNOWLEDGE AND CULTURALLY EMBEDDED CURRICULUM

Sharing the lessons learned from working with Yup’ik elders—toward a systematic approach to teaching mathematics.

National Taitung University Presenter: Jerry LipkaUniversity of Alaska FairbanksFebruary, 2010

Overview of Presentations Introductions Thankful for the Invitation Privilege to work with you by sharing the

Elders’ Gift Purposes

Sharing our Work Outlining key principles in developing math

curriculum based on indigenous knowledge Assist in the Development of your Work

Map of Southwest Alaska

Alaska’s Language Groups—Situating our Work

What is our work? We produced curriculum materials, PD, and implementation/evaluation

studies.

Situating MCC: In an Academic Context

Four major approaches to math reform: Everyday math—what we can learn as individuals

within a cultural context, Yup’ik elders and expert Yup’ik teachers perform everyday tasks

Literacy and Language Ethnomathematics—The culturally favored ways

of a perceiving and interacting with the world, understanding Yup’ik ways of being, values, and communication—unique worldview of Yup’ik people

Reform-oriented math—inquiry-oriented, conceptually driven, and proactively increasing access and equity to math

Today’s talk concentrates on the interface of these approaches

Goals of MCC Include the Culture of the Community in

Schooling—cultural continuity and cultural evolution/development

Improve the performance of Yup’ik elementary school students in math

Later, this goal evolved into improving the performance of all students

Newest goal, informing mainstream mathematics curriculum and instruction by sharing lessons learned from Yup’ik elders and teachers

Conceptions of Developing Mathematics Curriculum for

Indigenous Students

Language

Emphasis on Valued Aspects of the Culture

Verbs—actions,

processes

Windows to a

worldview, unique

perspectives

Worldview-Cosmology

Epistemology—Ways of knowing

Ways of Being

Ways of Relating and

Communicating

Cosmology—ways of perceiving the world

Star Navigation—perceiving the night sky

Elders we worked with say, “Always come with a story.”

Adventures of Kuku—story told by Annie Blue, respected storyteller from Togiak, Alaska.

Kuku entering the magical phantasmagorical portal

Literacy as window into a unique worldview

Examples of Everyday Activities—Building a Kayak and Cutting Salmon

Third Space: Mathematics, Curriculum, Pedagogy, and Culture

Samples of Everyday Work with Elders & Co-Constructing Curriculum Working with Elders Working with Yup’ik teachers Lessons learned from implementing MCC

curriculum Assessments and Evaluation Studies also

inform the curriculum, professional development component, and pedagogy

Counting--Numeration

Working together to Understand Yup’ik Numeration

Developing School-Based Mathematics Activities

Creating Numeration Activities—Drumming and Place Value

Teacher and Students Using and Extending Lessons Learned from

Elders

Measuring in the Context of MCC’s Summer Math Institute

An Example from an MCC treatment class

Nonzero starting point

Students create their own units

Yup’

ik B

orde

r Pa

tter

ns

Making Patterns/Geometric Shapes from Uneven Material

The Importance of the Center: Transformational Geometry

School-based definition of a square

Alternative definition to Euclid’s based on the everyday practices of Yup’ik elders, emphasizing the importance of center point, using transformational geometry, measuring, and folding.

Transforming a Square to a Circle

Putting it Together—Math and Pedagogy

Math Content from Subsistence Activities and Developing Math Curriculum in Indigenous Contexts—

Working with Elders

Subsistence Activities—Gathering Eggs and Berries, and catching,

drying, and smoking salmon

Constructing—fish racks, smokehouses, and kayaks

Navigating and locating—star navigation, search and rescue, and understanding landmarks

