Math 491

EthnoMathematics

Spring 2000

 

Instructor:    Dr. Claudia Giamati                                               Phone:836-2836(Office)

Office:             HHH 519                                                                   836-3301(math dept.)

Office hours: T 11-3                                                            Email:giamatcm@uwec.edu

                        Or by appointment

 

Course Description: An integrated study of ethnomathematics content, The course will begin with a historical overview of numeration systems of American Indian cultures. The extensive use of petroglyphs by many North and South American tribes will also be examined.  The discussion will also focus on the informal mathematics used including games, navigation, and astronomy.Students who take this course will earn 1 diversity credit. Each student will be required to write a paper. 

Course Prerequisites: Math 110 and high school Geometry.

Text: Many of the books necessary are out of print or are obscure, so we will rely on many handouts and various Web pages. I will furnish you with a bibliography by the end of the first week of class.

 

Syllabus: This is a tentative schedule.

Introduction:

I. What is Ethnomathematics?

A.                                                    Definitions

B.                                                     D’Ambrosio’s definition introducing and defining ethnomathematics

C.                                                    An example: the Iroquois and Cayuga game of Dish, a game of chance

i.                                                                                Probability

ii.                                                                             Cultural beliefs of probabilistic outcomes

 

 

II.        Historical Numeration Systems:

A.                                                    Incan Accounting

i.                                                                                Base Ten Numeration with knots          

ii.                                                                             The Quipu

A.                                                    Mayan uses of mathematics

i.                                                                                Influence of Astronomy: the calendar

ii.                                                                             Base not quite 60 numeration system with non numerical symbols

 

Historical Petroglyphs and Present Day Art

A.                                                    Petroglyphs as record keeping

B.                         Geometry of Petroglyphs

 

 

IV.      The Navajo culture

A.                                                    Navajo Astronomy and use of Geometry

B.                                                    The Navajo Language and its use of spatial and temporal relations

C.                                                     The influence of the language on geometric thinking

D.                                                     Sandpaintings, Symmetry and Asymmetry

 

 

Attendance every day is essential.  The material discussed will often be obtained from sources that can not easily be found. Your participation in large and small group discussions and assignments is part of your grade.  In-Class work can not be made up unless there are extenuating circumstances.  Notification of an extenuating circumstance prior to the class missed will be required in order to receive half credit for the missed assignment.  This notification should be done by e-mail. 

 

Other Policies: 

1) If you come to see me at my office, and I am not busy, I will discuss whatever you need to talk about.  I love to chat and do math. However, my office hours are very specific and I reserve the right to attend to my own business if I need to.

2) Plagiarism or cheating will not be tolerated.  Such activity will result in a failing grade.

 

Bibliography & Tentative Reading List:

                Ascher, M.(1992).  Ethnomathematics, A multicultural view of mathematical ideas, N.Y.: W.H. Freeman.

                Congdon-Martin, D. (1990). The Navajo Art of Sand Painting. Westchester, Pa., Schiffler Publishing Ltd.

                Eglash, R.(In-Press) Computation, Complexity and Coding in Native American Knowledge Systems To appear in Native American Mathematics by NCTM, Reston Va.

Giamati, C., Wieland , M. (1997). An Exploration into American Indian Students' Perception of Patterning, Symmetry, and Geometry. Journal of American Indian Education Vol. 36 N 27 (pp. 27 – 48) Arizona State University, Tempe, Az.

Gilliland, K.(1991). Patterns of Culture  unpublished manuscript, Lawrence Hall of Science.Berkeley Ca.

                Orban-Szontagh, M.(1992). Southwestern Indian Designs. Mineola, N.Y., Dover Publications.

                Peckham, S.(1990) From This Earth, the Ancient Art of Pueblo Pottery, U. of New Mexico Press Albuquerque, N.M.

                Pinxten, R.(1983).The Anthropology of Space: Explorations into the Natural Philosophy and Semantics of the Navajo. Philadelphia, University of Pennsylvania Press.

                Pinxten, R.(1985). Knowledge as a Cultural Phenomenon.  In Vandamme & Spoelders (Eds) Language acquisition and learning. Essays in Educational Pragmatics . New York, Plenum Press.

                Pinxten, R. (1991). Geometry Education and Culture, Learning and Instruction . Great Britain, Pergamon Press 1. 217-227 

Powell, A. & Frankenstein, M. editors(1997) Ethnomathematics: Challenging Eurocentrism in Mathemtics Education, SUNY Press, Albany

Rhodes, R.W. (1994). Nurturing Learning in Native American Students. Hotevilla, Az. Northland Graphics

                Watson, H.(1990). Investigating the Social Foundations of Mathematics: Natural Number in Culturally Diverse Forms of Life, Social Studies of Science. London, SAGE 20(1) 283-312

                Zaslavsky, C.(1991). World Cultures in the Mathematics Classroom. For the Learning of Mathematics. 11(2) 32-36