USING
ETHNOMATHEMATICS
IN YOUR CLASSROOM:
PRACTICAL SUGGESTIONS
This webpage supports the presentation at:
Maryland Council of Teachers of Mathematics
Annual Conference—Eastern Technical High School
October 17, 2008—11:30am – 12:30pm, Room 215,
Session 37
Lawrence
Shirley, Professor
of Mathematics and Associate Graduate Dean
College of Graduate Studies and Research
Towson University, Towson,
Maryland 21252
email: LShirley@towson.edu ; phone
4107043500
personal webpage: http://pages.towson.edu/shirley
Handout (click here)
Abstract
Ethnomathematics is the mathematics of cultural
groupsall cultural groups.
We will see examples of what this means and how you
can use ethnomathematics to enrich your mathematics classes at any grade level.
Useful resources will be included.
Outline
1. Introduction: the meaning of ethnomathematics Isn't mathematics culturefree?
2. Two models to help find ethnomathematics examples
A broader meaning of mathematics:
(Shirley, 1995)
pure
applied
formal
ACADEMIC
TECHNICAL
informal
RECREATIONAL
EVERYDAY
Bishop's list of the activities of societies:
(Bishop, 1988)
counting
explaining
measuring
designing
locating
playing
3. Historical development of ethnomathematics
(see "Ethnomathematics Looks Backward and Looks Forward" (a paper from ICME11)
early 20th Century (anthropologists)
the era of civil rights (especially in US) and decolonization
Zaslavsky, D'Ambrosio
International
Study Group on Ethnomathematics
(North American Study Group on Ethnomathematics)
International Conferences
Successes in multiculturalism, curriculum materials, instruction, and continued study
4. Ethnomathematics for social justice, global understanding
5. General activities for the classroom
countingother languages, numeration
measuringunits, techniques
locatingfinding your way? in the South Pacific, in video games
explainingalgorithms, stories, kinship (see Ascher, 1991)
designingfreizes, textiles (e.g.kente), fractals
playingmagic squares, Mu Torere, Oware—Mancala
6. Who are you? What is your own ethnomathematics? How does your culture influence your teaching?
Links
From the pages of the International Study Group on Ethnomathematics (North American Study Group on Ethnomathematics), you can jump to several ethnomathematical links. Here is a collection of ethnomathematics links from ISGEm and more references and links for ethnomathematics and even more ethnomathematics links. Also see the Ethnomathematics Digital Libary
You
can find counting words for
one
to ten in over 5000 languages(!) here.
Eulerian path sand
drawings from Slavik Jablan & Paulus Gerdes (see
Gerdes' books
below)
Akan cultural symbols project,
organized by George F. Kojo Arthur and Robert Rowe
Ron Eglash's African Fractals including activities for classrooms (see the Eglash book reference below)
You can play Mancala against the computer on the web! The rules are slightly different from ours, but are well explained. Another mankala page has more variations.
RadicalMath looks at blending mathematics content and issues of social justice. Similarly, the Algebra Project considers algebra and the opportunity to learn mathematics as civil rights. Rethinking Schoolsa nonprofit educational publisher on school reform (including mathematics)with a focus on issues of equity and social justice (See Gutstein below)
The Fourth International Conference on Ethnomathematics (ICEM4),
Towson, Maryland, July 2010
Bibliography (most with online ordering links)
Ascher, Marcia (1991) Ethnomathematics: a multicultural view of mathematical ideas, Wadsworth.
Ascher, Marcia (2002) Mathematics Elsewhere: an exploration of ideas across cultures, Princeton University Press.
Bishop, Alan (1988) Mathematical Enculturation: A Cultural Perspective on Mathematics Education, Kluwer.
Bazin, Maurice, Tamez, Modesto, and the Exploratorium Teacher Institute (2002) Math and Science Across Cultures: Activities and Investigations from the Exploratorium, The New Press (Norton).
D'Ambrosio, Ubiratan (1985) Sociocultural Bases for Mathematics Education, University of Campinas (Brazil).
Eglash, Ron (1999) African Fractals: modern computing and indigenous design, Rutgers University Press.
Gay, John, and Michael Cole (1967) The New Mathematics and an Old Culture: A study of learning among the Kpelle of Liberia, Holt, Rinehart, and Winston.
Gerdes, Paulus (1997) Lusona: Geometrical Recreations of Africa, Editions L'Harmattan.
Gerdes, Paulus (1998) Women, Art, and Geometry in Southern Africa, Africa World Press.
Gerdes, Paulus (1999) Geometry in Africa, Mathematical Association of America.
Gutstein, Eric and Peterson, Bob (editors) (2005) Rethinking Mathematics: Teaching Social Justice by the Numbers, Rethinking Schools, Ltd.
Ifrah, Georges (1994) The Universal History of Numbers, Wiley
National Council of Teachers of Mathematics (1995) Connecting Mathematics Throughout the Curriculum (1995 Yearbook), NCTM.
National Council of Teachers of Mathematics (1997) Multicultural and Gender Equity in the Mathematics Classroom: The Gift of Diversity (1997 Yearbook), NCTM.
Nelson, D., Joseph, G.G., and Williams, J. (1993) Multicultural Mathematics, Oxford University Press.
Powell, Arthur and Frankenstein, Marilyn (editors) (1997) Ethnomathematics: Challenging Eurocentrism in Mathematics Education, State University of New York Press
Shirley, Lawrence (1995) "Using Ethnomathematics to Help Find Multicultural Mathematical Connections" in House, Peggy (editor) Connecting Mathematics across the Curriculum (1995 Yearbook), National Council of Teachers of Mathematics.
Shirley, Lawrence (2001)"Ethnomathematics as a Fundamental of Instructional Methodology" Zentralblatt fur Didaktik der MathematikInternational Reviews on Mathematical Education, issue 2001/3 (June 2001), [ZDM].
Shirley, Lawrence (2006) http://pages.towson.edu/shirley/global.htm presented at the Third International Conference on Ethnomathematics, Auckland, New Zealand.
Zaslavsky, Claudia (1973, 1995) Africa Counts: Number and Pattern in African Culture, Lawrence Hill Books.
Zaslavsky, Claudia (1996) The Multicultural Mathematics Classroom, Heinemann.
(also see a full Zaslavsky bibliography)