Patterns—Designing, creating, and putting the pieces together

Math of Everyday Activities—Estimating, Measuring, Patterns,

Geometrical shapes and relationships, and Numbers/Number

Relations

Subsistence Activities

Berry Picking

Collecting

Filling --Volume

Units of Measure

Sorting

Re-distributing, units of measure

Storing, organizing

Designing

PatternsMeasuring

Folding

Finding the Center

Symmetry as Geometrical Proof

How different Shapes are Related—Square, Circle,

Rectangles, Rhombi

Star Navigatio

nLocating

Directions

Measuring Angles

Cultural, Context, and Measuring: A basis for developing curriculum

Cultural context-

embedded mathemati

cs

PersonTask

Resources

Dynamic Measuring

Estimating

Body Proportion

al Measuring

Finding Deeper Mathematical Connections Across Various

Subsistence Activities

Transformational, Bilateral

Symmetry, and center point

Geometry

Measuring Patterns

Numbers

Pedagogy

Pedagogy of the community Connected to the pedagogy of the school

Joint Productive

Activity

Cognitive Apprenticeship

Wondering aloud

Assist OthersNovice

becoming more expert

Practice

Observational Learning

Expert-Apprentice

Demonstration

Pedagogy

PUTTING THE PIECES TOGETHER—FINDING PATTERNS AND MAKING

CURRICULUM•Emphasis on ways of learning that enable students to verify results/inquiry•Organizing classroom activities that support ways of working together, familiar communication patterns and norms•Building on relative cognitive strengths•Building on familiar context prior to developing unfamiliar mathematics concepts•Learning many mathematics concepts through geometry and measuring•Connecting other mathematical concepts from geometry and measuring to numbers and number relations, for example•Constructing activities integrate multiple mathematics strands•Connecting mathematics to literacy•Organizing activities and presenting mathematical concepts in ways indicated by elders—concepts are active not static•Social-cultural emphasis on cooperation and harmony•Challenging mathematics

DOES IT WORK?What evidence do we have?

Efficacy studiesQualitative Case Studies

Does MCC Work? It Closes the Gap

-0.665

0.022

-0.186

0.707

-0.416

-0.151-0.118

0.309

-0.800

-0.600

-0.400

-0.200

0.000

0.200

0.400

0.600

0.800

average z-pre-test average z-post-test

stan

dard

ized

test

resu

lts

Standardized MCC Test Results for Rural/Urban by Treatment/Control

Fall 2002 - Spring 2005N is the number of classes

rural treatment N=78

urban treatment N=50

rural control N=43

urban control N=35

HLM Impact Results – Location and Subscales

Module Subgroups Impacts Effect Size

Fall 2005Gain ScoresBerries

Rural (35 schools) 10.77% pts(p=.000)

1.05 ***

Measurement Subscale Representing Data Subscale

11.14% pts (p=.000)17.22% pts (p=.002)

1.15 ***1.07 **

Urban (15 schools) 9.80% pts(p=.006)

0.83 **

Measurement Subscale Representing Data Subscale

8.48% pts (p=.017)14.40% pts (p=.040)

0.76 *0.66 *

Spring 2006Gain ScoresEgg Island

Rural 11.39% pts(p=.005)

0.54 **

Grouping Subscale Place Value Subscale

10.96% pts (p=.010) 9.46% pts (p=.050)

0.50 *0.37 *

Urban 7.79% pts(p=.025)

0.35 *

Grouping Subscale Place Value Subscale

5.18% pts (p=.223)9.65% pts (p=.025)

0.180.37 *

*** p<.001 ** p<.01 * p<.05

Evidence suggestive of MCC’s efficacy to improve the Math performance of AN students and other Alaskan students—

Subsequent Studies

MCC Works! Why it Works

Increase equity, access and engagement, and achievement in math education

Forging a model based on cultural strength and not on a deficit based model

Valuing and connecting Alaska Native cultures to schooling

Building on and from cultural knowledge, cognitive strengths, and ways of communicating

Principles within our project can serve as a model for developing culturally based curriculum

Our work has been published in numerous professional

Classroom StoriesI would like to add that I am seeing similar results with a couple of students this year. One boy in particular is typically all over the room - rarely on task. With the kayak model he was the first to measure out his kayak on the floor, first to test his boat, and the first to offer to help other students test their boats. He even tried to test stability by placing marbles just on one side of the boat during the load activity. A concept I have not even introduced yet. I can see he is understanding when I ask him questions verbally, however I can not attest to him making progress in writing yet. I will keep you posted (told to Jerry Lipka by Laurel Sands, a rural teacher, 2009).

Workshops will EmphasizeImportance of: Center point;

Balance; andSymmetry

Workshop 1– Making a Square from uneven materials [geometry, measuring, patterns, and numbers]

Workshop 2 –Building on the square--creating fraction sets