National Taitung University Presenter: Jerry Lipka University of Alaska Fairbanks

1. Workshop on Science and Mathematics for Indigenous EducationAlaska Native Knowledge and Culturally Embedded Curriculum National Taitung University Presenter: Jerry Lipka University of Alaska Fairbanks February, 2010 Sharing the lessons learned from working with Yup’ik elders—toward a systematic approach to teaching mathematics.

2. 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

3. Map of Southwest Alaska

4. Alaska’s Language Groups—Situating our Work

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

6. Situating MCC: In an Academic Context Four major approaches to math reform: Everyday math—whatwe 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

7. 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

8. Conceptions of Developing Mathematics Curriculum for Indigenous Students

9. Cosmology—ways of perceiving the world Star Navigation—perceiving the night sky

10. 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

11. Examples of Everyday Activities—Building a Kayak and Cutting Salmon

12. Third Space: Mathematics, Curriculum, Pedagogy, and Culture

13. 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

14. Counting--Numeration Working together to Understand Yup’ik Numeration

15. Developing School-Based Mathematics Activities

16. Creating Numeration Activities—Drumming and Place Value

17. Teacher and Students Using and Extending Lessons Learned from Elders

18. Measuring in the Context of MCC’s Summer Math Institute

19. An Example from an MCC treatment class • Nonzero starting point Students create their own units

20. Yup’ik Border Patterns

21. Making Patterns/Geometric Shapes from Uneven Material

22. The Importance of the Center: Transformational Geometry

24. School-based definition of a square

25. 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.

26. Transforming a Square to a Circle

27. Putting it Together—Math and Pedagogy

28. Math Content from Subsistence Activities and Developing Math Curriculum in Indigenous Contexts—Working with Elders

29. Subsistence Activities

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

31. Finding Deeper Mathematical Connections Across Various Subsistence Activities

32. Expert-Apprentice Demonstration Joint Productive Activity Observational Learning Pedagogy Cognitive Apprenticeship Wondering aloud Practice Assist Others Novice becoming more expert Pedagogy Pedagogy of the community Connected to the pedagogy of the school

34. 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

35. Does it Work? What evidence do we have? Efficacy studies Qualitative Case Studies

36. Does MCC Work? It Closes the Gap

37. HLM Impact Results – Location and Subscales *** p<.001 ** p<.01 * p<.05

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

39. 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

40. Classroom Stories I 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).

41. Workshops will Emphasize Importance of: Center point; Balance; and Symmetry Workshop 1– Making a Square from uneven materials [geometry, measuring, patterns, and numbers] Workshop 2 –Building on the square--creating fraction sets