M-T-W-Th 10-12:20 Four Week Session rmontgomery@sou.edu (541) 552-6580

Prerequisites. Upper-division standing and the following or their equivalent: Wr 122, Math 212, and Math 213; or Math 251 and Math 261. Math 581 has an additional prerequisite of senior standing or higher.

Content. This course will examine mathematical thought and practice of other cultures. Comparisons to the Western tradition will be made. The mathematics which underlies activities in other cultures will be investigated. We will consider how the mathematics found in other traditions reflects that culture's heritage and world view.

Mathematical topics include numbering and systems of organization; and geometry and perceptions of space. Other topics will be considered as they arise.

Activities and Requirements. There will be a variety of readings and resource investigations. There will be reports, both verbal and written, which share information. You will be expected: to contribute to the discussion of the common readings; to locate and share some ethnomathematics case studies; to join in the discussion which clarifies and integrates the examples presented by fellow students.

During class time there will be discussions, presentations, and an occasional 'scissors-activity'.

Outside of class time there will be critical readings, resource searches, and presentation preparations. Also, there will be the ongoing development of a course notebook.

Course Notebook. It is hoped that your notebook will be the beginning of a continuing collection of useful materials on ethnomathematics [Organize your notebook by categories: Readings with annotations and notes; Classroom notes with annotations; Overall observations and course summary; Appendices: Resources; Reports of other students.]

Grading. Your course grade will be based on four factors: (1) your participation in the class discussion of the required readings, (2) your contribution of new resources and instances (reports and projects), (3) your course notebook , and (4) your overall contribution to the success of the course.

(A complete list of required and optional readings is appended.)

Marcia Ascher & Robert Ascher. Mathematics of the Incas. Dover Press. 1997.

Marcia Ascher, Ethnomathematics. Chapman and Hall. 1994.

Michael Closs, Native American Mathematics. The University of Texas Press. 1986.

Gary Urton. The Social Life of Numbers: A Quechua Ontology of Numbers and Philosophy of Arithmetic. The University of Texas Press. 1997.

Claudia Zaslavsky, Africa Counts. Lawrence Hill Books. 1991.

Optional. Join the International Study Group on Ethnomathematics (the ISGEm) at $15.00/ year.

ISGEm home page address: http://www.cohums.ohio-state.edu/comp/isgem.htm

What is ethnomathematics? The word 'ethnomathematics' is itself rather new on the scene; only about a decade old. In recent years there has emerged a large, growing, and very active, international advocacy of 'ethnomathematics'. Today almost every major math conference has associated meetings of teachers and/or scholars concerned with the multicultural aspects of mathematics. Simply enter the word 'ethnomathematics' in a SEARCH box on the internet and you will be overwhelmed with information.

But, what is ethnomathematics? The domain of ethnomathematics has several overlapping aspects. (1.) Some 'ethnomathematicians' search out instances of activities in other traditions which can be analyzed in terms of western mathematics. (2.) Others are truly 'anthro-mathematicians;' these are trained anthropologists who, in order to better understand a particular culture, examine the mathematics woven into and shaped by the fabric of that culture's heritage and activities. (3.) Yet others are sociologically oriented, primarily concerned with the plight of peoples of non-western tradition who are asked to learn 'western mathematics' (often in a very formal structured way).

In practice, these three approaches to ethnomathematics are mutually supporting and often intermingled.

This course will be devoted primarily to the first two aspects. Hopefully, the third aspect will benefit as a corollary to the first two. I believe that if we begin to get an inkling of how other traditions perceive the world, we'll naturally become more sensitive and responsive to the varieties of cultural backgrounds found in our own classrooms. Indeed, we teachers will be more able to take advantage of the 'diversity of thought' sitting before us in our classrooms but may not now even see.

For this summer's course I have chosen two main mathematical themes: 'numbering' and 'the perception of space' (there will be others too). There will be a mix of activities (e.g. making and understanding the complexity and use of an Inca quipu) and readings from brief case studies (such as the Sikidy system of divination practiced in Madagascar) to a comprehensive study of mathematical concepts of an enduring culture (the Quechua language group of South America. And, in order to better appreciate the meaning of "Seeing With a Native Eye" (à la folklorist Barre Toelken), we will not forget to examine our own highly organized, 'western way' of structuring in the world.

What is the purpose of holding an ethnomathematics course? Simple. To better understand mathematical concepts and be better teachers. We will better understand our 'subject matter' (our 'western' mathematical system of structures) if we see how basic mathematical ideas arise and are used elsewhere. Moreover, if we recognize that there are culturally different ways of 'seeing, organizing, and thinking,' then there is promise that we may ourselves devise ways to better teach mathematics.

Math 481/581 Ethnomathematics Southern Oregon University Summer 1998 page 3 of 5

Tentative Schedule & Miscellaneous Information

Colloquium Participants: Jim Earley, Fred Hamlin, Mark Schwarz, Teresa Woolley

one Intro to Course: Format and Topic. Syllabus and Responsibilities.

two Case Study: Divination in Madagascar.

Readings: Ascher, "Introduction" from Ethnomathematics.

Ascher, "Malagasy Sikidy. . ." Discussion Leader: Jim Earley

three Cultural Worldviews: Navaho et.al.

Readings: Shirley, "Using Ethnomath to Find Multicultural Connections." Toelken, "Folklore and Cultural Worldview." Discussion Leader: Mark Schwarz

four Cultural Perceptions of 'Space.'

Readings: Ascher, "The Organization and Modeling of Space" Discussion Leader: Fred Hamlin

five Geometrical Perceptions From Around the World Discussion Leader: Teresa Woolley

Readings: Gerdes, "On Culture, Geometrical Thinking and Math Education."

Knijnik, "An Ethnomathematics Approach in Math Education:. . ."

six & seven The Inca Civilization

Readings: Ascher & Ascher, Math of the Incas.

Chapters 1, 2, 3, 4. Discussion Leader: Fred Hamlin Chapters 5, 6, 7. Discussion Leader: Mark Schwarz

eight & nine Number Systems From Around the World Discussion Leader: Teresa Woolley

(1) Zaslavsky, Africa Counts. Pages 2-11, 39-51. Read at a good pace.

(2) Closs, "Native American Number Systems." Read quickly for an overview:

(3) Urton, The Social Life of Numbers.

ten, eleven, The Quechua.

TWELVE, & Readings: Urton, The Social Life of Numbers: A Quechua...

THIRTEEN Chapter 4, 5, 1 Discussion Leader: Dick Montgomery Chapter 6 Discussion Leader: Jim Earley

fourteen & fifteen Individual Project Reports

sixteen & Seventeen Course summary & Conclusion. [Notebooks due.]

M-T-W-Th 10-12:20 Four Week Session rmontgomery@sou.edu (541) 552-6580

Literature and Resources

Basic Library of Books (R) Required

(R) Michael Closs, Native American Mathematics. The University of Texas Press. 1986.

(R) Claudia Zaslavsky, Africa Counts. Lawrence Hill Books. 1991.

ISGEm Home Page http://www.cohums.ohio-state.edu/comp/isgem.htm

Math 481/581 Ethnomathematics Page 5 of 5

Literature and Resources [Continued]