last updated 21 October 2008, links checked 13 October 2008 (please report any broken links to LShirley@towson.edu )
Maryland Council of Teachers of Mathematics
Annual Conference—Eastern Technical High School
October 17, 2008—11:30am – 12:30pm, Room 215 (Session 37)
http://pages.towson.edu/shirley/ethnomathematics.htm
Lawrence Shirley, Professor of Mathematics and Associate Graduate
Dean
College of Graduate Studies and Research
Towson University, Towson, Maryland 21252
email:
LShirley@towson.edu ; phone 4107043500
personal webpage:
http://pages.towson.edu/shirley
OUTLINE
ETHNOMATHEMATICS:
A BROADER MEANING OF MATHEMATICS

PURE 
APPLIED 
FORMAL

Academic 
technical 
INFORMAL

recreational 
everyday 
Shirley (1995)
Bishop’s (1988) list:
Counting
Measuring
Locating
Explaining
Designing Playing
YORUBA(southwest)
1 okon 
41 ookan le ogoji 45 aarun din aadota 47 eeta din aadota 50 aatota 60 ogota 70 aadorin 80 ogorin 90 aadorun 100 ogorun 110 aadofa 120 ogofa 130 aadoja 140 ogoja 150 aadojo 160 ogojo 170 aadosan 180 ogosan 190 aadowa 200 igba 300 oodunrun 400 irinwo 2000 egbewa 
MADA/
NINZAM/NINDEM(northcentral)

HINDI BINARY COUNTING
BASE TEN
BASE TWO
NUMERAL
NUMERAL
COUNTING WORD
1
1
EK
2
10
DO
3
11
DAK
4
100
DAWWA
5
101
DAWWEK
6
110
DAWWADO
7
111
DAWWADAK
8
1000
DODAWWA
9
1001
DODAWWEK
10
1010
DODAWWADO
11
1011
DODAWWADAK
12
1100
DODAWWADAWWA
13
1101
DODAWWADAWWEK
14
1110
DODAWWADAWWADO
15
1111
DODAWWADAWWADAK
16
10000
? ? ?
OWARE
Oware is a counting and
strategy game from West Africa.
Similar games, with the generic name of mancala, are played
throughout Africa and other parts of the world, with variations in the rules
and with many different names.
This version, oware, is from Ghana, and is similar to others played
in West Africa.
Materials and setup:
The playing board is an arrangement of twelve small pits in two rows of six.
An egg carton is a good example and can be used for the board or use
the board on the next page. In
West Africa, the game is played on boards ranging from twelve small holes
dug in the dirt to elaborate wooden carved boards with storage bins, stands,
and sometimes hinges so they can be folded closed.
One row of six pits belongs to each of the two players.
Counters, which may be pebbles, seeds, bottle caps, shells, coins, or
even (for the affluent) jewels, are shared into the twelve pits.
In this version, four seeds are put into each of the twelve pits to
start the game.
Rules of play:
The players take turns playing. One turn consists of picking up all the
seeds in one of the players's six pits.
The seeds are then distributed one into each pit, moving around the
board counterclockwise, including the use of the pits of the opponent if
necessary, or even, if there are enough seeds, going all the way around the
board (in this case, the original pit is skipped as a recipient of a seed).
Collecting seeds: If the last
seed lands in a pit on the opponent's side which had exactly one or two
seeds already, thus making its new total two or three, all the seeds in that
pit are collected by the player and stored out of play.
For a continuous chain of pits on the opponent's side, going back
from the last, if the pit now has two or three seeds exactly, those sides
can also be collected.
End of the game:
If the opponent has no seeds left, the player must try to play so as to put
at least one seed into a pit of the opponent.
Otherwise, if a player has no seeds, the game ends and the other
player keeps any remaining seeds.
Winning: The winner is the
player with the most seeds collected at the end of the game.
Etiquette: It is considered
improper to pick up and count the seeds in any pit, most especially a pit of
the opponent!
Strategy: Try to keep track
(mentally!) of the number of seeds in each pit and hence where the last seed
would land if the seeds in that pit were to be played, aiming at collecting
seeds from a long string of pits back from the last.
Sometimes building up many seeds in one pit can be helpful.
The endgame can be very important.
Learning: counting, mental
adding and subtracting, estimation, the geometry of the board,
problemsolving, strategic thinking, etc.
Also, analyses can be made of possible plays, even to designing a
computer program of the game.
WebMancala:
Another version of mancala is on the Web.
It’s rules are slightly different but wellexplained.
It allows you to play online against the computer!
Look at: http://imagiware.com/mancala/
Have fun!
Mancala (Oware)
board (start with 4 “seeds” in each “pit”)












WHO ARE YOU?
1.
The following is derived from the official US Census form for identifying
ethnicity. In 1990, the instructions
were to check one category only, but in 2000, respondents could check all
that apply (in fact, there were more categories than this; this will again
be the case in 2010). Please
check the categories that describe you, checking as many as you consider
accurate descriptions of yourself.
___
Black
___ American Indian
___ Asian or Pacific Islander
___
Hispanic
___ White
2.
In the blank space below, describe your own cultural heritage, without
being restricted to the items from the Census Bureau.
Use any terms that describe youethnic, religious, social class,
geographic, or whatever. Be
creative!
3. How could
you use your own cultural heritage in your teaching?
4. How does
your own cultural heritage influence your teaching?
Should it?
5. Can you
use your students' cultural heritages as resources for your teaching?
How?
Ascher, Marcia (1991)
Ethnomathematics: a multicultural view of mathematical ideas,
Ascher, Marcia (2002)
Mathematics Elsewhere: an exploration of ideas across cultures, Princeton
University Press.
Bishop, Alan (1988)
Mathematical Enculturation: A Cultural Perspective on Mathematics
Education, Kluwer.
D'Ambrosio, Ubiratan (1985) Sociocultural Bases for Mathematics Education,
Eglash, Ron (1999)
African Fractals: modern
computing and indigenous design, Rutgers University Press.
Gerdes, Paulus (1999)
Geometry in Africa, Mathematical Association of
National Council of Teachers of Mathematics (1997)
Multicultural and Gender Equity in the Mathematics Classroom: The Gift of
Diversity
(1997 Yearbook), NCTM.
Powell, Arthur and Frankenstein, Marilyn (editors) (1997)
Ethnomathematics: Challenging
Eurocentrism in Mathematics Education, State University of New York
Press
Zaslavsky, Claudia 1996) The Multicultural Mathematics Classroom,
Heinemann. (also see other Zaslavsky books and articles)